Datasets:

bryan7264
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LEDGER

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-# Bibliography Verification - LEDGER
-**Date**: 2026-08-17
-**Protocol**: bibliography-verifier triple-pass
-**Bibliography**: `paper/references.bib` - **15 entries** (12 Phase 0 + 3 added in v2), all DOI-bearing
-**Reproduce**: `python -m src.utils.verify_refs paper/references.bib`
-## Method
-Verification is scripted rather than eyeballed. `src/utils/verify_refs.py` parses every
-DOI-bearing entry from the `.bib` and resolves it against the **Crossref registry**, printing
-the authoritative title, complete author list, venue, year, volume, issue and pages for
-comparison against what is written. This makes the verification reproducible and re-runnable
-after any edit, instead of a one-time manual read-through.
-- **Pass 1 - Existence and title.** Every paper was first located by web search during the
-  landscape survey, and the exact title read from the publisher page or PMC full text.
-- **Pass 2 - Authors, positionally.** Full author lists were taken from the primary source
-  (publisher/PMC), with particular attention to middle authors, then cross-checked against the
-  Crossref record.
-- **Pass 3 - Full re-verification.** All **15** DOIs re-resolved against Crossref. **15/15
-  resolve; 0 unresolved; titles and author counts match the `.bib` in all 15 cases** (GBD by the
-  documented corporate-author convention).
-## Corrections Made
-### C1 - Missing middle author (Chong et al.) 🔴
-`Chong2026Defence` was written with 10 authors. Crossref reports **11**: a corporate author,
-**"Multi-Defence Consortium"**, sits at **position 10**, between Edze R. Westra and Kate S.
-Baker. This is exactly the failure mode the triple-pass protocol exists to catch - a
-non-personal middle author is easy to drop when transcribing from a rendered author list.
-**Fixed**: added as `{Multi-Defence Consortium}` in braces to prevent BibTeX name-parsing.
-### C2 - Wrong first author attributed from memory 🔴
-While drafting, the *Science Advances* phage-resistance panel was informally referred to as
-"Vasquez et al." No such author exists on that paper. The correct first author is **Ana Rita
-Costa**, with Stan J. J. Brouns as senior author. Caught by fetching the primary source rather
-than citing from recall. **No incorrect attribution reached the `.bib` or the paper.**
-### C3 - Guessed PMC identifier resolved to an unrelated paper 🔴
-An attempt to fetch the Liu/Botelho/Iranzo paper via a guessed PMC ID (`PMC11800629`) returned
-a **cardiology paper on P2Y12 inhibitors in cardiogenic shock**. The correct identifier is
-`PMC11874982`. Recorded because it illustrates why identifiers must be resolved rather than
-inferred; a less careful pass could have attached a real DOI to the wrong reference.
-## Deliberate Editorial Decisions
-### D1 - Collaboration authorship (GBD 2021 AMR Collaborators)
-Crossref lists **525 individual authors** for `GBD2024AMR`, beginning Mohsen Naghavi, Stein
-Emil Vollset, Kevin S. Ikuta. The entry uses the corporate form
-`{GBD 2021 Antimicrobial Resistance Collaborators}`, which is how *The Lancet* itself cites the
-paper. The project rule forbidding "et al." exists to prevent silent truncation of author
-lists; citing a 525-author collaboration by its registered collaboration name is standard
-scholarly practice, not truncation, and is recorded here explicitly so the decision is visible
-rather than implicit.
-### D2 - PLSDB year
-Crossref dates `Molano2025PLSDB` to 2024 (online publication) while the article appears in
-volume 53, issue D1 - the 2025 *Nucleic Acids Research* Database Issue. The entry uses **2025**,
-matching the issue and the database's own branding ("PLSDB 2025 update").
-### D3 - Preprint status
-`Lopatina2024Interpretable` is a bioRxiv preprint (Crossref type `posted-content`, group
-"Microbiology") and is marked `note = {Preprint}`. It is cited as the closest methodological
-neighbour; its preprint status is stated in the text.
-## Claims Verified Beyond the Bibliography
-The landscape survey independently verified 11 quantitative claims carried over from the
-supplied research plan. Six confirmed, four corrected, one unsupported. The corrections that
-affect the paper's framing:
-| Claim | Outcome |
-|---|---|
-| "53 isolates × 40 phages panel, defense count did not correlate with resistance" | **Unsupported** - no such panel located. The two real panels report the *opposite* sign: Burke et al. (100 × 70, significant but weak, R² = 0.26) and Costa et al. (32 × 28, resistance scales with defense count). The paper uses the verified panels and the corrected direction. |
-| RM target-density scale-dependence attributed to Liu/Botelho/Iranzo | **Mis-attributed** - that paper does not analyse RM target-site density at all. The correct source is Shaw, Rocha & MacLean (2023), which finds 6 bp target avoidance correlated with the taxonomic distribution of R-M systems and stronger in plasmid than core genes. Re-grounded. |
-| *P. aeruginosa* CRISPR-Cas prevalence 49.9% | **Correction withdrawn - the original figure was right.** We flagged it as unverified because Chong et al. report only Type I-F (~33%). We then measured it ourselves on real annotated genomes: **49.2%** (n=120) and **53.5%** (n=785) carry any Class 1 CRISPR-Cas subtype. Our correction had over-read a subtype-specific figure as a total. See `LANDSCAPE_SURVEY.md` claim 7. |
-| Mean 8.5 defense systems, 63 distinct systems | **Corrected** - Chong et al. report mean 7.5 and 130 distinct systems. |
-| PLSDB 72,556 plasmids | **Corrected** - 72,360. |
-## v2 additions (2026-08-17)
-Three references were added for the expansion, each resolved against Crossref before use:
-| Key | Source | Authors (bib / Crossref) |
-|---|---|---|
-| `Kuang2026Lateral` | *Science Advances* 12(4):eadx5749, 2026 - lateral transduction of defense genes | 9 / 9 |
-| `Shu2026CRISPRregulates` | *Nature*, 2026 (advance online) - CRISIS, defense modules embedded in CRISPR-Cas loci | 17 / 17 |
-| `Cinelli2025Omitted` | *Biometrika*, 2025 - omitted-variable-bias sensitivity analysis for IVs | 2 / 2 |
-`Cinelli2025Omitted` is cited as **the framework we attempted and abandoned**, not as the method
-used: the posited-offset construction it inspired was implemented and found invalid for this model
-(the offset is absorbed by the other exposure parameters). The citation is retained because the
-attempt and its failure are reported, and because the framework's underlying logic - that an
-omitted path's strength is the right thing to reason about - is what led to estimating λ directly.
-`Shu2026CRISPRregulates` has no volume, issue or page numbers at Crossref (advance online
-publication) and is marked accordingly rather than having placeholder numbers invented.
-## Final Status
-| | |
-|---|---|
-| Entries | **15** |
-| DOIs resolving against Crossref | **15 / 15** |
-| Titles matching authoritative record | **15 / 15** |
-| Author lists matching (count and order) | **15 / 15** (GBD by documented corporate-author convention) |
-| Entries using "et al." | **0** |
-| Entries missing a DOI | **0** |
-| Corrections applied | 3 |
-| Editorial decisions documented | 4 |

docs/LANDSCAPE_SURVEY.md DELETED Viewed

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-# Landscape Survey: Defense Systems, Exposure, and Horizontal Gene Transfer
-**Project**: LEDGER - Latent Exposure Deconfounding for Gene-Element Receptivity
-**Date**: 2026-08-16
-**Purpose**: Verify the load-bearing empirical claims of the user-supplied research plan, establish
-the citation backbone, and position LEDGER against the closest prior work.
-**Method**: Every quantitative claim in the supplied plan was independently web-searched and, where
-possible, verified against the primary source (publisher page, PMC full text, or PubMed record).
-Claims are marked ✅ CONFIRMED, ⚠️ CORRECTED, or ❌ UNSUPPORTED. Corrections propagate into
-`RESEARCH_PLAN.md`.
----
-## 1. Verification Ledger
-| # | Claim in supplied plan | Status | Verified value / source |
-|---|---|---|---|
-| 1 | Liu, Botelho & Iranzo tested 7 defense systems vs MGE abundance across 197 species; effects "highly taxon and system dependent and in most cases not statistically significant" | ✅ CONFIRMED | Verbatim from abstract. 196 bacterial + 1 archaeal species. *Genome Research* 35(2):268-278, 2025. DOI 10.1101/gr.279300.124 |
-| 2 | Defense systems are strongly linked with MGEs, coacquired and co-lost at fast rates, masking inhibition | ✅ CONFIRMED | >95% of defense acquisitions occur on branches where MGEs are also gained (random expectation 71%); >90% of losses coincide with MGE losses (random 63%); defense acquisition ~50× more likely on MGE-gain branches |
-| 3 | Defense systems must persist a long time before showing a negative effect; short timescales give positive association | ✅ CONFIRMED | Lineage depth <10⁻⁵ subs/site → positive; >10⁻³ → negative |
-| 4 | RM target-density effects visible at broad taxonomic scale but RM significantly less effective at species level - attributed to the same paper | ⚠️ **CORRECTED** | **Liu/Botelho/Iranzo do NOT analyze RM target-site density or avoidance at any scale. RM was treated categorically with no mechanistic investigation.** The target-avoidance literature is a separate lineage: Oliveira, Touchon & Rocha, *NAR* 42(16):10618-10631 (2014), and Oliveira et al., *NAR* 51(13):6806 (2023) on RM shaping plasmid distribution. **H2 must be re-grounded on these sources.** |
-| 5 | Chong et al.: little known about which defense interactions are mechanistic vs co-localisations of convenience | ✅ CONFIRMED | Chong et al., *ISME Communications* 6(1):ycag130, 2026. They test co-localisation directly: associating pairs co-located in only 22% of cases, dissociating pairs 0.5% |
-| 6 | Curated global collection of 2,940 *P. aeruginosa* genomes analysed for defense systems across niches | ✅ CONFIRMED | Chong et al. 2026. Non-CF mean 7.9 systems, CF mean 6.5 |
-| 7 | *P. aeruginosa* CRISPR-Cas prevalence 49.9% | ✅ **VINDICATED BY OUR OWN MEASUREMENT** (correction withdrawn) | Initially marked "CORRECTED - not found in any primary source", because Chong et al. report only Type I-F (969/2,940 ≈ 33%). **We subsequently measured it directly.** Annotating real complete *P. aeruginosa* genomes with DefenseFinder 3.0.0 and counting any Class 1 CRISPR-Cas subtype (I-C, I-E, I-F) gives **49.2% of 120 genomes** carrying a system. The originally cited 49.9% is therefore essentially right for *total* CRISPR-Cas across subtypes; our correction had over-read a subtype-specific figure as a total. Recorded here rather than silently amended, because a survey that only ever corrects the source and never itself is not doing its job. Prevalence is still swept in simulation, which remains the right choice. |
-| 8 | Mean 8.5 defense systems per genome, across 63 distinct mechanisms | ⚠️ **CORRECTED** | Chong et al.: mean **7.5** overall; **130** distinct defense systems detected (DefenseFinder-DB v1.2.2) |
-| 9 | External test panel: 53 clinical MDR isolates × 40 phages spanning six phylogenetic groups, finding defense system count did NOT correlate with innate phage resistance | ❌ **UNSUPPORTED - no such panel located** | Two real panels found, **both reporting the opposite sign**: (a) Burke et al., *IJMS* 25(3):1424, 2024 - 100 isolates × 70 phages, 14 genera, significant *positive* correlation, p<0.0001, but **weak: R² = 0.2620**; (b) Costa et al., *Science Advances* 10(8):eadj0341, 2024 - 32 strains × 28 phages, 12 groups, resistance scales with defense count. **See §3 - this correction strengthens rather than weakens LEDGER's motivation.** |
-| 10 | Nahant collection: 65,232 experimentally determined interactions | ✅ CONFIRMED | Nahant cross-infection matrix, co-occurring *Vibrio* and their viruses; 251 dsDNA viruses characterised (Kauffman et al., *Scientific Data* 5:180114, 2018) |
-| 11 | PLSDB ~72,556 plasmids | ⚠️ minor | PLSDB 2025 hosts **72,360** entries. *NAR* 53(D1):D189 |
-| 12 | Spacer acquisition ~1 in 10⁷ non-immune infected cells; higher in cells entering lysogeny | ✅ CONFIRMED | ~1 cell per 10⁷-10⁶ (*S. aureus* systems). Lysogeny enhancement: "Bacteria exploit viral dormancy to establish CRISPR-Cas immunity," *Cell Host & Microbe*, 2025. Priming substantially increases rates over naive acquisition |
-| 13 | ~85% of predicted defense protein families uncharacterized from PLM applied to >32,000 genomes | ⏳ NOT YET VERIFIED | Deferred - affects only the low-rank channel's motivation, not the core identification argument |
-**Score after the v2 real-data pass: 7 confirmed (one by our own measurement), 3 corrected,
-1 unsupported, 1 minor, 1 deferred.** Claim 7 moved from "corrected" to "confirmed" once we
-measured it ourselves - see the row above. Claim 9 (the 53x40 panel) remains unsupported.
----
-## 2. Current Dominant Methods
-**Phylogeny-aware co-occurrence regression.** The current standard, exemplified by Liu/Botelho/Iranzo
-(2025): species-wise phylogenetic generalized linear mixed models (PGLMMs, Poisson) regressing MGE
-counts on defense presence, with gene gain/loss rates from GLOOME and sister-clade Wilcoxon
-comparisons. Strength: controls phylogeny properly. **Limitation: regresses observed presence, which
-is the product of exposure and establishment.** This is precisely the estimand problem LEDGER targets.
-**Co-occurrence network analysis.** Chong et al. (2026) use Coinfinder + Goldfinder for
-phylogenetically-controlled association testing across 2,940 genomes, yielding 426 associations and
-50 dissociations. Strength: large, curated, niche-annotated. Limitation: association ≠ mechanism, and
-the authors say so explicitly.
-**Composition-based host-range prediction.** Oligonucleotide composition distance between plasmid and
-candidate host, leaning on amelioration. Breaks down for broad-host-range plasmids.
-**Interpretable ML on experimental infection matrices.** See §3 - the closest prior work.
----
-## 3. The Closest Prior Work, and Why LEDGER Is Still Novel
-The most important discovery of this survey is **"Interpretable machine learning reveals a diverse
-arsenal of anti-defenses in bacterial viruses"** (bioRxiv 2024, doi 10.1101/2024.06.14.598830). It
-uses interpretable ML on diverse bacteria-virus infection data - including the Nahant matrix - to
-identify defense/anti-defense genetic interactions, and **experimentally validated eight previously
-unknown anti-defense proteins** counteracting AbiH, AbiU, Septu, DRT, CBASS, and Retron.
-This is genuinely adjacent to LEDGER's sparse bilinear defense × anti-defense block, and the research
-plan as supplied did not cite it. It must be cited and positioned against.
-**Why LEDGER remains distinct - and the distinction is sharp:**
-That work learns from **experimental cross-infection matrices, where exposure is guaranteed by
-construction.** Every host-virus pair in a Nahant-style matrix was physically mixed in a well. There
-is no exposure confound to solve, because the experimenter created the exposure. The method is
-therefore unavailable for the ~10⁵-10⁶ sequenced genomes where no one ran an infection assay.
-LEDGER's claim is the **observational analogue**: recovering the same class of compatibility
-structure from genome co-occurrence data, where exposure is latent and confounded with phylogeny.
-The CRISPR spacer channel is what makes that possible. Framed this way, the anti-defense ML paper
-becomes LEDGER's **validation target rather than its competitor** - if LEDGER's observationally
-estimated *g* recovers pairings that were experimentally confirmed there, that is E6 passing on
-externally validated ground truth, which is stronger evidence than the plan originally scoped.
----
-## 4. Known Open Problems
-1. **The estimand problem.** Observed presence = exposure × establishment. Every comparative study
-   regresses on presence. Susceptibility is not separately identified. *No prior work located
-   attempts to separate these two terms from observational genomic data.*
-2. **Linkage masking.** Defense systems ride on MGEs and are coacquired with them at ~50× baseline
-   rate, producing positive associations that mask inhibition (Iranzo).
-3. **Mechanism vs. convenience.** Co-occurrence cannot distinguish mechanistic interaction from
-   co-localisation (Chong).
-4. **Count is a weak predictor.** Even where defense count correlates with resistance, R² ≈ 0.26
-   (Burke). ~74% of variance is unexplained by counting systems. Compatibility is structural, not
-   scalar.
----
-## 5. Standard Datasets & Benchmarks
-| Resource | Scale | Role in LEDGER |
-|---|---|---|
-| *P. aeruginosa* curated global set (Chong et al.) | 2,940 genomes, niche-annotated | Primary host panel |
-| PLSDB 2025 | 72,360 plasmids + metadata | Element catalogue |
-| Nahant cross-infection matrix | 65,232 interactions | OOD generalization test (E3) |
-| Burke et al. panel | 100 isolates × 70 phages | External experimental test (E3) - **replaces the unlocatable 53×40 panel** |
-| Costa et al. panel | 32 strains × 28 phages | Second external test (E3) |
-| DefenseFinder / PADLOC | 130 systems detected in *P. aeruginosa* | Susceptibility features |
-| REBASE | enzyme → recognition sequence | RM motif mechanism features |
----
-## 6. What Everyone Is Already Doing (AVOID)
-- More co-occurrence association testing on larger genome sets with better phylogenetic control.
-  This is a crowded, well-executed space (Iranzo, Chong) and it does not address the estimand problem.
-- Cataloguing new defense systems. Extremely crowded.
-- Composition-based host-range prediction with a bigger model.
-- Supervised infection-outcome prediction on experimental matrices - now occupied by the
-  interpretable-ML anti-defense work, with experimental validation attached.
-## 7. Gaps Identified
-- **Exposure is never modelled.** LEDGER's core contribution. The Y=0, S=1 cell - spacer present,
-  element absent, i.e. demonstrated encounter followed by non-establishment - is discarded by every
-  method surveyed. It is the only cell that directly observes rejection.
-- **CRISPR arrays as an exposure instrument** appear unused for this purpose. Spacers are used for
-  host attribution and phage-host matching, never as a *record of encounter independent of outcome*.
-- **The chromosomal-only restriction** is a targeted fix to the exact masking mechanism Iranzo
-  identified, and is well-supported by their finding that CRISPR-Cas is the least MGE-borne system
-  (10.0% vs 20.1% for all others) - so the instrument itself is the system least contaminated by the
-  confound. This is a stronger argument than the plan made for itself.
----
-## 8. Consequences for the Research Plan
-1. **H2 must be restated.** Its RM scale-dependence target does not exist in the cited paper.
-   Re-grounded on Oliveira/Touchon/Rocha target-avoidance work, or demoted to a soft threshold.
-2. **E3's Pseudomonas panel is replaced** by Burke et al. (100×70) and Costa et al. (32×28), both
-   publicly described. The motivating claim inverts: defense count *does* correlate with resistance,
-   but weakly (R²=0.26). LEDGER's pitch becomes "counting systems explains a quarter of the variance;
-   a compatibility function should explain more" - which is more defensible and directly testable.
-3. **CRISPR prevalence must be swept, not assumed.** The 49.9% figure is unverified; ~33% is the
-   verified Type I-F figure. Phase 0 must characterise recovery across a prevalence range spanning
-   both.
-4. **The anti-defense ML paper must be cited**, positioned as the experimental-matrix counterpart,
-   and used as external ground truth for E6.

docs/RESEARCH_PLAN.md DELETED Viewed

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-# LEDGER: Latent Exposure Deconfounding for Gene-Element Receptivity
-**Field**: Computational microbial genomics / horizontal gene transfer
-**Constraints**: Data - public only, <50 GB | Compute - 2× A100 80GB (GPUs 1,3), multi-day
-**Date**: 2026-08-16
-**License**: MIT - Bryan Cheng, 2026
-**Origin**: Research direction, hypotheses, and experimental design supplied by the user. This
-document formalizes that plan, folds in corrections from `LANDSCAPE_SURVEY.md`, and adds the
-quantitative thresholds required to drive autonomous execution.
----
-## 0. Session Scope (explicit, so that no deliverable is silently narrowed)
-The supplied plan is a 16-week project (§11). It cannot be executed end-to-end in one session. The
-plan itself resolves the ordering: *"The single most important thing to do first is Phase 0.
-Everything else depends on whether the exposure and susceptibility layers actually separate at
-realistic spacer coverage."*
-**Executed this session, to completion and to publication standard:**
-- Phase 0 in full - generative simulator, estimator, baselines, identifiability curves, go/no-go.
-- All four baselines (B1-B4) implemented and compared on simulated data where ground truth exists.
-- Negative control E5 (within-lineage permutation).
-- Figures, LaTeX paper, verified bibliography.
-**Not executed this session, and reported as such rather than estimated:**
-- Weeks 3-16: the real-genome annotation pipeline (DefenseFinder/PADLOC/CRISPRCasTyper/geNomad over
-  2,940 *P. aeruginosa* genomes), E2, E3, E4, E6, and the *E. coli* extension. These require tool
-  installation, database downloads, and multi-day CPU annotation runs beyond one session.
-No number for an unexecuted stage will appear anywhere in this project. `[NOT RUN]` is used instead.
----
-## 1. Abstract
-When a mobile element is absent from a bacterial genome, that absence is ambiguous: the host may
-never have encountered the element, or may have encountered and rejected it. Every comparative-genomics
-study of transfer barriers regresses observed presence on host features, which estimates the *product*
-of exposure and establishment; because exposure covaries with the same phylogeny that carries the
-defense repertoire, susceptibility is not separately identified. We propose LEDGER, a three-component
-latent-variable model that uses CRISPR spacers as a record of encounter observed independently of
-outcome, thereby identifying a molecular susceptibility function. Phase 0 asks the only question that
-matters first: under a generative simulator calibrated to reported CRISPR biology, can the exposure and
-susceptibility layers be separated at realistic spacer coverage, and does the estimator recover a
-planted susceptibility function where the standard phylogenetic-regression approach fails?
-## 2. Background & Motivation
-Liu, Botelho and Iranzo (*Genome Research* 2025) quantified associations between seven widespread
-defense systems and MGE abundance across 196 bacterial and one archaeal species using phylogeny-aware
-PGLMMs, and found the impact of defense systems on HGT to be highly taxon- and system-dependent and,
-in most cases, not statistically significant. Their explanation is linkage: >95% of defense-system
-acquisitions occur on branches where MGEs are simultaneously gained (random expectation 71%), and
-defense acquisition is ~50× more likely on MGE-gain branches, so inhibition is masked by
-coacquisition. Chong et al. (*ISME Communications* 2026), analysing 2,940 *P. aeruginosa* genomes,
-state the residual problem directly: co-occurrence cannot separate mechanistic interaction from
-co-localisation of convenience.
-The consequence is that a *susceptibility function* - the probability that host H establishes element
-E given that H met E - has never been estimated from observational data, because exposure has never
-been observed. See `LANDSCAPE_SURVEY.md` for the full survey and for six corrections to figures in
-the original plan draft.
-## 3. Technical Approach
-### 3.1 Overview
-For host *i* and element *j* define three binary quantities:
-- **Y(i,j)** - observed presence of element *j* in genome *i*
-- **Z(i,j)** - *latent* exposure: whether *i* ever encountered *j*
-- **S(i,j)** - observed spacer receipt: a spacer in *i* matching *j* at high identity with valid PAM
-### 3.2 Model
-Three coupled components:
-**Exposure.**  P(Z=1) = σ( f(collection year, country, isolation source, BioProject co-membership,
-element prevalence in stratum, host lineage) )
-**Establishment given exposure.**
-P(Y=1 | Z=1) = σ( g(host defense features, element evasion features, compatibility features, lineage) )
-P(Y=1 | Z=0) = 0
-**Receipt detection.**
-P(S=1 | Z=1) = ρ(host CRISPR type, array length, Y)
-P(S=1 | Z=0) = ε  (false-match rate, held near zero by strict matching)
-Because Z is a single binary latent, the likelihood marginalizes **exactly** - no variational
-approximation. The four observed cells:
-| Cell | Probability | Meaning |
-|---|---|---|
-| Y=1, S=1 | π·θ·ρ₁ | exposed, established, receipt kept |
-| Y=1, S=0 | π·θ·(1−ρ₁) | exposed, established, no receipt |
-| Y=0, S=1 | π·(1−θ)·ρ₀ + (1−π)·ε | **exposed, rejected - the informative cell current methods discard** |
-| Y=0, S=0 | π·(1−θ)·(1−ρ₀) + (1−π)·(1−ε) | mixture of never-exposed and exposed-then-rejected - the confound |
-where π = P(Z=1), θ = P(Y=1|Z=1), and ρ_y = P(S=1|Z=1,Y=y).
-Fit by direct gradient ascent on the marginal log-likelihood; EM as fallback if unstable.
-### 3.3 Why this identifies θ
-Without S, only P(Y=1) = π·θ is observed; any (π,θ) with equal product is observationally
-equivalent, so θ is unidentified. Two things break the degeneracy:
-1. **The receipt channel.** With ε≈0, S=1 ⟹ Z=1. The S=1 subsample is a *known-exposed* subsample in
-   which θ is directly estimable: P(Y=1|S=1) = θρ₁ / (θρ₁ + (1−θ)ρ₀), which reduces to exactly θ when
-   ρ₁=ρ₀ and is corrected by the detection model otherwise.
-2. **Exclusion restrictions.** Exposure-only covariates (year, country, isolation source, project,
-   local prevalence) enter *f* but not *g* - a plasmid's interaction with a restriction enzyme does
-   not depend on which hospital the isolate came from. Susceptibility-only covariates (chromosomal
-   defense content, cognate motif counts) enter *g* but not *f*.
-### 3.4 Parameterization of g
-*g* is the object of interest and is built to be readable:
-1. Sparse bilinear block over named defense × named anti-defense families, group-lasso penalized.
-2. Low-rank bilinear term (rank ≈16) over embeddings of unannotated protein clusters.
-3. Explicit mechanism features: host RM recognition-motif counts in element *j*, normalized against a
-   composition-matched null; spacer targeting indicator; replicon incompatibility; GC/codon distance.
-4. Host lineage random effect, absorbing phylogenetically structured signal before defense content is
-   credited.
-### 3.5 The linkage objection and its mitigation
-The obvious objection: defense systems ride on MGEs, so carrying defenses correlates with having met
-MGEs, violating the exclusion restriction. Mitigation is direct - **restrict all susceptibility
-features to defense systems located on the chromosome and outside prophages, plasmids and ICEs.**
-MGE-borne systems are dropped from *g* and used instead as exposure covariates in *f*. This targets
-exactly the masking mechanism Iranzo identified, and is supported by their finding that CRISPR-Cas is
-the *least* MGE-borne system (10.0% vs 20.1% for all others) - the instrument is the system least
-contaminated by the confound.
-## 4. Phase 0 Experimental Design (executed this session)
-### 4.1 Simulator
-Generates host populations with: a planted susceptibility function *g\**; phylogenetically correlated
-defense content; exposure structure driven by ecology/geography that is *deliberately collinear with
-phylogeny* at a controllable strength; and a spacer detection process calibrated to reported biology
-(acquisition ~10⁻⁷-10⁻⁶ per infected cell, elevated in cells entering lysogeny, with retention
-depending on outcome).
-### 4.2 Experiments
-| ID | Test | Question |
-|---|---|---|
-| **E1** | Recovery of planted *g* vs. spacer coverage and CRISPR prevalence | Does the design have power at realistic parameters? |
-| **E1b** | Recovery vs. exposure-phylogeny collinearity | How much confounding can it absorb before failing? |
-| **E1c** | Recovery vs. dataset scale (N hosts × M elements) | How many genomes are needed? |
-| **E5** | Within-lineage permutation of defense repertoire | Does signal vanish under the null? **Non-negotiable.** |
-| **A1-A4** | Ablations: remove receipt channel; remove exclusion restrictions; remove lineage effect; restore MGE-borne defense features | Which components carry the identification? |
-### 4.3 Baselines
-- **B1** - host lineage only.
-- **B2** - composition distance (simulated analogue of oligonucleotide host-range prediction).
-- **B3** - **phylogenetic mixed-effects logistic regression of Y on defense presence.** A faithful
-  analogue of the current standard method (Iranzo's PGLMM). *This is the headline comparison.*
-- **B4** - full model with exposure layer clamped to Z=1, isolating the exposure layer's contribution.
-## 5. Dataset Strategy
-Phase 0 is simulation-only - no download, zero data footprint. Real-data layers (NCBI/AllTheBacteria,
-PLSDB, INPHARED, DefenseFinder, PADLOC, dbAPIS, REBASE, MOB-suite, ICEberg, CRISPRCasTyper) are
-specified in the supplied plan §4 and are **[NOT RUN]** this session per §0.
-## 6. Implementation Roadmap
-| Milestone | Deliverable | Verification |
-|---|---|---|
-| M1 | Generative simulator | Simulated marginals match target rates; planted *g* recoverable in the oracle-exposure limit |
-| M2 | LEDGER estimator (exact marginal likelihood) | Gradient check; recovers *g* when Z is revealed (oracle upper bound) |
-| M3 | Baselines B1-B4 | B3 reproduces the known attenuation/masking on simulated data |
-| M4 | Identifiability sweeps E1, E1b, E1c | Recovery curves with replicate CIs |
-| M5 | Negative control E5 + ablations A1-A4 | E5 signal at chance |
-| M6 | Figures, LaTeX paper, verified bibliography | Compiled PDF; triple-pass bib audit |
-## 7. Evaluation Criteria
-### 7.1 Primary Metrics
-- **Spearman correlation** between estimated and planted *g* coefficients.
-- **RMSE** on *g* coefficients (LEDGER vs B3), paired across replicates.
-- **Sign-recovery accuracy** on planted nonzero interaction weights.
-### 7.2 Secondary Metrics
-- 95% CI coverage of planted coefficients.
-- AUROC for predicting held-out establishment among *known-exposed* pairs.
-- Bias direction of B3 (expected: attenuation toward zero / sign inversion under linkage).
-### 7.3 Definition of Success (drives autonomous execution)
-#### Hard Thresholds (must meet ALL)
-- **HT1**: At CRISPR prevalence ≥ 0.30 and spacer coverage ρ ≥ 0.20, LEDGER recovers planted *g* with
-  mean Spearman ≥ **0.60** across ≥ 20 replicates.
-- **HT2**: LEDGER coefficient RMSE at least **30% lower** than B3 at those parameters, paired
-  Wilcoxon **p < 0.01**.
-- **HT3**: Sign-recovery accuracy on planted nonzero weights ≥ **80%**.
-- **HT4** *(revised during execution - see justification below)*: Under E5 **global**
-  permutation of the host defense repertoire, mean |Spearman| on the **host-side**
-  coefficients (α, W) < **0.15** (signal vanishes).
-  > **Threshold revision, recorded in full.** As originally written, HT4 required the signal
-  > to vanish under a *within-lineage* permutation. Run as specified, it **failed**: mean
-  > Spearman 0.536, support AUROC 0.951. Diagnosis showed the control itself was invalid, not
-  > the estimator. Defense content is phylogenetically autocorrelated, so roughly half its
-  > variance lies *between* lineage clusters and is left completely untouched by a
-  > within-cluster shuffle: measured residual corr(D, D_permuted) = **0.493**. A control that
-  > preserves 49% of the signal is not a null, and an estimator recovering ~0.49 from it is
-  > behaving correctly. Two further contaminations were found: the metric `spearman_all`
-  > includes the element-side effects β, which a *host*-side permutation cannot touch, so an
-  > estimator that correctly zeroes W and fits β scores well under a null; and the sparse W
-  > tie ceiling inflates the apparent score.
-  >
-  > The revision replaces the control with a **global** permutation (measured residual
-  > corr(D, D_permuted) ≈ 0.01, a genuine null) scored on host-side coefficients only. This
-  > is a **strictly harder** test than the original: it destroys all defense signal rather
-  > than half of it, and removes the metric contamination that made the original easier to
-  > pass on a technicality. The within-lineage permutation is retained as an interpretive
-  > diagnostic - it measures how much of the estimator's signal comes from within- versus
-  > between-lineage comparison - but is no longer a pass/fail gate, because it is not a null.
-#### Soft Thresholds (should meet most)
-- ST1: 95% CI coverage within [0.90, 0.98].
-- ST2: Ablation A1 (remove receipt channel) degrades Spearman by ≥ 0.20 - i.e. the spacer channel is
-  demonstrably load-bearing rather than decorative.
-- ST3: Ablation A4 (restore MGE-borne defense features) reintroduces a positive Y-defense association,
-  reproducing the published confound on demand.
-- ST4: LEDGER ≥ B3 across the *entire* swept parameter grid (no regime where the standard method wins).
-#### Failure Criteria (trigger deep diagnosis)
-- Spearman < 0.60 at realistic parameters after 3 improvement cycles → report honestly as a negative
-  identifiability result. **This is a publishable answer**: it would mean the field's nulls are not
-  fixable by this instrument.
-- E5 permutation signal ≥ 0.15 → estimator is fitting an artifact; halt and debug. Non-negotiable.
-#### Iteration Budget
-- Max autonomous improvement cycles: 3. Max additional runs per cycle: 20 simulation sweeps.
-## 8. Risk Mitigation
-| Risk | Likelihood | Impact | Mitigation |
-|---|---|---|---|
-| Spacer coverage too thin for identification | M | H | Exactly what Phase 0 measures; sweep ρ down to 0.05 and report the breakdown point |
-| Optimizer instability on the marginal likelihood | M | M | Gradient checks, multiple restarts, EM fallback, log-space arithmetic |
-| Estimator fits artifacts | L | H | E5 permutation control is a hard gate |
-| Weak exclusion restrictions under high collinearity | H | H | E1b explicitly characterises degradation vs collinearity |
-| Simulator too kind to the estimator | M | H | Mis-specification stress test: fit under a *different* generative process than assumed |
-## 9. Timeline (this session)
-| Phase | Status |
-|---|---|
-| Simulator + estimator + baselines | This session |
-| Identifiability sweeps + controls + ablations | This session |
-| Figures, LaTeX paper, bibliography verification | This session |
-| Real-genome pipeline (supplied plan weeks 3-16) | **[NOT RUN]** - see §0 |
-## 10. Expected Deliverables
-- [ ] Simulator, estimator, baselines (MIT-licensed, documented)
-- [ ] Identifiability curves with replicate confidence intervals
-- [ ] Negative control and ablation results
-- [ ] RESULTS.md, TRAINING_LOG.md
-- [ ] LaTeX paper + compiled PDF
-- [ ] Triple-pass verified references.bib
-- [ ] Pre-training and post-results review reports

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-# LEDGER - Research Plan v2 (Post-Phase-0 Revision)
-**Supersedes**: `RESEARCH_PLAN.md` (v1). v1 is retained unaltered as the pre-registered record.
-**Date**: 2026-08-17
-**Field**: Computational microbial genomics / horizontal gene transfer
-**Constraints**: Data - public only, <50 GB | Compute - 2× A100 (GPUs 1,3), 32 CPU cores, multi-day
-**License**: MIT - Bryan Cheng, 2026
----
-## 0. Why v1 needs revising
-Phase 0 passed its go/no-go gate - all four hard thresholds - but in doing so it **falsified the
-premise the project was built on**. v1 is not wrong so much as aimed at the wrong target. Three
-independent inputs force a revision:
-### 0.1 Phase 0 result: the instrument is not where identification lives
-v1 §3.3 argued that CRISPR spacers identify the susceptibility function because they observe
-encounter independently of outcome. Phase 0 measured this directly and found:
-| Evidence | Result |
-|---|---|
-| Recovery across a 47× range in informative (Y=0,S=1) cells (214 → 10,007) | changes by **6%** |
-| Removing the receipt channel entirely (A1) | costs **2.9%** RMSE |
-| Hypothesis that noisy exposure metadata makes spacers matter | **rejected** - gain flat |
-| Removing exposure-layer heterogeneity (A2) | costs **23.2%** RMSE |
-| Standard method (B3) vs LEDGER | **77.4%** RMSE reduction |
-Identification comes from the **structural exclusion of defense features from the exposure
-layer**, not from spacer evidence. Because *f* cannot express defense-driven variation in *Y*,
-that variation must be attributed to *g*.
-**Consequence.** The method's validity now rests on an *assumption* rather than on an
-*observation*. Assumptions fail silently in ways instruments do not. v1 contained no machinery
-for quantifying that failure. This is the single largest gap and §2 addresses it.
-**Second consequence.** The method needs no CRISPR at all where the restriction holds, which
-*widens* its domain to low-CRISPR species and to element classes that leave no spacer record.
-v1's species-selection logic (choose *P. aeruginosa* for high CRISPR prevalence) is no longer
-the binding criterion.
-### 0.2 New literature (published since v1 was written) attacks the load-bearing assumption twice
-Deep research surfaced two 2026 papers that bear directly - and adversely - on v1's central
-mitigation, which was to restrict susceptibility features to defense systems located on the
-chromosome and outside prophages, plasmids and ICEs.
-**Threat A - lateral transduction makes "chromosomal" a weak proxy for "not mobile."**
-Kuang, Gorzynski, Touchon, Shkoporov, Rocha, Fitzgerald, Chen, Rostøl & Penadés
-(*Science Advances*, Jan 2026) show that phage- and PICI-mediated lateral transduction transfers
-defense genes between bacteria, and that **defense systems are often positioned near phage or
-PICI attachment sites so as to exploit lateral transduction for their own mobility**. A defense
-system can therefore sit outside any recognised prophage boundary - passing v1's filter - and
-still be routinely mobilised. v1's filter removes systems that are *inside* elements; it does
-nothing about systems that are *adjacent to attachment sites*. The exclusion restriction leaks
-through exactly the door v1 left open.
-**Threat B - CRISPR is not an independent instrument.**
-Shu, Wang, Zhou and colleagues (*Nature*, 2026) describe CRISIS, a widespread paradigm in which
-**more than twenty innate defense modules are genomically embedded within type I CRISPR-Cas
-loci** and are transcriptionally repressed by the Cascade complex via crRNA-like RNAs; when
-CRISPR-Cas is compromised by mutation or anti-CRISPR proteins, those embedded systems burst into
-expression. This is doubly damaging to v1:
-1. **Physical coupling.** CRISPR presence and other defense content are not independent
-   features; some defenses live *inside* CRISPR loci. v1's *g* treats defense repertoire as the
-   treatment and CRISPR status as feeding only the detection model ρ.
-2. **Functional coupling.** The *effectiveness* of embedded defenses depends on CRISPR status.
-   So the true susceptibility *g* depends on CRISPR, which is also the variable driving ρ. v1's
-   model assumes ρ depends on CRISPR and *g* does not - a now-known-false assumption.
-*P. aeruginosa*'s dominant system is type I-F (969/2,940 genomes in Chong et al.), so this is not
-a peripheral concern for the chosen study system.
-### 0.3 Empirical scale is now known, and one v1 risk was mis-rated
-- Phase 0 Finding 7: below ~250 hosts LEDGER is **worse** than the baseline it replaces
-  (RMSE 0.769 vs 0.537 at N=81). It is a large-collection method.
-- **2,757 complete *P. aeruginosa* genomes with all three exposure covariates are available**
-  (measured, §5.1) - comfortably above threshold.
-- v1 §8 rated exposure-phylogeny collinearity the only High/High risk. Phase 0 Finding 6 showed
-  recovery is flat to c = 0.99. **That risk did not materialise and is downgraded.** The risk
-  register was pointed at the wrong hazard.
-- v1's "metadata sparsity" risk is also milder than assumed: measured coverage is 83.2%
-  (collection date), 94.3% (geography), 92.5% (isolation source), 100% (BioProject).
----
-## 1. Revised central hypothesis
-v1 asked whether defense repertoires gate establishment once exposure is observed. That question
-survives, but the operative question has moved upstream:
-> **H0 (new, and now primary).** The exclusion restriction - that chromosomal defense content
-> does not predict exposure once lineage and ecology are controlled - is *approximately* true in
-> real genomes, and the residual violation is small enough that the estimated susceptibility
-> function is robust to it.
-This is now the load-bearing claim, so it is stated as a hypothesis and tested rather than
-assumed. The original hypotheses are retained with revisions:
-- **H1** (unchanged in substance): after conditioning on exposure and lineage, chromosomally
-  encoded defense content predicts establishment of specific elements.
-- **H2** (**re-grounded**): v1 attributed a restriction-modification target-density
-  scale-dependence to Liu/Botelho/Iranzo. That paper does not analyse RM target-site density at
-  all. The real source is Shaw, Rocha & MacLean (*NAR* 2023), who find 6 bp target avoidance
-  correlated with the taxonomic distribution of R-M systems and stronger in plasmid than core
-  genes. H2 becomes: *one fitted g reproduces broad-scale RM target avoidance (Shaw et al.)
-  alongside species-level RM non-significance (Liu et al.).* Demoted from hard to soft.
-- **H3** (**sharpened**): the susceptibility function transfers to experimentally measured
-  infection matrices it was never trained on - specifically improving on a **scalar defense
-  count**, which explains only R² ≈ 0.26 of resistance variance (Burke et al. 2024). v1's target
-  panel ("53 × 40, no correlation") does not exist; see `LANDSCAPE_SURVEY.md`.
-- **H4 (new).** CRISPR status is not conditionally independent of susceptibility (CRISIS,
-  Threat B). Excluding CRISPR-embedded defense modules from *g* changes the estimated
-  interaction map measurably.
----
-## 2. New workstream: sensitivity analysis (highest priority)
-Because identification rests on an assumption, the correct statistical response is not to defend
-the assumption but to **quantify how much violation the conclusions can absorb**. We adopt the
-omitted-variable-bias framework of Cinelli & Hazlett (*Biometrika* 2025), which was designed for
-exactly this situation: instruments with possible side-effects (exclusion violations) and
-confounding, summarised by **robustness values** - the minimum strength an omitted path needs in
-order to overturn a study's conclusion.
-> **§2 REVISED DURING EXECUTION.** The posited-offset construction specified below was
-> implemented and **found invalid**, then superseded by something stronger. Recorded in full
-> because a discarded method is part of the result.
->
-> **What failed.** Adding a fixed, non-trainable offset $\lambda \cdot \text{load}$ to the
-> exposure layer does not perturb the susceptibility estimates: the other free exposure
-> parameters (lineage effects, per-element terms, intercept) simply absorb it. Measured on
-> clean data, $\hat\alpha$ moved from $-1.06$ at $\lambda=0$ to $-0.98$ at $\lambda=4$,
-> non-monotonically. No robustness value can be read off a curve that does not move, so the
-> statistic would have been meaningless had we reported it.
->
-> **What replaced it.** The violation turns out to be **estimable rather than merely
-> boundable**. Permitting the exposure layer a *free* defense-load coefficient recovers the
-> true violation strength almost exactly ($\lambda_{\text{true}} = 0, 1, 2, 3 \rightarrow
-> \hat\lambda = -0.01, 1.04, 2.08, 3.24$) and **de-biases the susceptibility coefficients**
-> ($\hat\alpha \approx -1.03$ throughout, against a true $-1.09$) - where omitting the term
-> leaves $\hat\alpha$ attenuated by up to 70%. Estimating a violation strictly dominates
-> bounding it, so §2's workstream becomes *estimate and report $\hat\lambda$*, and the
-> Cinelli-Hazlett framework is cited as the approach considered rather than the one used.
->
-> **What sensitivity analysis is still needed for.** Violations that are *not* of the estimable
-> form - in particular Threat B's functional coupling, where CRISPR status modulates $g$ and
-> $\rho$ together, and any element-specific violation. Those are covered by the §3 stress tests.
-### 2.1 The LEDGER robustness value *(superseded - see the note above)*
-Define the violation as a defense-load term entering the exposure layer with coefficient
-$\lambda$ (v1 §3.5 assumed $\lambda = 0$). Define:
-$$\lambda^{*} = \inf\{\lambda \ge 0 : \text{conclusion overturned at } \lambda\}$$
-with three conclusion variants reported separately:
-- $\lambda^{*}_{\text{sign}}$ - smallest $\lambda$ flipping the sign of a defense main effect
-- $\lambda^{*}_{\text{sig}}$ - smallest $\lambda$ at which the effect loses significance
-- $\lambda^{*}_{\text{rank}}$ - smallest $\lambda$ degrading interaction-map recovery below a
-  usable level
-**This project has an advantage no observational study normally has**: the simulator controls
-the true $\lambda$, so the computed robustness value can be *validated* against ground truth
-rather than merely asserted. If $\lambda^{*}$ predicts the observed breakdown point, the
-statistic is trustworthy for real data where $\lambda$ is unknown.
-### 2.2 Deliverable
-A reported robustness value alongside every estimated coefficient, plus a benchmark: $\lambda^*$
-expressed as a multiple of the *observed* defense→exposure association measured on real data
-(§5.2). A conclusion is credible when $\lambda^*$ comfortably exceeds what the data suggest
-$\lambda$ actually is.
----
-## 3. New workstream: stress tests for the two newly-published threats
-Both threats are simulatable, which means both can be quantified before any real-genome claim
-is made.
-### 3.1 Threat A - lateral-transduction leak (`att_leak`)
-A configurable fraction of *chromosomal* defense systems (those that pass v1's filter) are
-designated attachment-site-proximal and made mobile, contributing to exposure. This models a
-filter that removes element-internal systems but misses att-proximal ones.
-**Question**: at what leak fraction does recovery break, and does the §2 robustness value
-detect it?
-### 3.2 Threat B - CRISPR/defense coupling (`crisis_coupling`)
-Two couplings, switchable independently so their contributions separate:
-- **Physical**: a subset of defense systems is co-inherited with CRISPR presence.
-- **Functional**: the effect of those systems in *g* is modulated by CRISPR status - i.e. *g*
-  depends on the same variable as ρ, breaking v1's assumption.
-**Question**: does LEDGER's estimate of *g* become biased, and is the bias detectable without
-knowing the truth? Mitigation to test: drop CRISPR-embedded modules from *g*, and allow *g* a
-CRISPR-status interaction term.
-### 3.3 Threat C - misassigned element boundaries
-Annotation error in prophage/ICE boundary calling misclassifies element-borne systems as
-chromosomal. Swept as a misclassification rate.
----
-## 4. Revised experimental program
-Ordering is driven by what Phase 0 learned: validate the assumption before scaling the pipeline
-that depends on it.
-| Stage | Experiment | Question | Depends on |
-|---|---|---|---|
-| **S1** | Sensitivity machinery (§2), validated against known λ from E1d | Can we quantify assumption failure? | simulation only |
-| **S2** | Stress tests A, B, C (§3) | Do the new 2026 threats break the method? | simulation only |
-| **S3** | **Exclusion-restriction audit on real genomes** (§5.2) | Is the load-bearing assumption true in practice, and by how much is it violated? | real annotation |
-| **S4** | Defense-content ↔ CRISPR coupling audit | Is Threat B real in *P. aeruginosa*? | real annotation |
-| **S5** | Full element/spacer pipeline and model fit | Does H1 hold on real data? | S3, S4 |
-| **S6** | External validation vs Burke and Costa panels; H2; Lopatina pairings | Does *g* transfer? | S5 |
-S1-S4 are in scope for immediate execution. S5-S6 require the full element and spacer layers and
-are scoped but not claimed.
----
-## 5. Data
-### 5.1 Realised host panel (measured, not projected)
-| Property | Value |
-|---|---|
-| *P. aeruginosa* complete assemblies at NCBI | 3,466 |
-| With collection date + geography + isolation source | **2,757** |
-| Distinct BioProjects | 559 |
-| Collection years | 1955-2026 (median 2018) |
-| Median assembly length | 6.78 Mb |
-| Download footprint | ≈ 19 GB (within the 50 GB limit) |
-Only complete assemblies are used, because the outcome is element presence/absence and a plasmid
-missing from a fragmented draft is a false negative that the model would read as a rejection.
-Geography is genuinely varied (China 677, USA 439, Belgium 188, Denmark 174, UK 138, Germany 133,
-Taiwan 114, Australia 98) and isolation source spans clinical (sputum 409, CF lung 172, urine
-148, blood 89, wound 64) and environmental (wastewater 58, soil 39) niches. This variation is
-what the exposure layer needs; without it *f* would be unidentifiable in practice.
-### 5.2 The exclusion-restriction audit (S3) - design
-The audit needs only host-side data, which is why it can run far ahead of the full pipeline.
-1. Annotate defense systems with DefenseFinder 3.0.0 (152 systems; AntiDefenseFinder included).
-2. Assign lineage clusters with skani ANI (analogue of the 95%/99.9% clusters in v1 §4).
-3. Regress **chromosomal defense content on exposure-only covariates** (collection year, country,
-   isolation source, BioProject) with lineage random effects.
-4. Report the residual association. Under a valid exclusion restriction it should be ≈ 0 after
-   conditioning on lineage.
-5. Feed the measured value into §2 as the empirical benchmark for λ.
-**This is the experiment that decides whether the whole approach transfers to real data**, and v1
-did not contain it.
-### 5.3 Remaining layers (S5, scoped not claimed)
-Elements: PLSDB (72,360 plasmids), INPHARED, geNomad prophage calls. Spacers: CRISPRCasTyper, or
-the CRISPRCasdb precomputed spacer dump. Anti-defense: AntiDefenseFinder, dbAPIS. RM motifs:
-REBASE. Mobility: MOB-suite, ICEberg.
----
-## 6. Evaluation criteria
-### 6.1 Definition of success (revised; v1 §7.3 superseded)
-#### Hard thresholds
-- **HT-A** *(restated after the §2 revision)*: the exclusion-restriction violation is
-  **recoverable**: across ≥ 20 replicates and a λ grid spanning 0-4, the fitted $\hat\lambda$
-  tracks $\lambda_{\text{true}}$ with slope in [0.8, 1.25] and $R^2 \ge 0.95$, **and** the
-  de-biased $\hat\alpha$ stays within 20% of the true value at every λ. The original HT-A
-  (validating a posited-offset robustness value) is void because that construction was shown
-  invalid, not because it was inconvenient - see §2.
-- **HT-B**: Under the lateral-transduction leak (Threat A) at a leak fraction of 0.25, LEDGER
-  retains Spearman ≥ 0.60 **or** the robustness value correctly flags the conclusion as fragile.
-  (Either outcome is acceptable; silently degrading while reporting confidence is not.)
-- **HT-C**: The exclusion-restriction audit (S3) completes on ≥ 500 real genomes and reports a
-  quantitative residual defense↔exposure association with confidence intervals.
-- **HT-D**: All Phase 0 hard thresholds continue to hold after the model is extended
-  (no regression).
-#### Soft thresholds
-- ST-A: Under CRISIS coupling (Threat B), the mitigation (dropping CRISPR-embedded modules and
-  adding a CRISPR interaction to *g*) recovers ≥ 80% of the lost recovery.
-- ST-B: Measured real-data residual defense↔exposure association is below $\lambda^{*}$ - i.e.
-  the assumption is violated by less than the method can absorb.
-- ST-C: Annotation throughput sufficient for ≥ 2,000 genomes.
-#### Failure criteria
-- If the S3 audit shows a **large** residual defense↔exposure association exceeding $\lambda^{*}$,
-  the honest conclusion is that the observational approach does not identify susceptibility in
-  *P. aeruginosa* without a genuine instrument - in which case the CRISPR channel returns to
-  centre stage and species selection should be driven by CRISPR prevalence after all. **This is
-  a publishable negative result and must be reported as such, not engineered away.**
-- If Threat B proves severe and unmitigable, CRISPR cannot serve as an exposure instrument in
-  type I-F-dominated species, which would need stating plainly.
-### 6.2 What each outcome means
-- **H0 holds, threats mild** → proceed to S5/S6; the method is a general tool for large genome
-  collections, CRISPR optional.
-- **H0 fails, spacers rescue** → the method is restricted to CRISPR-rich species; v1's original
-  framing was right for the wrong reason.
-- **H0 fails, spacers do not rescue** → observational susceptibility estimation is not
-  identifiable at population scale by these means. Reports as a negative result answering an
-  open dispute.
----
-## 7. Revised risk register
-v1's register was mis-calibrated: its top risk did not materialise while its actual failure modes
-were unlisted. Revised:
-| Risk | Likelihood | Impact | Status / mitigation |
-|---|---|---|---|
-| Exclusion restriction violated in real data (Threats A/B) | **H** | **H** | **New top risk.** S3 audit measures it; §2 quantifies tolerance |
-| CRISPR/defense coupling breaks ρ⊥g (Threat B) | **H** | **H** | **Newly identified from 2026 literature.** S2/S4 |
-| Att-site proximity defeats the chromosomal filter (Threat A) | **M-H** | **H** | **Newly identified.** S2; add att-proximity filter |
-| Annotation boundary error | M | M | Threat C sweep; report sensitivity |
-| Small-N instability | L | H | Quantified (N≳250); 2,757 available |
-| Exposure-phylogeny collinearity | L | L | **Downgraded** - Phase 0 showed flat to c=0.99 |
-| Metadata sparsity | L | M | **Downgraded** - coverage measured at 83-100% |
-| Spacer coverage too thin | L | L | **Downgraded** - recovery flat over a 47× range |
-The three top risks are all consequences of the same fact: the method rests on an assumption
-about what does *not* influence exposure, and mobile genetic elements are very good at
-violating such assumptions.
----
-## 8. Deliverables
-- [ ] Sensitivity-analysis module with validated robustness values
-- [ ] Stress-test results for the three threats, with recovery curves
-- [ ] Real-genome annotation pipeline (DefenseFinder + skani), reproducible
-- [ ] Exclusion-restriction audit on ≥ 500 (target 2,757) real genomes
-- [ ] Updated RESULTS.md, TRAINING_LOG.md, review reports
-- [ ] Extended paper incorporating v2 results
-- [ ] Verified bibliography including the three new 2026 references

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-# LEDGER - Research Plan v3
-**Supersedes**: `RESEARCH_PLAN_V2.md` for forward work. v1 and v2 are retained unaltered as the
-pre-registered record.
-**Date**: 2026-08-17
-**Constraints**: public data <50 GB (18 GB used) | 2× A100, 32 CPU cores, multi-day
----
-## 0. Where the project actually stands
-| Established | Where |
-|---|---|
-| Exposure and susceptibility separate in simulation; LEDGER within 14% of an oracle, standard method 4.5× worse | Phase 0 |
-| Identification comes from the exclusion restriction, not the CRISPR instrument | Phase 0, Finding 5 |
-| The exclusion-restriction violation is **estimable** (slope 1.032, R²=0.9993); assuming it costs up to 79% attenuation | v2, HT-A |
-| The restriction **is violated in real *P. aeruginosa***: 70-79 of 116 systems leak (BH q<0.10) | v2, S3 audit |
-| CRISIS coupling resists every mitigation tried (best 38% vs an 80% bar) | v2, ST-A **FAIL** |
-**Two things are conspicuously unfinished, and they are the same thing.**
-1. **LEDGER has never been fitted to real data.** Every recovery number in the project is a
-   planted-coefficient simulation. v2's own conclusion was that the directly comparable quantity is
-   λ̂ itself, "estimable on real data only once the element layer exists."
-2. **The one mitigation that should work for CRISIS was specified and not run**, because it needs
-   to know which defense systems are CRISPR-embedded. v2 noted this "is obtainable in real data
-   from genomic co-location with CRISPR loci" - and we now hold 1,200 annotated genomes with
-   per-system gene coordinates, so it is obtainable *now*.
-v3 does both, plus the empirical test of the 2026 CRISIS claim that neither is possible without.
----
-## 1. Hypotheses
-- **H5 (new, empirical).** CRISIS is detectable in *P. aeruginosa*: a identifiable subset of
-  innate defense systems sits significantly closer to CRISPR-Cas loci than chance allows, and that
-  subset is recoverable from coordinates alone.
-- **H6 (new, methodological).** Given the empirically identified embedded subset, an interaction
-  between CRISPR status and *embedded-subset* load absorbs the CRISIS functional coupling where
-  the total-load absorber failed. This is the specific claim v2 declined to make.
-- **H7 (new, the headline).** LEDGER can be fitted to a real host×element matrix built from
-  prophages and CRISPR spacers, yielding the first measured λ̂ on real genomes - a number the
-  project has argued for throughout and never produced.
-- **H8.** The real λ̂ is large enough that assuming the exclusion restriction would materially
-  bias a susceptibility estimate, i.e. the v2 simulation result has real-world bite.
----
-## 2. Stage S5 - build the element and spacer layers (the headline work)
-The audit of v2 was host-side only. S5 builds the two missing observables.
-### 2.1 Elements (Y)
-Complete *P. aeruginosa* assemblies rarely carry plasmids (only ~2% of detections are
-extrachromosomal), so the mobile reservoir here is **integrated prophages**, which are chromosomal
-by coordinate. This is the same fact that made v1's replicon filter leaky, and it is now turned to
-use: prophages are the element class.
-1. Call prophages with **geNomad** on all 1,200 cohort genomes.
-2. Dereplicate prophage sequences into **element clusters** (skani/mmseqs), so that "the same
-   prophage in two hosts" is one element.
-3. `Y[i,j] = 1` iff host *i* carries a prophage in cluster *j*.
-### 2.2 Spacers (S)
-1. Extract CRISPR arrays and spacers with **minced** on all 1,200 genomes.
-2. Match spacers against prophage cluster representatives by BLASTN (short-word settings), with
-   an identity/coverage threshold chosen to keep the false-match rate ε low - the model assumes
-   ε ≈ 0 and that assumption must be earned, not asserted.
-3. `S[i,j] = 1` iff a spacer in host *i* matches a member of cluster *j*.
-**Critical self-check.** A spacer matching a prophage *resident in the same host* is
-self-targeting. The model already predicts these are purged (ρ₁ < ρ₀), so the (Y=1, S=1) cell
-should be depleted relative to (Y=0, S=1). If it is not, the receipt model's central assumption
-is wrong on real data and that must be reported.
-### 2.3 Fit
-Fit LEDGER with the free defense-load coefficient, and report **λ̂ measured on real genomes** with
-a bootstrap interval. Compare against the simulation-calibrated bias curve to state what
-magnitude of attenuation an analyst who assumed the restriction would have suffered.
----
-## 3. Stage S7 - is CRISIS real in *P. aeruginosa*? (new)
-Uses data already on disk: per-system gene coordinates from DefenseFinder.
-1. For every non-Cas defense system, compute the gene-distance to the nearest Cas system on the
-   same replicon.
-2. Build a null by permuting system positions within replicon, preserving system counts and
-   replicon lengths.
-3. Per system type, test whether observed proximity to Cas exceeds the null (BH-corrected).
-4. The significantly proximal set is the **empirical embedded subset**.
-This is a direct test of \citet{Shu2026CRISPRregulates} in a species they did not study, and it
-is the input H6 needs.
----
-## 4. Stage S8 - the mitigation v2 specified and did not run
-With the embedded subset known (from §3 in real data, and by construction in simulation):
-1. Add to *g* an interaction between CRISPR status and **embedded-subset load** (not total load).
-2. Re-run the CRISIS threat sweep with this absorber.
-3. **Pre-registered prediction**: this recovers ≥80% of the functional-coupling loss where the
-   total-load absorber recovered −31%. If it does not, CRISIS is unmitigable by any absorber of
-   this family and we say so.
-## 5. Success criteria
-### Hard
-- **HT-E**: The element/spacer pipeline produces a real Y and S matrix with ≥300 element clusters
-  and a non-trivial informative cell count (Y=0,S=1), with the self-targeting depletion check
-  reported whichever way it comes out.
-- **HT-F**: λ̂ is estimated on real data with a bootstrap interval, and the corresponding
-  attenuation-if-assumed is stated.
-- **HT-G**: The CRISIS proximity test (§3) completes with a permutation null and BH correction,
-  reporting the embedded subset or its absence.
-### Soft
-- **ST-D**: The embedded-subset absorber recovers ≥80% of the functional-coupling loss (H6).
-- **ST-E**: Real λ̂ differs from zero by more than its bootstrap interval (H8).
-- **ST-F**: Self-targeting spacers are depleted in the (Y=1,S=1) cell, as the receipt model assumes.
-### Failure criteria
-- If spacer→prophage matching yields too few matches to identify ρ, the CRISPR instrument is
-  unusable at this scale in this species and that is the reportable result.
-- If λ̂ on real data is indistinguishable from zero, the v2 machinery is correct but unnecessary
-  here, which would be a genuine and useful negative.
-## 6. Risks
-| Risk | Mitigation |
-|---|---|
-| geNomad runtime on 1,200 genomes | Parallelise; subset if needed and report N honestly |
-| Spacer matches too sparse | Report as a finding; it is the empirical answer to "does the instrument exist at scale" |
-| Prophage clustering granularity arbitrary | Sweep the threshold as the audit swept ANI |
-| False-positive spacer matches inflate S | Choose thresholds to bound ε; report the estimated ε |
-| Self-targeting assumption wrong | Explicit check in §2.2; report either way |

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@@ -1,369 +0,0 @@
-# Results - LEDGER
-**Last Updated**: 2026-08-17
-**Status**: Phase 0 COMPLETE - 3,340 production fits (plus 40 from the superseded control, retained in `experiments/e5_ORIGINAL_MISSPECIFIED_CONTROL.jsonl`)
-**Threshold Status**: **All four hard thresholds PASS.** HT1 0.746 (≥0.60) · HT2 77.4% RMSE
-reduction, p=2×10⁻²¹ (≥30%, p<0.01) · HT3 sign accuracy 1.000 (≥0.80) · HT4 global-permutation
-null 0.075 (<0.15). Soft: ST3 and ST4 pass, **ST2 fails** (reported, not dropped).
-> **Scope reminder.** This document covers Phase 0 only - the simulation-based identifiability
-> study. The real-genome pipeline (weeks 3-16 of the supplied plan) is **[NOT RUN]**. No number
-> attributable to it appears anywhere in this project.
----
-## Summary Table
-| Experiment | Fits | Headline outcome | Status |
-|---|---|---|---|
-| E1 - coverage × CRISPR prevalence | 1,600 | Recovery flat across a 47× range in spacer evidence | ✅ |
-| E1b - exposure/phylogeny collinearity | 480 | Flat to c=0.99; top-ranked risk did not materialise | ✅ |
-| E1c - dataset scale | 320 | Needs ≳250 hosts; worse than baseline at N=81 | ✅ |
-| E1d - linkage strength | 300 | B3 collapses 0.650→0.364; LEDGER flat; confound reproduced | ✅ |
-| E5 - permutation controls | 120 | Global null 0.075; original control shown invalid | ✅ |
-| Mis-specification | 400 | Degrades gracefully, tracks the oracle | ✅ |
-| Ablations A1-A3 | 120 | 77.7% RMSE reduction vs B3; within 14% of oracle | ✅ |
----
-## Finding 1 - LEDGER approaches the oracle bound, and the naive method does not
-Headline production result, from the ablation sweep (20 replicates per mode). LEDGER
-essentially attains the oracle upper bound that is allowed to see the latent exposure, while a
-faithful analogue of the current standard method is 4.5× worse in coefficient RMSE.
-The naive baseline's coefficients are attenuated (optimal rescaling factor ≈ 1.6), but - the
-important part - remain roughly 3.6× worse than LEDGER *after* optimal rescaling (0.343 vs
-0.095). The failure is therefore not mere attenuation, which a critic could fairly dismiss as
-fixable by recalibration, but differential bias across coefficients.
-The detection model also recovers the outcome-dependent spacer retention it was designed to
-absorb: estimated $\rho_0 = 0.306$ against a true $0.300$, and $\rho_1 = 0.093$ against a true
-$0.090$. This is a strong internal-validity check, since those parameters are identified only
-through the receipt likelihood.
-### Ablation table (production, 20 replicates per mode, 120 fits)
-| Method | Spearman(g) | frac. of ceiling | RMSE | RMSE rescaled | Sign acc. | Support AUROC | AUROC (exposed) |
-|---|---|---|---|---|---|---|---|
-| Oracle (sees true Z) | 0.740 ± 0.023 | 0.961 | 0.085 | 0.084 | 1.000 | 1.000 | 0.913 |
-| **LEDGER (full)** | 0.736 ± 0.019 | 0.956 | **0.097** | 0.095 | 1.000 | 1.000 | 0.913 |
-| A1 − receipt channel | 0.734 ± 0.021 | 0.953 | 0.100 | 0.098 | 1.000 | 1.000 | 0.913 |
-| A2 constant exposure | 0.712 ± 0.030 | 0.925 | 0.127 | 0.123 | 1.000 | 1.000 | 0.912 |
-| B4 exposure clamped | 0.632 ± 0.066 | 0.821 | 0.437 | 0.343 | 0.995 | 0.993 | 0.905 |
-| B3 phylo. logistic | 0.632 ± 0.066 | 0.821 | 0.437 | 0.343 | 0.995 | 0.993 | 0.905 |
-Paired Wilcoxon tests (n = 20 replicates, paired on seed):
-| Comparison | RMSE | vs | Relative reduction | p |
-|---|---|---|---|---|
-| LEDGER vs B3 naive | 0.0973 | 0.4371 | **+77.7%** | 1.9 × 10⁻⁶ |
-| LEDGER vs A2 constant exposure | 0.0973 | 0.1267 | +23.2% | 1.9 × 10⁻⁶ |
-| LEDGER vs A1 no receipt | 0.0973 | 0.1001 | +2.9% | 8.5 × 10⁻⁴ |
-| LEDGER vs Oracle | 0.0973 | 0.0852 | −14.2% (oracle better) | 1.9 × 10⁻⁶ |
-| B3 naive vs B4 clamped | 0.4371 | 0.4371 | +0.0% | 0.93 |
-**HT2 passes with large margin** (77.7% reduction against a 30% threshold, p ≪ 0.01), and
-LEDGER lands within 14% of the oracle bound. **HT3 passes** (sign accuracy 1.000 ≥ 0.80).
-**ST2 fails, as Finding 2 predicted.** Removing the receipt channel degrades Spearman by 0.002,
-not the ≥ 0.20 the plan anticipated. The degradation is real and statistically detectable
-(p = 8.5 × 10⁻⁴) but scientifically negligible in this regime. Reported as a failed soft
-threshold rather than quietly dropped.
-**The verified prediction.** RESEARCH_PLAN.md §3.3 predicted analytically that B4 would be
-near-equivalent to B3. Measured across 20 paired replicates they are identical to four decimal
-places (0.4371 vs 0.4371, p = 0.93).
-### A trap worth recording: predictive AUROC hides the bias almost completely
-AUROC for establishment among genuinely exposed pairs is **0.913** for LEDGER and **0.905** for
-the naive baseline - a difference of 0.008. On that evidence alone one would conclude the
-standard method is essentially fine. Yet its coefficients are wrong by a factor of 4.5 in RMSE.
-Ranking is far less sensitive than coefficient recovery, because a monotone distortion of $g$
-leaves the ordering largely intact. Since the scientific deliverable here is an *interpretable*
-susceptibility function - per-strain effect sizes and a candidate defense/anti-defense
-interaction map for experimental follow-up - evaluating on predictive performance alone would
-have concealed the entire problem this method exists to solve.
----
-## Finding 2 - Identification comes from the exclusion restriction, not from spacer coverage
-**This contradicted our own expectation and redirected the study.**
-The premise of LEDGER is that CRISPR spacers are what make the susceptibility function
-estimable. We tested this by ablating the receipt channel (A1). It barely mattered: across 20
-production replicates, Spearman 0.734 without the channel versus 0.736 with it, RMSE 0.100
-versus 0.097 - a 2.9% RMSE cost. (The pre-gate single-seed probe gave 0.759 vs 0.760 and
-0.101 vs 0.090; the production figures supersede it.)
-We hypothesised the channel would matter when exposure metadata is poorly measured, and swept
-observation noise on the ecology covariate over $\{0, 1, 2, 4\}$ standard deviations. **The
-hypothesis was wrong** - the receipt gain stayed flat at $\Delta$RMSE $\approx 0.011$ across
-all noise levels.
-The reason is structural. Identification does not come from covariate quality; it comes from
-the exposure layer $f$ containing *no defense features at all*. Because $f$ structurally cannot
-express defense-driven variation in $Y$, any such variation must be attributed to $g$. That is
-a far stronger restriction than any covariate, and it holds regardless of how noisily ecology
-is measured.
-This has a direct consequence for the real-data phase, and it is not the one the plan assumed:
-the value of the CRISPR instrument is *conditional on the exclusion restriction failing*. That
-is exactly the regime the literature says is real - MGE-borne defense systems - which motivated
-adding sweep E1d.
----
-## Finding 3 - Under linkage, the receipt channel earns its place, and the published confound reproduces on demand
-When chromosomal defense load is made to raise exposure directly (the masking mechanism
-Liu, Botelho and Iranzo identify), the marginal association between defense load and element
-presence **flips sign**, from $\rho = -0.462$ with the exclusion restriction intact to
-$\rho = +0.485$ under linkage. This reproduces the published positive association on demand,
-from a model that is simultaneously recovering a correctly-signed inhibitory susceptibility
-function - which is strong evidence the model is doing what it claims.
-### Production sweep E1d (5 linkage strengths × 20 replicates × 3 methods, 300 fits) - COMPLETE
-Marginal association between defense load and element presence, as linkage strengthens -
-a clean monotone dose-response crossing zero near strength 0.4:
-| Linkage strength | 0.0 | 0.5 | 1.0 | 1.5 | 2.5 |
-|---|---|---|---|---|---|
-| Marginal ρ(defense load, presence) | **−0.239** | +0.075 | +0.355 | +0.547 | **+0.746** |
-Recovery of the planted susceptibility function (mean Spearman):
-| Linkage strength | LEDGER (full) | − receipt | B3 naive |
-|---|---|---|---|
-| 0.0 | 0.745 | 0.738 | 0.650 |
-| 0.5 | 0.740 | 0.733 | 0.594 |
-| 1.0 | 0.744 | 0.732 | 0.522 |
-| 1.5 | 0.742 | 0.731 | 0.457 |
-| 2.5 | 0.724 | 0.714 | **0.364** |
-**The standard method degrades steadily as linkage strengthens (0.650 → 0.364) while LEDGER is
-essentially flat (0.745 → 0.724).** ST3 passes: the published positive association is reproduced
-on demand, with a monotone dose-response, by a model that is simultaneously recovering a
-correctly-signed inhibitory susceptibility function.
-**Correction to the earlier single-seed estimate.** The pre-gate probe DEV-005 reported
-LEDGER 0.752 versus no-receipt 0.661 at linkage 1.5, suggesting the receipt channel was
-decisive in this regime. Across 20 replicates the gap is far smaller - 0.742 versus 0.731. The
-single-replicate figure was not representative, and the production numbers supersede it.
-The receipt channel's contribution is nonetheless **real, highly significant, and grows
-monotonically with linkage exactly as predicted**, though it remains modest in absolute terms:
-| Linkage strength | RMSE, LEDGER | RMSE, − receipt | Relative reduction | p (paired, n=20) |
-|---|---|---|---|---|
-| 0.0 | 0.0994 | 0.1046 | +5.0% | 3.8 × 10⁻⁶ |
-| 0.5 | 0.1007 | 0.1077 | +6.5% | 1.9 × 10⁻⁵ |
-| 1.0 | 0.1022 | 0.1119 | +8.6% | 2.7 × 10⁻⁵ |
-| 1.5 | 0.1040 | 0.1192 | +12.7% | 5.7 × 10⁻⁶ |
-| 2.5 | 0.1095 | 0.1290 | **+15.2%** | 1.9 × 10⁻⁶ |
-The channel's value triples across the swept range. The honest summary is therefore that the
-exposure layer does the heavy lifting and the spacer record adds a real but secondary
-correction that matters most in exactly the regime the literature says is real.
-See `figures/e1d_linkage.png`.
----
-## Finding 4 - The plan's permutation control was not a null, and HT4 as written failed
-**Run exactly as specified, HT4 failed: mean Spearman 0.536, support AUROC 0.951.** The plan
-called this non-negotiable, so execution paused for diagnosis before anything else proceeded.
-The estimator was not at fault; the control was invalid. Three separate problems:
-1. **The permutation preserves half the signal.** Defense content is phylogenetically
-   autocorrelated, so roughly half its variance lies *between* lineage clusters and is left
-   completely untouched by a within-cluster shuffle. Measured directly:
-   **corr(D, D_permuted) = 0.493** (per-system range 0.221-0.816). A control that retains 49%
-   of the signal is not a null, and an estimator recovering ~0.49 from it is behaving
-   correctly. A *global* permutation gives corr = 0.013 - a genuine null.
-2. **The metric was contaminated.** `spearman_all` includes the element-side effects $\beta$,
-   which a *host*-side permutation cannot affect. An estimator that correctly zeroes $W$ and
-   correctly fits $\beta$ therefore scores well under a null where it should score nothing.
-3. **The tie ceiling inflates the apparent number.** With 86 zeros of 96 entries the maximum
-   attainable Spearman on the interaction block is exactly 0.530, so 0.536 is near-ceiling by
-   construction.
-**Revision (documented in RESEARCH_PLAN.md §7.3).** HT4 now uses a *global* permutation scored
-on host-side coefficients $(\alpha, W)$ only. This is **strictly harder** than the original: it
-destroys all defense signal rather than half of it, and removes the contamination that made
-the original passable on a technicality. The within-lineage permutation is retained as an
-interpretive diagnostic measuring how much of the estimator's signal comes from within- versus
-between-lineage comparison - a real limitation worth reporting, since between-lineage
-comparisons in real data are confounded with everything else that varies between lineages.
-**Final result (20 replicates per arm, 120 fits).** All three arms are scored on the same
-metric and the same seeds, so they are directly comparable:
-| Permutation | residual corr(D, D_perm) | Spearman(α, W) - LEDGER | - B3 naive |
-|---|---|---|---|
-| None (unpermuted reference) | +1.000 | **+0.701** | - |
-| Within-lineage | +0.489 | +0.460 | +0.500 |
-| **Global** (genuine null) | −0.007 | **−0.054** (mean \|·\| = 0.075) | −0.051 (0.080) |
-Recovery is a monotone function of how much defense signal the permutation left standing, and
-reaches zero precisely when the control is a genuine null:
-$1.000 \rightarrow 0.701$, $0.489 \rightarrow 0.460$, $-0.007 \rightarrow -0.054$.
-See `figures/e5_permutation_null.png`.
-**HT4 PASSES on the corrected control**: mean |Spearman| = 0.075 against a threshold of 0.15.
-Under a genuine null the estimator recovers nothing.
-The within-lineage row is the quantitative confirmation of the diagnosis, and is worth stating
-precisely: the estimator recovers **0.460** from a permutation that left **0.489** of the
-defense signal in place. Recovery tracks residual signal almost one-to-one. The estimator was
-never inventing structure; it was recovering exactly the structure the broken control failed to
-destroy.
-A third confirmation comes from the contaminated metric itself: under the *global* permutation
-`spearman_all` is still +0.111 while `spearman_host` is −0.054. That residual is precisely the
-element-side effects β, which a host-side permutation cannot touch - exactly as predicted when
-the contamination was diagnosed.
----
-## Finding 5 - The CRISPR instrument barely matters when the exclusion restriction holds (E1, 1,600 fits)
-This is the study's most consequential result, and it is a negative result about the project's
-own headline premise.
-LEDGER RMSE across the full grid (rows = CRISPR prevalence, columns = spacer coverage $\rho_0$):
-| prevalence \ coverage | 0.05 | 0.10 | 0.20 | 0.30 | 0.50 |
-|---|---|---|---|---|---|
-| 0.10 | 0.097 | 0.097 | 0.096 | 0.096 | 0.095 |
-| 0.20 | 0.097 | 0.096 | 0.095 | 0.095 | 0.093 |
-| 0.33 | 0.096 | 0.095 | 0.094 | 0.093 | 0.092 |
-| 0.50 | 0.095 | 0.094 | 0.093 | 0.092 | 0.091 |
-Number of informative $(Y{=}0, S{=}1)$ cells over the same grid ranges from **214** in the
-worst corner to **10,007** in the best - a 47-fold range in the quantity that is supposed to
-make the method work. Recovery moves by 6%.
-B3 is *exactly* constant at RMSE 0.410 and Spearman 0.655 in every cell, which is the correct
-internal consistency check: the naive method never touches $S$, so no CRISPR parameter can
-affect it.
-**Interpretation.** The premise of LEDGER was that CRISPR spacers are what make the
-susceptibility function estimable. Under the conditions of this experiment they are very nearly
-irrelevant. What identifies $\theta$ is the *structural* exclusion of defense features from the
-exposure layer: because $f$ cannot express defense-driven variation in $Y$, that variation must
-be attributed to $g$. This holds whether spacer evidence is abundant or almost absent.
-The contribution therefore reframes. The defensible claim is not "CRISPR spacers identify
-susceptibility" but "modelling exposure as a separate latent layer, with defense features
-structurally excluded from it, identifies susceptibility - and the standard method is badly
-biased without it." The spacer channel is a real but secondary correction whose value is
-concentrated in the linkage regime (Finding 3), where the exclusion restriction is exactly what
-fails.
-## Finding 6 - The top-ranked risk did not materialise: recovery is flat in exposure-phylogeny collinearity (E1b, 480 fits)
-RESEARCH_PLAN.md §8 rated "weak exclusion restrictions under high collinearity" as the only
-High-likelihood/High-impact risk. It did not materialise.
-| collinearity $c$ | 0.00 | 0.30 | 0.50 | 0.70 | 0.90 | 0.99 |
-|---|---|---|---|---|---|---|
-| LEDGER Spearman | 0.729 | 0.732 | 0.733 | 0.733 | 0.733 | 0.732 |
-| LEDGER RMSE | 0.100 | 0.100 | 0.101 | 0.100 | 0.101 | 0.101 |
-| B3 RMSE | 0.406 | 0.406 | 0.405 | 0.405 | 0.406 | 0.406 |
-Recovery is flat even at $c = 0.99$, where host ecology is almost perfectly determined by
-phylogeny. The reason is the same as Finding 5: the lineage random effect absorbs the
-phylogenetic component of exposure, and defense content is identified from residual
-within-lineage variation, which collinearity between ecology and phylogeny does not remove.
-## Finding 7 - The method needs data, and below ~250 genomes it is worse than the baseline (E1c, 320 fits)
-| hosts $N$ | 81 | 256 | 625 | 1296 |
-|---|---|---|---|---|
-| Oracle RMSE | 0.578 | 0.204 | 0.087 | 0.048 |
-| **LEDGER RMSE** | **0.769** | 0.240 | 0.099 | 0.055 |
-| − receipt RMSE | 1.022 | 0.257 | 0.104 | 0.057 |
-| **B3 naive RMSE** | **0.537** | 0.430 | 0.423 | 0.415 |
-| LEDGER Spearman | 0.552 | 0.688 | 0.729 | 0.751 |
-| B3 Spearman | 0.546 | 0.618 | 0.645 | 0.663 |
-**At $N = 81$ LEDGER is worse than the naive baseline on RMSE (0.769 vs 0.537).** This is
-reported prominently because it is the clearest limitation found. With 81 hosts the model is
-badly overparameterized - roughly 116 susceptibility coefficients plus per-element exposure
-parameters against 8,100 pairs - and the extra flexibility of the exposure layer costs more in
-variance than it buys in bias. The oracle is also poor here (0.578), confirming this is a
-data-volume limit rather than a defect of the exposure machinery.
-The crossover is between 81 and 256 hosts; by 625 the advantage is decisive and by 1,296 it is
-nearly an order of magnitude. The intended real-data panel of 2,940 *P. aeruginosa* genomes sits
-comfortably above this threshold, but the result is a warning against applying the method to
-small species-level collections.
-Note this is also the one place where the ST4 claim ("LEDGER beats B3 across the entire swept
-grid") does not generalise: ST4 was evaluated on the prevalence × coverage grid, where it holds
-in 20/20 cells, but it does **not** hold at $N = 81$ in the scale sweep.
-## Finding 8 - Graceful degradation under mis-specification (400 fits)
-The stress test adds latent rank-3 host-element compatibility structure that $g$ has no
-capacity to represent.
-| mis-spec. strength | 0.00 | 0.25 | 0.50 | 1.00 | 2.00 |
-|---|---|---|---|---|---|
-| Oracle RMSE | 0.084 | 0.084 | 0.086 | 0.123 | 0.258 |
-| LEDGER RMSE | 0.098 | 0.097 | 0.099 | 0.126 | 0.255 |
-| B3 naive RMSE | 0.417 | 0.417 | 0.418 | 0.427 | 0.457 |
-| LEDGER Spearman | 0.743 | 0.735 | 0.732 | 0.729 | 0.722 |
-Recovery degrades gracefully, and - the important part - **LEDGER tracks the oracle throughout,
-matching it at the highest mis-specification (0.255 vs 0.258)**. The degradation is therefore
-attributable to irreducible model mis-specification rather than to failure of the exposure
-machinery: an estimator that was handed the true exposure would do no better. LEDGER retains a
-large advantage over B3 at every level.
----
-## Improvement Iterations
-**None triggered.** All four hard thresholds passed on the first production run, so the
-autonomous improvement protocol (up to 3 diagnosis/revision cycles) was never entered.
-The HT4 failure was resolved as a control-design defect rather than an estimator deficiency and
-so did not consume an iteration cycle; had the *global* permutation also shown surviving
-signal, that would have triggered halt-and-debug under the plan's failure criteria.
-The one failed soft threshold, ST2, was deliberately **not** treated as something to optimise
-away. Removing the receipt channel costs 2.9% of RMSE because identification comes from the
-exclusion restriction, not from spacer evidence. That is a finding about the method, and tuning
-the model until the spacer channel looked indispensable would have amounted to fitting the
-result to the hypothesis.
----
-## Running Commentary
-**2026-08-16** - Landscape survey completed with 11 load-bearing claims from the supplied plan
-independently verified: 6 confirmed, 4 corrected, 1 unsupported. Most consequential: the plan's
-external test panel ("53 isolates × 40 phages, defense count did not correlate with resistance")
-could not be located, and the two real panels that exist both report the *opposite* sign -
-Burke et al. (100 × 70) find a significant positive correlation but a weak one ($R^2 = 0.26$),
-and Costa et al. (32 × 28) find resistance scaling with defense count. This inverts the
-motivating claim but strengthens it: counting defense systems explains about a quarter of the
-variance in phage resistance, so a *structural* compatibility function has clear room to
-improve on a scalar count. Also identified close prior work the plan did not cite
-(Lopatina et al.), which turns out to be complementary rather than competing - it learns from
-experimental matrices where exposure is guaranteed by construction, whereas LEDGER targets the
-observational case where exposure is latent.
-**2026-08-16** - Pre-training review gate passed after remediating four issues, two of them
-substantive: a divergent simulator code path that would have invalidated the entire E1d sweep,
-and an unimplemented mis-specification stress test that the plan's own risk table requires.
-**2026-08-17** - Production sweeps running (3,340 fits total including the E5 rerun). E5
-diagnosis completed and thresholds revised; see Finding 4.

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-## Threshold evaluation
-| ID | Criterion | Observed | Target | Status |
-|---|---|---|---|---|
-| HT1 | LEDGER Spearman >= 0.60 at CRISPR prevalence >= 0.30, coverage >= 0.20 | 0.746 | 0.6 | PASS |
-| HT2 | LEDGER RMSE >= 30% lower than naive (B3), paired Wilcoxon p < 0.01 | 0.774 | 0.3 | PASS |
-| HT3 | Sign-recovery accuracy on planted nonzero interactions >= 0.80 | 1.000 | 0.8 | PASS |
-| HT4 | GLOBAL permutation null (host-side coefficients): mean |Spearman| < 0.15 | 0.075 | 0.15 | PASS |
-| HT4b_within_lineage_diagnostic | Within-lineage permutation - NOT a null; retains between-lineage signal | 0.460 | - | - |
-| ST2 | Removing the receipt channel degrades Spearman by >= 0.20 | 0.002 | 0.2 | FAIL |
-| ST3 | Restoring MGE-borne linkage flips the marginal association positive | 0.0:-0.239, 0.5:+0.075, 1.0:+0.355, 1.5:+0.547, 2.5:+0.746 | - | PASS |
-| ST4 | LEDGER beats the naive baseline across the ENTIRE swept grid | 20/20 grid cells | - | PASS |
-## Ablations and baselines
-| Method | Spearman(g) | RMSE | RMSE rescaled | Sign acc. | Support AUROC | n |
-|---|---|---|---|---|---|---|
-| Oracle (sees Z) | 0.740 ± 0.023 | 0.085 ± 0.009 | 0.084 | 1.000 | 1.000 | 20 |
-| LEDGER (full) | 0.736 ± 0.019 | 0.097 ± 0.010 | 0.095 | 1.000 | 1.000 | 20 |
-| − receipt channel | 0.734 ± 0.021 | 0.100 ± 0.011 | 0.098 | 1.000 | 1.000 | 20 |
-| constant exposure | 0.712 ± 0.030 | 0.127 ± 0.018 | 0.123 | 1.000 | 1.000 | 20 |
-| B4 exposure clamped | 0.632 ± 0.066 | 0.437 ± 0.082 | 0.343 | 0.995 | 0.993 | 20 |
-| B3 phylo. logistic | 0.632 ± 0.066 | 0.437 ± 0.082 | 0.343 | 0.995 | 0.993 | 20 |
-## Permutation controls
-| Permutation | Method | residual corr(D) | Spearman(α,W) | mean |Spearman| | n |
-|---|---|---|---|---|---|
-| global | LEDGER (full) | -0.007 | -0.054 ± 0.079 | 0.075 | 20 |
-| global | B3 phylo. logistic | -0.007 | -0.051 ± 0.087 | 0.080 | 20 |
-| within_lineage | LEDGER (full) | 0.489 | 0.460 ± 0.112 | 0.460 | 20 |
-| within_lineage | B3 phylo. logistic | 0.489 | 0.500 ± 0.101 | 0.500 | 20 |
-## Sweep: Exposure-phylogeny collinearity
-| Exposure-phylogeny collinearity | Oracle (sees Z) | LEDGER (full) | − receipt channel | B3 phylo. logistic |
-|---|---|---|---|---|
-| 0 | 0.738 / 0.086 | 0.729 / 0.100 | 0.723 / 0.105 | 0.650 / 0.406 |
-| 0.3 | 0.739 / 0.085 | 0.732 / 0.100 | 0.728 / 0.104 | 0.651 / 0.406 |
-| 0.5 | 0.739 / 0.085 | 0.733 / 0.101 | 0.726 / 0.105 | 0.651 / 0.405 |
-| 0.7 | 0.739 / 0.084 | 0.733 / 0.100 | 0.725 / 0.105 | 0.649 / 0.405 |
-| 0.9 | 0.740 / 0.086 | 0.733 / 0.101 | 0.729 / 0.105 | 0.651 / 0.406 |
-| 0.99 | 0.738 / 0.087 | 0.732 / 0.101 | 0.727 / 0.105 | 0.652 / 0.406 |
-## Sweep: Number of hosts
-| Number of hosts | Oracle (sees Z) | LEDGER (full) | − receipt channel | B3 phylo. logistic |
-|---|---|---|---|---|
-| 81 | 0.581 / 0.578 | 0.552 / 0.769 | 0.530 / 1.022 | 0.546 / 0.537 |
-| 256 | 0.697 / 0.204 | 0.688 / 0.240 | 0.673 / 0.257 | 0.618 / 0.430 |
-| 625 | 0.733 / 0.087 | 0.729 / 0.099 | 0.723 / 0.104 | 0.645 / 0.423 |
-| 1296 | 0.753 / 0.048 | 0.751 / 0.055 | 0.751 / 0.057 | 0.663 / 0.415 |
-## Sweep: Mis-specification strength
-| Mis-specification strength | Oracle (sees Z) | LEDGER (full) | − receipt channel | B3 phylo. logistic |
-|---|---|---|---|---|
-| 0 | 0.748 / 0.084 | 0.743 / 0.098 | 0.740 / 0.103 | 0.648 / 0.417 |
-| 0.25 | 0.746 / 0.084 | 0.735 / 0.097 | 0.735 / 0.101 | 0.646 / 0.417 |
-| 0.5 | 0.741 / 0.086 | 0.732 / 0.099 | 0.731 / 0.102 | 0.646 / 0.418 |
-| 1 | 0.736 / 0.123 | 0.729 / 0.126 | 0.723 / 0.129 | 0.646 / 0.427 |
-| 2 | 0.728 / 0.258 | 0.722 / 0.255 | 0.695 / 0.253 | 0.653 / 0.457 |
-## Sweep: linkage strength
-| Linkage strength | LEDGER (full) | − receipt channel | B3 phylo. logistic |
-|---|---|---|---|
-| 0 | 0.745 / 0.099 | 0.738 / 0.105 | 0.650 / 0.437 |
-| 0.5 | 0.740 / 0.101 | 0.733 / 0.108 | 0.594 / 0.450 |
-| 1 | 0.744 / 0.102 | 0.732 / 0.112 | 0.522 / 0.462 |
-| 1.5 | 0.742 / 0.104 | 0.731 / 0.119 | 0.457 / 0.472 |
-| 2.5 | 0.724 / 0.109 | 0.714 / 0.129 | 0.364 / 0.492 |

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-# Results - LEDGER v2 (post-Phase-0 expansion)
-**Last Updated**: 2026-08-17
-**Plan**: `RESEARCH_PLAN_V2.md` (supersedes v1; v1 retained as the pre-registered record)
-**Companion**: `RESULTS.md` holds the Phase 0 record and is unchanged.
-> **Scope.** Simulation stages S1-S2 are complete. Real-data stage S3 (the exclusion-restriction
-> audit) is complete on **all 1,200 genomes** of a stratified cohort of real *P. aeruginosa*
-> assemblies. Stages
-> S5-S6 (element layer, spacer layer, external panels) remain **[NOT RUN]**.
----
-## Headline: the load-bearing assumption does not need to be assumed
-Phase 0 ended on an uncomfortable note - identification rested almost entirely on the
-assumption that chromosomal defense content does not predict exposure, and v2 was planned around
-*bounding* how wrong that assumption could be. The main v2 result is that bounding is
-unnecessary, because **the violation is directly estimable**.
-| λ_true (true violation) | 0.00 | 0.25 | 0.50 | 1.00 | 2.00 | 3.00 | 4.00 |
-|---|---|---|---|---|---|---|---|
-| **λ̂ (fitted)** | 0.003 | 0.254 | 0.515 | 1.027 | 2.039 | 3.092 | 4.134 |
-| α̂ when λ is estimated | −1.109 | −1.104 | −1.100 | −1.095 | −1.092 | −1.079 | −1.075 |
-| α̂ when the restriction is *assumed* | −1.122 | −1.032 | −0.927 | −0.724 | −0.421 | −0.285 | −0.227 |
-| attenuation if assumed | 0% | 6% | 16% | 34% | 62% | 74% | **79%** |
-Planted truth differs slightly between the two sweeps because they draw independent
-coefficients from different seed ranges: **α = −1.108** for the estimated arm (seeds 8000+,
-360 fits) and **α = −1.103** for the assumed arm (seeds 8500+, 540 fits). Each row is scored
-against its own sweep's truth. Regression of λ̂ on λ_true: **slope 1.032, intercept −0.006,
-R² = 0.9993**. Maximum |α̂ bias| across the whole grid: **2.9%** (5.6% without the receipt
-channel).
-**HT-A PASSES** (slope within [0.8, 1.25], R² ≥ 0.95, α bias < 20%).
-The practical statement is a one-line model change with a large consequence: give the exposure
-layer a free defense-load coefficient and the estimate is unbiased across a fourfold range of
-violation; omit it and the effect you are trying to measure attenuates by up to 79%.
-Recovery (Spearman) tells the same story: **0.741 → 0.360** as λ grows if the restriction is
-assumed, versus **0.725 → 0.714** if it is estimated. The marginal defense/presence association
-crosses zero between λ = 0.5 (−0.083) and λ = 0.75 (+0.079), so the published sign flip is
-reproduced again here on an independent sweep.
-The receipt channel finally has a clean role. It is not needed for λ recovery - the no-receipt
-model also recovers λ (slope 1.038, R² = 0.9991) - but it **halves the residual bias in α̂**
-(2.9% vs 5.6%) and gives lower RMSE at every λ (0.099-0.128 vs 0.103-0.141). Spacers improve
-the de-biasing rather than enabling it.
-### A method we implemented, tested, and threw away
-`RESEARCH_PLAN_V2.md` §2 specified a Cinelli-Hazlett-style robustness value: posit an omitted
-defense→exposure path of fixed strength λ, sweep it, and record where the conclusion breaks.
-**We built it and it does not work.** Adding a fixed, non-trainable λ·load offset to the
-exposure layer is absorbed by the other free exposure parameters (lineage effects, per-element
-terms, intercept). Measured on clean data, α̂ went −1.063 (λ=0) → −1.199 (λ=1) → −1.130 (λ=2)
-→ −0.978 (λ=4): non-monotone, and never approaching a sign change. No robustness value can be
-read off a curve that does not move.
-This is recorded rather than deleted because the discarded method is part of the result: the
-reason the posited offset fails is the same reason the free coefficient succeeds - the
-likelihood has enough information to *locate* the violation, so it will not simply absorb a
-wrong one.
-### A gap in Phase 0 that this exposed
-Phase 0's linkage sweep (E1d) reported LEDGER as nearly flat under linkage. That was true but
-contingent: E1d always *permitted* the estimator a defense-load term. It therefore tested the
-analyst who already knows the restriction fails, and never tested the analyst who applies a
-chromosomal-only filter and trusts it. The `assumed_restriction` sweep above is that missing
-arm, and it is where the damage is (Spearman 0.741 → 0.360). Phase 0's robustness claim should
-be read as conditional on modelling the violation, not as a property of the method per se.
----
-## Threat A - lateral-transduction leak (Kuang et al., *Sci Adv* 2026)
-Defense systems positioned near phage/PICI attachment sites are mobilised by lateral
-transduction while sitting outside any recognised prophage boundary, so they pass a
-chromosomal-only filter and still predict exposure. Swept as the fraction of nominally
-chromosomal systems that leak (400 fits; true α = −1.086).
-| leak fraction | 0.00 | 0.10 | 0.25 | 0.50 | 0.75 |
-|---|---|---|---|---|---|
-| α̂, restriction assumed | −1.087 | −0.874 | −0.808 | ���0.703 | −0.611 |
-| **α̂, violation estimated** | −1.088 | −1.008 | **−1.027** | **−1.044** | **−1.076** |
-| Spearman, assumed | 0.729 | 0.612 | 0.621 | 0.593 | 0.584 |
-| Spearman, estimated | 0.729 | 0.646 | **0.698** | **0.700** | **0.717** |
-| **λ̂ detected** | 0.002 | 0.473 | 0.716 | 1.030 | 1.327 |
-**HT-B PASSES**: at leak fraction 0.25 Spearman is 0.621 (assumed) and 0.698 (estimated), both
-above the 0.60 bar.
-Two things matter here. First, estimating the violation recovers most of the loss - α̂ stays
-within 1-7% of truth where assuming the filter worked costs up to 44%. Second, and more useful
-in practice, **λ̂ rises monotonically with the leak**. A nonzero λ̂ on real data is therefore a
-measurable warning light that the chromosomal filter has failed, available without knowing the
-truth. That is the closest thing to the sensitivity diagnostic §2 originally wanted, and it
-arrives as a by-product of estimation rather than as a posited bound.
----
-## Threat B - CRISIS coupling (Shu et al., *Nature* 2026): the one we could not fix
-More than twenty innate defense modules are embedded inside type I CRISPR-Cas loci and are
-transcriptionally repressed by Cascade; when CRISPR is compromised they are de-repressed. Since
-*P. aeruginosa* is I-F dominated this is directly on point. Two couplings were simulated
-separately: **physical** (embedded systems co-inherited with CRISPR presence) and **functional**
-(CRISPR status modulates their effectiveness, breaking the v1 assumption that ρ depends on
-CRISPR and *g* does not).
-Final results, 20 replicates per arm (280 fits), all arms sharing an identical planted
-α = −1.094. These supersede the single-seed figures quoted while the sweep was running.
-| arm | α̂ | \|bias\| | RMSE | Spearman |
-|---|---|---|---|---|
-| none (baseline) | −1.094 | 0.01% | 0.097 | 0.737 |
-| **physical** | −1.099 | 0.45% | **0.215** | 0.727 |
-| **functional** | −1.283 | **17.3%** | 0.182 | 0.734 |
-| **both** | −1.061 | 3.0% | **0.242** | 0.723 |
-| B3 naive (none) | −0.646 | 41.0% | 0.414 | 0.668 |
-The two couplings damage *different* things, which is why no single absorber fixes both.
-**Physical** coupling leaves the mean defense effect essentially intact (0.45% bias) while more
-than doubling coefficient RMSE (0.097 → 0.215) - the signature of individual coefficients trading
-off against one another rather than of aggregate bias. If embedded systems occur only in CRISPR⁺
-hosts, their coefficients cannot be separated from CRISPR status by any reparameterisation; this
-is an identifiability limit, not a modelling oversight. **Functional** coupling instead biases the
-mean by **17.3%**, inflating the apparent protective effect, because the de-repression term acts
-as an omitted host-level covariate.
-### ST-A fails: mitigation recovers at most 38% of the loss
-Two mitigations were tested. Recovery is measured as the fraction of the RMSE increase (relative
-to the undamaged baseline) that the mitigation removes:
-| mitigation | damaged RMSE | mitigated RMSE | loss recovered |
-|---|---|---|---|
-| physical, drop embedded systems from *g* | 0.215 | 0.192 | **+19.3%** |
-| physical, CRISPR-status + CRISPR×load term in *g* | 0.215 | 0.220 | −4.6% |
-| functional, drop embedded systems | 0.182 | 0.247 | **−75.1%** |
-| functional, CRISPR-status + CRISPR×load term | 0.182 | 0.209 | −31.4% |
-| both, drop embedded systems | 0.242 | 0.187 | **+38.0%** |
-| both, CRISPR-status + CRISPR×load term | 0.242 | 0.246 | −2.3% |
-**ST-A requires ≥ 80% recovery and the best result is 38%, so it FAILS.** Dropping the
-CRISPR-embedded systems gives partial relief where physical coupling dominates (+19% to +38%) and
-actively harms the purely functional case (−75%). The CRISPR-status absorber - the
-theoretically motivated fix, and the one `RESEARCH_PLAN_V2.md` §3.2 nominated - **does not work at
-all**: it recovers approximately nothing everywhere, and on the functional arm it drives α̂ bias
-from 17.3% up to **35.9%**, making the estimate substantially worse than leaving the threat
-untreated.
-We take the failure at face value rather than searching for a mitigation that happens to score
-well. The diagnosis for why the nominated absorber fails is specific: it interacts CRISPR status
-with *total* defense load, whereas the truth involves the *embedded-subset* load. A mis-specified
-absorber adds variance without removing bias, which is exactly what the numbers show.
-**The untested mitigation that should work** is an interaction between CRISPR status and the
-embedded-subset load specifically. That requires knowing which systems are CRISPR-embedded, which
-is obtainable in real data from genomic co-location with CRISPR loci but is not something our
-simulator's estimator is given. It is specified and not run, and is therefore not claimed.
-CRISIS coupling is the most serious unresolved threat in the project. It was found by reading the
-literature, not by any internal check, and it remains unmitigated.
-### Two implementation faults found and fixed before reporting
-1. **The `both` arm was numerically identical to `physical`** (α̂ and RMSE agreeing to three
-   decimals). De-repression had been keyed on CRISPR *absence*; under physical coupling embedded
-   systems exist only in CRISPR⁺ hosts, so the functional term was identically zero. Shu et al.
-   describe de-repression when CRISPR is *present but compromised* (mutation or anti-CRISPR), so
-   a compromised state is now modelled explicitly. The mechanism as first written was
-   biologically wrong, not merely degenerate.
-2. **The arms did not share a planted truth.** The physical-coupling manipulation drew from the
-   main random stream, so switching it on shifted every later draw - including the planted
-   susceptibility coefficients (true α = −1.251 with the threat on, −1.090 with it off). The
-   comparison was invalid. Threat manipulations now use a dedicated RNG and all arms share an
-   identical planted α (−1.0896, verified). This is the second instance of this exact failure
-   mode in the project; the first was in the v1 linkage code path.
-### A sweep we withdrew
-`threat_boundary` (element-boundary annotation error) was implemented and then withdrawn before
-reporting. It manipulates the same simulator knob as the att-leak sweep at a different strength,
-because the mechanism is identical - a system that is element-borne in truth but counted as
-chromosomal predicts exposure, and the estimator cannot tell whether that arose from
-attachment-site proximity or a misplaced prophage boundary. Reporting both would have presented
-one manipulation as two independent findings. It is retained in the code, unrun and labelled.
----
-## Stage S3 - the exclusion-restriction audit on real genomes
-This is the experiment v1 did not contain and that Phase 0 showed to be the most important one
-in the project: is the load-bearing assumption true in real *P. aeruginosa*, and by how much is
-it violated?
-### Cohort (measured, not projected)
-| Property | Value |
-|---|---|
-| *P. aeruginosa* complete assemblies at NCBI | 3,466 |
-| With collection date + geography + isolation source | 2,757 |
-| Downloaded | 2,757 (18 GB) |
-| Stratified analysis cohort | 1,200 (60 countries, 423 BioProjects) |
-| Annotated with DefenseFinder 3.0.0 | **1,200 / 1,200** (20 transient failures, all resolved on retry) |
-| Exposure-covariate coverage | 83.2% date, 94.3% geography, 92.5% source, 100% BioProject |
-| Mean chromosomal system *detections* / genome | 13.97 |
-| Mean *distinct* chromosomal subtypes / genome (the audit regressor) | 12.34 |
-| Genomes carrying any CRISPR-Cas | **53.6%** |
-### Lineage clustering is threshold-sensitive, and one threshold is degenerate
-| ANI threshold | clusters | singletons | largest | usable for within-lineage analysis |
-|---|---|---|---|---|
-| 99.9% | 344 | 153 | 72 | 1,047 (87.2%) |
-| 99.5% | 184 | 59 | 213 | 1,141 (95.1%) |
-| 99.0% | **5** | 2 | **1,177** | 1,198 (99.8%) |
-At 99.0% single-linkage chains essentially the whole species into one component, so "within
-lineage" ceases to mean anything. 99.9% is used as primary and 99.5% as sensitivity; 99.0% is
-reported as degenerate rather than quietly dropped.
-### Audit results (final: all 1,200 cohort genomes annotated, 2,000 permutations)
-| Test | 99.9% ANI (344 clusters, median size 2.0) | 99.5% ANI (184 clusters, median size 2.0) |
-|---|---|---|
-| **A** - all defense load ~ ecology \| lineage | excess R² **+0.0310, p = 0.0055** | **+0.0441, p = 0.0005** |
-| **A** - CRISPR-Cas only ~ ecology \| lineage | +0.0048, p = 0.293 (ns) | **+0.0348, p = 0.0005** |
-| **B** - defense load vs plasmid burden | ρ **+0.082, p = 0.0045** | ρ **+0.154, p < 0.0001** |
-| **B** - defense load vs extrachrom. systems | ρ **+0.080, p = 0.0056** | ρ **+0.082, p = 0.0046** |
-| **B** - CRISPR load vs plasmid burden | ρ +0.023, p = 0.431 (ns) | ρ **−0.089, p = 0.0022** |
-| Systems leaking, BH q < 0.10 (of 116 tested) | **70** | **79** |
-**The exclusion restriction is violated in real *P. aeruginosa*.** At the full cohort both
-thresholds agree: chromosomal defense content still predicts ecology after conditioning on
-lineage (p = 0.0055 and p = 0.0005), defense load still correlates with mobile-element burden
-(p = 0.0045 and p < 0.0001), and **70-79 of 116 defense systems (60-68%) leak individually** at
-BH q < 0.10 against 5.8 expected by chance. The largest leaks are BREX_II, Rst_3HP, DS-38 and
-BstA, all with adjusted q ≤ 0.017.
-**The earlier threshold-dependence was a power artifact, now resolved.** At n = 785 the 99.9%
-analysis was not significant (p = 0.109) while 99.5% was, and we reported the disagreement as the
-finding. With all 1,200 genomes annotated the median cluster size at 99.9% rises from 1.0 to 2.0,
-enough within-cluster contrast survives, and **both thresholds now agree**. The earlier
-non-significance was underpowering, exactly as diagnosed at the time. This supersedes the n = 785
-reading.
-**What remains threshold-dependent, and is therefore not claimed.** The CRISPR-specific results
-do *not* agree across thresholds: CRISPR content shows no ecology association at 99.9%
-(p = 0.293) but a significant one at 99.5% (p = 0.0005), and CRISPR load shows no association
-with plasmid burden at 99.9% (ρ = +0.023, ns) but a significant negative one at 99.5%
-(ρ = −0.089, p = 0.0022). We had highlighted that negative association at n = 785 as cleanly
-separating the two published mechanisms - total defense load positively linked to MGE burden
-(coacquisition) versus CRISPR-Cas negatively linked (genuine blocking). **At the full cohort that
-separation survives only at the coarser clustering, so it is reported as suggestive rather than
-established.** The honest statement is that the *aggregate* violation is robust to clustering
-granularity while the *CRISPR-specific* contrast is not.
-### The permutation null was indispensable
-Raw partial R² for Test A at 99.9% is 0.0610, of which **0.0300 is pure overfitting**: 21
-covariates against a within-cluster design with limited effective degrees of freedom. Reporting
-the raw figure would have doubled the apparent violation. In the 120-genome pilot the inflation
-was far worse (0.527 raw against a null of 0.432). Any within-cluster partial R² reported without
-such a null should be treated as uninterpretable.
-### Per-system leakage is the operationally important result
-At 99.9% ANI, 65 of 116 systems reach p < 0.05 uncorrected against 5.8 expected by chance, and
-**70 survive Benjamini-Hochberg at q < 0.10**; at 99.5%, 79 survive. Correction is applied because
-these permutation p-values have a hard floor of 1/(n_perm+1) and several systems sit on it.
-That roughly two thirds of defense systems individually predict ecology within lineage is the
-strongest single argument in this project for **estimating** λ rather than filtering for it. A
-method that requires the exclusion restriction to hold uniformly across the repertoire does not
-have that luxury in real data.
-### A preliminary finding that did not replicate
-The 120-genome pilot showed CRISPR content strongly associated with ecology within lineage
-(excess R² 0.284, p = 0.008). At the full cohort the magnitude is an order of magnitude smaller
-(+0.0048 at 99.9%, +0.0348 at 99.5%). The pilot magnitude was a small-sample artifact, and it is
-recorded because it was flagged as underpowered when first observed rather than after it failed.
-### What the audit cannot do
-The measured associations cannot be converted into a λ-equivalent, and we do not attempt it. The
-simulated λ is the coefficient of defense load in the exposure layer; the real-data proxies are
-associations with plasmid burden and with ecology. These are different quantities and a mapping
-between them would be invented rather than derived. The directly comparable quantity is λ̂ itself,
-which becomes estimable on real data only once the element layer exists (stage S5).
-### Weaker filter than v1 assumed
-Replicon-based filtering classifies only **1.79%** of detections as extrachromosomal, against the
-~20% MGE-borne rate reported in the literature. The reason is structural: only 2 of the first 48
-cohort genomes carry more than one replicon, so in complete *P. aeruginosa* assemblies the real
-mobile reservoir is **integrated prophages and ICEs, which are chromosomal by coordinate**. v1's
-stated mitigation ("outside prophages, plasmids and ICEs") therefore requires prophage/ICE
-calling that replicon assignment alone cannot provide. Implemented as specified, the filter would
-have been far leakier than the plan supposed - independent motivation for Threat A and for
-estimating λ.
----
-## Threshold status (RESEARCH_PLAN_V2.md §6.1)
-| ID | Criterion | Observed | Result |
-|---|---|---|---|
-| HT-A | Violation recoverable (slope, R², α bias) | slope 1.032, R² 0.9993, bias 2.9% | ✅ PASS |
-| HT-B | Spearman ≥ 0.60 at leak 0.25, or fragility flagged | 0.621 assumed / 0.698 estimated; λ̂ flags it | ✅ PASS |
-| HT-C | Audit completes on ≥ 500 real genomes with CIs | **1,200 genomes**, permutation-calibrated, two ANI thresholds | ✅ PASS |
-| HT-D | Phase 0 hard thresholds still hold | unchanged; 58/58 audit claims still reproduce | ✅ PASS |
-| ST-A | CRISIS mitigation recovers ≥ 80% of loss | recovers ~0%; one variant is worse | ❌ **FAIL** |
-| ST-B | Real-data violation below tolerance | **restriction violated at both thresholds**; 70-79 of 116 systems leak (BH q<0.10); λ-equivalence not computable | ❌ **FAIL** - and this is why λ must be estimated |
-| ST-C | Throughput for ≥ 2,000 genomes | 2,757 downloaded; **1,200 annotated end-to-end** | ⚠️ **PARTIAL** (cohort complete; full 2,757 not annotated) |

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-# Results - LEDGER v3
-**Last Updated**: 2026-08-17
-**Plan**: `RESEARCH_PLAN_V3.md`
-**Companion**: `RESULTS.md` (Phase 0) and `RESULTS_V2.md` (expansion) are unchanged.
-> **Scope.** v3 builds the element and spacer layers on real genomes and fits LEDGER to real data
-> for the first time. The sparse bilinear compatibility block **W is not fitted** here: elements
-> are 32 bp protospacers with no element-side annotation, so there is no anti-defense feature
-> matrix. What is fitted is the defense main effects α, the exposure layer, the violation λ, and
-> the receipt parameters ρ₀, ρ₁.
----
-## 1. The CRISPR instrument exists at scale - and it is measured, not assumed
-MinCED on all 1,200 cohort genomes yields **27,620 spacers**, and the calls track DefenseFinder's
-independent Cas annotation closely, which is the check that matters:
-| | CAS⁺ genomes (611) | CAS⁻ genomes (589) |
-|---|---|---|
-| median spacers / genome | **40** | 0 |
-| genomes with ≥10 spacers | 611 (100%) | 81 (14%) |
-| genomes with ≥30 spacers | 510 (83%) | 1 (0.2%) |
-Two independent tools - a repeat-structure finder and an HMM-based system annotator - agree on
-which genomes carry CRISPR. Spacer count also supplies a **measured** `crispr_capacity`, the
-quantity the simulator had to assume.
-## 2. Element layer: 1,200 × 2,589, built from spacers
-Elements are **spacer clusters**: 27,620 spacers collapse (strand-canonicalised) to 3,980 distinct
-protospacers, of which **2,589 appear in ≥2 hosts**. Then `S[i,j]` = host *i* carries a spacer of
-cluster *j*; `Y[i,j]` = host *i*'s genome contains a ≥95% identity match to *j*. Both observables
-live on the same element index, which is what makes them commensurate.
-**This is 3.1 million host-element pairs - an order of magnitude larger than any simulation in
-this project (625 × 300).**
-### 2.1 A flaw that would have invalidated everything, caught by a diagnostic
-The first build produced **`(Y=0, S=1) = 0` out of 3.1M pairs** and a self-targeting cell
-**13× enriched** rather than depleted. The cause: BLAST was finding *the spacer itself* inside the
-host's own CRISPR array, so `Y ≡ S` by construction. Every downstream quantity would have been
-meaningless, and the informative cell - the one the entire project is built on - was empty.
-Fixed by masking all **1,767 detected CRISPR arrays (1.72 Mb)** out of the genomes before
-searching. The diagnostic that caught it was in the code before the data existed, which is the
-only reason it was caught at all.
-### 2.2 Three model assumptions, validated on real data
-| Quantity | Measured | What the model assumes |
-|---|---|---|
-| Informative (Y=0, S=1) cell | **25,099 pairs** | must be non-empty for identification |
-| Self-targeting depletion ratio | **0.539** | ρ₁ < ρ₀ ⇒ depleted below independence ✓ |
-| ε, false-match rate (decoy control) | **0.000** | ε ≈ 0 ✓ |
-The ε control is a dinucleotide-preserving shuffle of every element sequence, BLASTed under
-identical settings: **2,589 decoys produced zero hits** against 1,200 genomes. A mononucleotide
-shuffle would have been an easier and less honest control.
-**Self-targeting spacers are depleted roughly two-fold** (916 observed against 1,700 expected
-under independence). The receipt model's central premise - that a spacer against a resident
-element is self-targeting and purged - is confirmed empirically here for the first time.
-**ST-F PASSES.**
----
-## 3. Stage S7 - is CRISIS detectable in *P. aeruginosa*? No.
-Across **7,314 defense-system/Cas pairs** in 1,200 genomes, measuring gene-distance from each
-non-Cas defense system to the nearest Cas system:
-| within | 0 genes | 5 | 10 | 50 | 100 |
-|---|---|---|---|---|---|
-| systems | 0 | **0** | 6 (0.08%) | 19 (0.26%) | 43 (0.59%) |
-Minimum observed distance **10 genes**; median **1,166 genes**. **Nothing is embedded.**
-\citet{Shu2026CRISPRregulates} describe defense modules sitting *inside* type I CRISPR-Cas loci;
-in this species, with this annotation, that configuration is essentially absent.
-**Two nulls were tried and both were wrong, which is the methodological content of this section.**
-A uniform-position null called 23 of 67 system types significant - but it was detecting **defense
-islands**, the well-known clustering of defense systems, which a uniform null destroys. Switching
-to a label permutation over fixed positions did not fix it either, because distance was being
-measured to the Cas *interval* and Cas systems span 6-8 genes against 1-3 for most defense
-systems, so whichever system received the "Cas" label under permutation presented a shorter target.
-Only midpoint-to-midpoint distance under label permutation is a fair test.
-Even then the permutation returns many "significant" types, and **we decline to report that as
-CRISIS**: the effect operates at a scale of hundreds of genes, which cannot represent embedding
-within a locus. The raw proximity distribution, not the p-value, is the interpretable output.
-**Bounded negative.** DefenseFinder may annotate a module embedded in a Cas operon as *part of*
-the Cas system, in which case embedding is invisible to any between-system distance. This is
-therefore a negative about between-system proximity given DefenseFinder's boundaries, not a
-refutation of Shu et al.
-**Consequence for the model.** H6 wanted the embedded subset identified empirically so the
-correctly-specified absorber could be built. That grounding is unavailable in this species, so the
-absorber can only be tested in simulation where the subset is known by construction (§4).
----
-## 4. Stage S8 - the absorber v2 specified: refuted, for a principled reason
-v2 failed ST-A and named the untested fix: interact CRISPR status with the **embedded-subset**
-load rather than total defense load, since a mis-specified absorber adds variance without removing
-bias. v3 implements it (`FitConfig.n_embedded`) and runs it.
-It makes things **worse**, not better. Final sweep, 20 replicates per arm (340 fits), all arms
-sharing an identical planted α = −1.094:
-| arm | α̂ | \|bias\| | RMSE |
-|---|---|---|---|
-| none (baseline) | −1.094 | 0.01% | 0.097 |
-| physical | −1.099 | 0.45% | 0.215 |
-| functional | −1.283 | 17.3% | 0.182 |
-| both | −1.061 | 3.0% | 0.242 |
-| **physical + embedded-subset absorber** | −0.949 | 13.3% | 0.234 |
-| **functional + embedded-subset absorber** | −1.552 | **41.8%** | 0.282 |
-| **both + embedded-subset absorber** | −0.913 | 16.5% | 0.260 |
-Recovery of the RMSE loss, against the pre-registered 80% bar:
-| mitigation | physical | functional | both |
-|---|---|---|---|
-| **embedded-subset (S8 - the one v2 nominated)** | −16.3% | **−116.7%** | −12.4% |
-| total-load CRISPR term | −4.6% | −31.4% | −2.3% |
-| drop embedded systems from *g* | **+19.3%** | −75.1% | **+38.0%** |
-**ST-D FAILS, and the nominated absorber is the worst of the three.** On the functional arm it
-more than doubles the loss it was meant to remove (−116.7%) and drives α̂ bias from 17.3% up to
-**41.8%** - substantially worse than leaving the threat untreated. The best mitigation of any kind
-remains simply dropping the embedded systems, at +38%, still less than half the bar.
-**H6 is refuted, and the reason is structural rather than a tuning failure.** The true
-de-repression term is keyed on CRISPR being *present but compromised* - an inactivating mutation
-or an anti-CRISPR protein. That state is **latent**: it is not observable from CRISPR presence or
-absence. An absorber built on observable CRISPR status therefore cannot represent the term no
-matter how its load argument is specified, and adding it only injects variance.
-The honest conclusion is stronger than v2's: **the CRISIS functional coupling is not mitigable by
-any absorber built on observed CRISPR presence/absence.** Mitigation would require observing the
-compromised state - anti-CRISPR gene content, or cas-gene inactivation calls - which is a
-different and larger data requirement than v2 supposed.
----
----
-## 5. LEDGER fitted to real genomes - the first time, and a null
-1,200 hosts × 2,421 elements × 108 defense systems, fitted with the same exact four-cell marginal
-likelihood used throughout, with the violation λ free.
-| Quantity | Estimate | Uncertainty |
-|---|---|---|
-| **λ̂** (exclusion-restriction violation) | **0.266** | bootstrap 95% CI **[−0.288, 0.542]** |
-| α̂ mean (defense effect on establishment) | 0.017 | 95% CI [−0.107, 0.095] |
-| α̂ mean if the restriction is assumed | 0.042 | - |
-| ρ₀ (receipt \| exposed, not established) | 0.083 | - |
-| ρ₁ (receipt \| exposed, established) | 0.025 | - |
-| **ρ₁/ρ₀** | **0.307** | - |
-Bootstrap resamples **lineage clusters**, not host-element pairs. Pairs within a clone share
-nearly everything, so a pair bootstrap would be spurious precision.
-### 5.1 The methodological headline: LRT and bootstrap disagree by an enormous margin
-The likelihood-ratio statistic for adding λ is **507.6 on 1 df** - nominally p ≈ 10⁻¹¹². The
-lineage-cluster bootstrap gives a 95% interval that **comfortably spans zero**.
-Both numbers are correct; they answer different questions. The LRT treats 3.1 million
-host-element pairs as independent observations, and they are emphatically not: 1,200 genomes fall
-into 344 clusters, and hosts inside a clone are near-identical. **The gap between χ² = 508 and a
-CI containing zero is pseudo-replication made visible**, in a field where non-independence is
-routinely acknowledged and then handled with a phylogenetic correction on the outcome alone.
-We report the bootstrap as the honest uncertainty and the LRT only as a descriptive
-fit-improvement statistic, labelled as anti-conservative in the output itself.
-### 5.2 What the measured λ̂ would cost, on the simulation-calibrated curve
-The v2 sweep gives attenuation as a function of true λ when the restriction is assumed:
-| λ | 0.00 | 0.25 | 0.50 | 0.75 | 1.00 |
-|---|---|---|---|---|---|
-| attenuation | −1.7% | 6.4% | 16.0% | 25.2% | 34.3% |
-Interpolating the measured λ̂ = 0.266 gives **≈ 7% attenuation**. So even taking the point
-estimate at face value and ignoring that its interval spans zero, **the violation in this dataset
-is small enough that assuming the restriction would cost little.** This answers H8 in the
-negative: the v2 machinery is correct, and in this particular operationalisation it was not
-needed.
-### 5.3 The substantive result is a null, and it should be said plainly
-α̂ is 0.017 with an interval spanning zero. **Chromosomal defense repertoire does not detectably
-predict which protospacer-elements are resident in a host, given encounter.** Individual systems
-span a wide range (Armada_Type_II at −1.86, gcu24 at +1.55) but are individually imprecise.
-This is the project's central hypothesis tested on real data for the first time, and it did not
-confirm. Four readings are compatible with the data and we cannot separate them here:
-1. The null is real for this element class.
-2. **The element definition is the weak link.** Elements are 32 bp protospacers, and "the
-   protospacer is present in the genome" is a coarse proxy for "the element established". A
-   prophage-level element layer would be a sharper test.
-3. The exposure layer over-absorbs: with free per-element parameters in both *f* and *g*
-   (2,421 each), there is a great deal of flexibility competing with 108 α coefficients.
-4. Power, once non-independence is respected: 344 effective clusters, not 1,200 genomes.
-### 5.4 Positive controls: the project's central thesis, visible directly in the data
-Before interpreting a null it is worth asking whether the data contain any signal at all. Three
-host-level associations, computed raw and again within lineage clusters (n = 1,200):
-| Association | Raw | **Within lineage** |
-|---|---|---|
-| spacers held vs resident elements | **ρ = −0.210** (p = 2 × 10⁻¹³) | **ρ = +0.009 (p = 0.75)** |
-| defense load vs resident elements | ρ = +0.351 (p = 5 × 10⁻³⁶) | **ρ = +0.123 (p = 2 × 10⁻⁵)** |
-| defense load vs spacers held | - | ρ = −0.074 (p = 0.010) |
-**The first row is the whole argument of this project, in one line of real data.** Analysed
-naively, holding more spacers is strongly associated with carrying fewer of the targeted elements
-- which reads exactly like CRISPR immunity working, and is the kind of result the field reports.
-Condition on lineage and it **disappears entirely** (ρ = +0.009, p = 0.75). The apparent immunity
-signal was population structure.
-**The second row is the masking effect, observed rather than simulated.** Chromosomal defense load
-is *positively* associated with carrying the targeted elements, both raw (+0.35) and within
-lineage (+0.12). This is the coacquisition linkage that \citet{Liu2025Timescale} identify as the
-reason defense/HGT associations come out null or positive, and it appears here in an independent
-species and an independent element operationalisation.
-This reframes the α̂ ≈ 0 result of §5.3. The model's near-zero estimate sits between two strongly
-confounded naive readings - one that says defenses are protective (−0.21) and one that says they
-travel with the elements they defend against (+0.35). A deconfounded estimate landing near zero is
-what one would expect if a genuine protective effect and coacquisition roughly cancel. We cannot
-demonstrate that cancellation from this data, and do not claim it; but it is a more informative
-null than "no signal anywhere", because the raw signals are large and point in opposite directions.
-### 5.5 No contradiction with the v2 audit, and the distinction matters
-v2 found the exclusion restriction violated (70-79 of 116 systems leak). v3 finds λ̂ ≈ 0.27 with
-an interval spanning zero. These are **different quantities**: v2 measured whether defense content
-predicts *ecology and plasmid burden*; v3 measures whether defense load predicts *exposure to
-these particular protospacer elements*. Exposure to phage-derived protospacers need not be driven
-by the same processes as plasmid carriage. The two results are consistent, and conflating them
-would be an error.
-### 5.6 An incidental agreement, flagged as coincidence
-The simulator's default `established_retention` was set to 0.30 by judgement before any real data
-existed; the measured ρ₁/ρ₀ is **0.307**. This is a coincidence and is recorded as one - 0.30 was
-chosen arbitrarily, so the agreement is not a validation of anything. What *is* meaningful is that
-ρ₁ < ρ₀ at all, which the direct cell-count depletion (§2.2) establishes independently of the fit.
-### 5.7 Threshold outcomes
-| ID | Criterion | Observed | Result |
-|---|---|---|---|
-| HT-E | Real Y/S with ≥300 elements and non-trivial informative cell; self-targeting check reported | 2,589 elements, 25,099 informative pairs, depletion 0.539 | ✅ PASS |
-| HT-F | λ̂ estimated with a bootstrap interval; attenuation-if-assumed stated | 0.266 [−0.288, 0.542]; ≈7% | ✅ PASS |
-| HT-G | CRISIS proximity test with permutation null and BH correction | completed; negative | ✅ PASS |
-| ST-D | Embedded-subset absorber recovers ≥80% | makes it worse | ❌ **FAIL** (H6 refuted) |
-| ST-E | Real λ̂ differs from zero beyond its interval | CI spans zero | ❌ **FAIL** |
-| ST-F | Self-targeting spacers depleted | ratio 0.539 | ✅ PASS |
----
-## 7. v3 threshold summary
-| ID | Criterion | Observed | Result |
-|---|---|---|---|
-| HT-E | Real Y/S, ≥300 elements, non-trivial informative cell, self-targeting check reported | 2,589 elements; 25,099 informative pairs; depletion 0.539 | ✅ PASS |
-| HT-F | λ̂ estimated with bootstrap interval; attenuation-if-assumed stated | 0.266 [−0.288, 0.542]; ≈7% | ✅ PASS |
-| HT-G | CRISIS proximity test with permutation null and BH correction | completed; negative | ✅ PASS |
-| ST-D | Embedded-subset absorber recovers ≥80% of loss | **−117% on the functional arm** | ❌ FAIL (H6 refuted) |
-| ST-E | Real λ̂ differs from zero beyond its interval | CI spans zero | ❌ FAIL |
-| ST-F | Self-targeting spacers depleted | 0.539 | ✅ PASS |
-**Hypotheses.** H5 (CRISIS detectable in *P. aeruginosa*) - **rejected**. H6 (embedded-subset
-absorber works) - **refuted**, and for a structural reason. H7 (LEDGER fittable to real genomes,
-first measured λ̂) - **achieved**. H8 (real λ̂ large enough to matter) - **rejected**: ≈7%
-attenuation, interval spanning zero.
-Two of four hypotheses were rejected and one refuted. The programme is nonetheless further along
-than it was, because each rejection is accompanied by a measured reason rather than a shrug.
-## 8. Errors found and corrected during v3
-Recorded because three of the four would have produced confidently wrong science.
-1. **BLAST found spacers inside their own CRISPR arrays** → `Y ≡ S`, informative cell exactly 0 of
-   3.1M pairs, self-targeting 13× *enriched*. Fixed by masking 1,767 arrays. Caught by a diagnostic
-   written before the data existed.
-2. **A uniform-position null in the CRISIS test detected defense islands**, not CRISPR proximity,
-   calling 23 of 67 system types significant. Discarded.
-3. **The replacement label-permutation null was confounded by interval length** - Cas systems span
-   6-8 genes against 1-3 for most defense systems, so the permuted "Cas" label presented a shorter
-   target. Fixed by midpoint-to-midpoint distance. Even the corrected test is not reported as
-   evidence of CRISIS, because its scale is wrong for embedding.
-4. **The real fit was under-converged at 2,500 steps**, producing a *nested model with a lower
-   likelihood than its own submodel* - impossible, and a clear signal not to report anything from
-   it. λ̂ stabilises from 6,000 steps. An automatic nesting check now runs on every fit and warns.
-Also: `blastn-short` defaults (word size 7, permissive e-value) do not terminate in reasonable time
-against an 8 GB database; word size 18 with in-BLAST identity filtering is exact for the hits we
-accept and finishes in under two minutes.
-## 9. What should happen next
-1. **A prophage-level element layer.** The leading explanation for the α̂ null is that 32 bp
-   protospacer residency is a coarse proxy for element establishment. geNomad on the cohort would
-   give genuine element calls and make the bilinear block *W* estimable, which this element
-   definition cannot support.
-2. **Anti-defense annotation**, so *A* exists and the defense × anti-defense interaction map - the
-   project's original scientific deliverable - can be fitted on real data.
-3. **Observing the compromised-CRISPR state** (anti-CRISPR gene content, cas-gene inactivation)
-   without which CRISIS is unmitigable, as §4 establishes.
-4. **A second species.** Every real-data conclusion here is *P. aeruginosa*-specific, and the
-   CRISIS negative in particular is bounded by one annotation tool in one species.

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-# Review Report - LEDGER
-**Review Mode**: Post-Results
-**Date**: 2026-08-17
-**Stage**: post-results review
-**Scope**: All 3,340 production fits, `RESULTS.md`, `paper/sections/*.tex`, figures, and the
-full source tree.
-## Summary
-**Overall Status**: 🟢 PASS
-Every quantitative claim made in `RESULTS.md` and the paper was recomputed from the raw
-per-fit records by an independent audit script: **58 of 58 claims reproduced**. No fabrication
-was found, no data leakage was found, and the two places where results contradict the project's
-own hypotheses are reported prominently rather than buried.
-## Integrity Verdict
-| Check | Verdict |
-|---|---|
-| Fabrication detected | **No** - 58/58 claims recomputed from raw JSONL |
-| Data leakage detected | **No** - latent Z used only in explicitly labelled oracle roles |
-| All results traceable to code | **Yes** - `python -m src.evaluation.audit` |
-| Statistical claims valid | **Yes** - 20 replicates per cell, paired tests, 95% CIs |
-| Negative results reported | **Yes** - ST2 failure and the N=81 regression are both headline items |
-## 6.1 Code-to-Result Traceability
-`src/evaluation/audit.py` recomputes every headline number independently of the code that
-produced the prose. Coverage includes all six ablation rows, all three paired Wilcoxon
-reductions, the HT1/HT2 operating-point statistics, both E1 grid corners, informative-cell
-counts, all five E1d marginal associations, both E1d receipt gains, all three E5 arms, the E1b
-endpoints, four E1c scale points, four mis-specification points, and both fit counts.
-**Result: 58/58 reproduced within tolerance.** Run it with `python -m src.evaluation.audit`.
-Three specific anti-fabrication properties hold structurally rather than by discipline:
-1. Every figure is generated by `src/evaluation/figures.py` reading raw JSONL. No figure is
-   drawn from typed-in numbers.
-2. Every table is generated by `src/evaluation/report.py` from the same records.
-3. Each fit writes its own configuration, realised marginal rates and convergence status into
-   its record, so any cell can be traced back to the exact configuration that produced it.
-## 6.2 Statistical Validity
-- **Replication**: 20 independent replicates per configuration, each drawing a fresh phylogeny,
-  defense repertoire, planted susceptibility function and element panel. Replicate variation
-  therefore reflects genuine sampling variation in the estimand, not just optimizer noise.
-- **Pairing**: all method comparisons are paired on replicate seed. This is necessary here -
-  between-replicate variation in the planted coefficients is large relative to the
-  between-method differences.
-- **Tests**: paired Wilcoxon signed-rank; 95% intervals are t-based over replicates.
-- **Effect sizes are reported alongside p-values.** The A1 ablation is the case where this
-  matters: p = 8.5 × 10⁻⁴ but the effect is 2.9% of RMSE and 0.002 of Spearman. The report says
-  so explicitly rather than letting the small p-value imply importance.
-- **No multiple-comparison inflation of headline claims**: the four hard thresholds were
-  pre-specified in RESEARCH_PLAN.md §7.3 before any production sweep ran.
-## 6.3 Cross-Check: RESULTS.md ↔ TRAINING_LOG.md ↔ paper
-- Every production sweep in TRAINING_LOG.md has a corresponding JSONL file with the expected
-  record count (e1 1,600; e1b 480; e1c 320; e1d 300; e5 120; misspec 400; ablations 120).
-- Failed and superseded runs **are** logged, not just successful ones: the original
-  mis-specified E5 control is retained at
-  `experiments/e5_ORIGINAL_MISSPECIFIED_CONTROL.jsonl` and its failure is described in
-  RESULTS.md Finding 4, RESEARCH_PLAN.md §7.3 and paper §Results.
-- Development smoke tests are logged separately from production runs and are explicitly marked
-  as not contributing to any reported result.
-- Timestamps are plausible: mean wall time per fit is recorded per record (~21 s under
-  10-way GPU contention), consistent with 3,340 fits over the observed elapsed window.
-## 7. Overfitting and Generalization
-Not applicable in the usual sense - this study measures recovery of known planted parameters,
-not held-out predictive performance, so there is no train/test split to leak across. The
-relevant analogue is whether the estimator is fitting artifacts, which the permutation control
-addresses directly: under a genuine global permutation, recovery is 0.075 against an unpermuted
-0.701.
-Robustness was assessed on three axes and all three are reported, including the unflattering
-one: mis-specification (graceful, tracks the oracle), collinearity (flat), and scale (**LEDGER
-is worse than the baseline at N = 81**).
-## 8. Figure Audit
-| Check | Verdict |
-|---|---|
-| Figures generated from raw records | Yes |
-| Axes labelled, units clear | Yes |
-| Confidence bands shown | Yes - 95% t intervals over replicates |
-| Same scale across compared methods | Yes; `sharey` on faceted panels |
-| Y-axes not truncated to exaggerate | Yes - verified on the E1 panels, where the honest
-  presentation makes LEDGER's advantage look *less* dramatic than a truncated axis would |
-| Captions match content | Yes |
-| Colour not the sole identity channel | Yes - distinct marker shapes per method; palette
-  validated (CVD ΔE 9.2 deutan, normal-vision ΔE 27.6) |
-| Oracle visually distinguished from methods | Yes - neutral grey, dashed, and labelled as a
-  bound rather than a competitor |
-One figure defect was found and fixed during review: `fig_e5` originally drew its reference
-line from `spearman_all` in the ablations sweep while the axis showed `spearman_host`, placing
-two different metrics on one axis. A dedicated unpermuted reference arm was run
-(`src/training/run_e5_reference.py`, 40 fits) so the reference is now on the same metric and
-the same seeds.
-## 9. Paper Cross-Check
-- Every number in `paper/sections/results.tex` appears in `RESULTS.md` and is covered by the
-  audit.
-- No result is described in the paper that is absent from `RESULTS.md`.
-- The methods section matches the implementation, including the detail that with scalar entries
-  the planned group lasso reduces to ℓ1.
-- Limitations are stated honestly and include the two most damaging findings: identification
-  rests almost entirely on an assumption rather than on the CRISPR instrument, and the method
-  is worse than the baseline below ~250 genomes.
-- Scope discipline holds: the unexecuted real-genome phase is marked `[NOT RUN]` and no
-  quantity attributable to it appears anywhere.
-## Issues Found During This Review
-### 🟡 W1 - Metric-mismatched reference line in the E5 figure - ✅ FIXED
-See §8. Fixed by adding a proper unpermuted reference arm.
-### 🟡 W2 - Inconsistent fit-count reporting - ✅ FIXED
-Early drafts quoted 3,380 fits (production plus the 40 superseded-control fits) in some places
-and 3,340 in others. Standardised on 3,340 production fits, with the 40 superseded fits
-described separately.
-### 🟡 W3 - Stale single-seed numbers in narrative sections - ✅ FIXED
-`RESULTS.md` Findings 1-3 originally quoted pre-gate single-replicate probe values. Two of
-these materially overstated an effect: DEV-005 reported the receipt channel gap under linkage
-as 0.752 vs 0.661, where the 20-replicate production value is 0.742 vs 0.731. All narrative
-sections now lead with production values, and the superseded single-seed figures are explicitly
-marked as such rather than deleted.
-### 🟢 O1 - Ceiling ambiguity in methods text - ✅ FIXED
-The two distinct Spearman ceilings (0.530 on the interaction block, 0.770 on the full
-coefficient vector) were disambiguated.
-### 🟢 O2 - Records from sweeps launched before the `spearman_host` metric was added lack that
-field. This is harmless: `spearman_host` is required only for the permutation controls, which
-were run afterwards. Noted for reproducibility.
-## Checklist Summary
-| Category | Checked | Passed | Fixed | N/A |
-|---|---|---|---|---|
-| Result Authenticity | 58 | 58 | 0 | 0 |
-| Data Leakage | 6 | 5 | 0 | 1 |
-| Statistical Validity | 6 | 6 | 0 | 0 |
-| Figure Audit | 8 | 7 | 1 | 0 |
-| Paper Cross-Check | 6 | 6 | 0 | 0 |
-| Consistency (logs/results/paper) | 4 | 2 | 2 | 0 |
-## Gate Decision
-**PASS - cleared to finalise the paper.** Zero fabrication, full traceability, no leakage, and
-the results that contradict the project's own hypotheses are reported as prominently as the
-supporting ones.

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-# Review Report - LEDGER
-**Review Mode**: Pre-Training
-**Date**: 2026-08-16
-**Stage**: pre-training review
-**Scope**: `src/data/simulator.py`, `src/models/ledger.py`, `src/evaluation/metrics.py`,
-`src/utils/phylo.py`, `src/training/run_sweep.py`, against `RESEARCH_PLAN.md`.
-## Summary
-**Overall Status**: 🟢 PASS (after remediation of 4 issues found during review)
-Four substantive issues were found and fixed before any production sweep was launched. One
-of them - a divergent code path in the linkage simulator - would have invalidated an entire
-sweep and produced a confidently wrong scientific conclusion. Two others (a saturated metric
-and a permanently-true convergence flag) would have produced misleading reporting rather than
-wrong numbers. No fabrication risk exists at this stage: no results have been produced, and
-`RESULTS.md` is still the empty template.
-## Critical Issues (Found → Fixed)
-### C1. Divergent code path confounded the linkage sweep 🔴 → ✅ FIXED
-**Where**: `src/data/simulator.py`, former `simulate_linkage_violation()`.
-**What was wrong**: the linkage-violation generator recomputed `g_logit` *without* the
-`lineage_g` random-effect term while reusing `base.true_intercept`, which had been calibrated
-*with* that term. It also redrew `element_ecology_pref`, so the element niche structure
-differed from the baseline arm. In `sweep_e1d`, the `linkage_strength=0.0` arm was produced by
-`simulate()` and all other arms by `simulate_linkage_violation()`. The arms therefore differed
-in the presence of a lineage effect in *g*, in the element niche vector, and in effective
-establishment calibration - not only in linkage. Any dose-response curve read off that sweep
-would have been uninterpretable, and the headline claim ("the receipt channel earns its place
-under linkage") would have rested on it.
-**Fix**: linkage folded into `SimConfig.linkage_strength` and applied inside `simulate()` on a
-single code path; the divergent function deleted. Verified: linkage 0.0 → marginal association
-ρ = −0.462; linkage 1.5 → ρ = +0.485, with all other structure held fixed.
-### C2. Mis-specification stress test specified but never implemented 🔴 → ✅ FIXED
-**Where**: `RESEARCH_PLAN.md` §8 lists "simulator too kind to the estimator" (likelihood M,
-impact H) with mitigation "fit under a *different* generative process than assumed". No such
-experiment existed.
-**Why it matters**: the estimator's *f* and *g* had **exactly** the functional forms that
-generated the data - correctly specified in both layers. Every recovery number would have been
-collected under conditions maximally favourable to the estimator, and reported without that
-caveat being tested.
-**Fix**: added `SimConfig.misspec_strength`, which injects a latent rank-3 host-element
-compatibility term that `g` has no capacity to represent, plus a `misspec` sweep over
-strengths (0, 0.25, 0.5, 1.0, 2.0). Marginal rates verified stable across strengths
-(P(Y|Z) = 0.218 → 0.225), so the sweep varies specification error and not base rates.
-## Warnings (Found → Fixed)
-### W1. `spearman_W` was saturated at its tie ceiling 🟡 → ✅ FIXED
-The planted interaction block has 86 zeros out of 96 entries. Ties cap the attainable Spearman
-at **0.5302**, computed exactly. Oracle, LEDGER and the naive baseline all scored 0.529-0.530 -
-i.e. all three were at the ceiling, and the metric had zero discriminative power. Reporting
-"0.53" as moderate recovery would have materially misdescribed a perfect score.
-**Fix**: `spearman_W` removed; replaced with `support_auroc`, `support_auprc`,
-`precision_at_k`, and `spearman_W_nonzero` (restricted to true nonzeros, hence tie-free). A
-`spearman_ceiling()` helper is now computed and reported alongside every tie-prone Spearman,
-with `spearman_all_frac_ceiling` as the interpretable quantity.
-### W2. `converged` flag was unconditionally True 🟡 → ✅ FIXED
-`converged = (step - best_step) > patience or step == n_steps - 1` is True whether early
-stopping fires *or* the step budget is exhausted - the two outcomes it was meant to
-distinguish. It could never be False and was useless as a diagnostic.
-**Fix**: reduced to the plateau condition alone. The corrected flag immediately proved its
-worth: it reports `False` at 2,500 and 6,000 steps, with true convergence at ~11,100. Recovery
-metrics are nonetheless stable from 2,500 steps onward (Spearman 0.738 → 0.739, RMSE 0.100 →
-0.100), so sweeps run at 4,000 steps and convergence status is recorded per fit rather than
-assumed.
-### W3. Lineage granularity was over-flexible 🟡 → ✅ FIXED
-`clusters_at_level(n_levels - 2)` produced 125 clusters of 5 hosts for a 625-host tree, i.e.
-125 free random effects in *both* f and g - a nuisance parameterization flexible enough to
-absorb genuine signal, and unrepresentative of real ANI clusters.
-**Fix**: `SimConfig.lineage_level` added, defaulting to `n_levels - 3` → 25 clusters of 25
-hosts. Verified.
-## Observations (Not Blocking)
-- **O1 - Oracle mode reads `data.Z` by design.** `fit(mode="oracle")` and
-  `establishment_auroc(exposed_only=True)` both use the latent exposure. This is legitimate
-  (an oracle upper bound and an oracle-restricted evaluation) but is ground truth unavailable
-  in real data. Must be labelled as such in the paper; it is not a competing method.
-- **O2 - `torch.manual_seed` is vestigial.** All parameters are zero-initialized, so no torch
-  RNG is consumed and fits are deterministic given data. Harmless.
-- **O3 - Environment not yet pinned.** `requirements.txt` should be captured before release.
-- **O4 - `naive` (B3) and `clamped` (B4) are analytically near-equivalent.** With π ≡ 1 the
-  receipt likelihood factorizes given Y and contributes nothing about θ. Confirmed empirically
-  (both 0.635 / RMSE 0.428, identical to three decimals). This is a correct prediction of the
-  plan's own §3.3 and is worth one sentence in the paper rather than being presented as two
-  independent baselines.
-## Data Leakage Assessment
-| Check | Verdict |
-|---|---|
-| Latent Z used in fitting | Only in `oracle` mode, by design and labelled |
-| True coefficients used in fitting | **No** - `true_alpha/beta/W` touched only by `metrics.py` |
-| Estimator sees true ecology | **No** - `fit()` reads `ecology_observed`, never `ecology` |
-| Train/test contamination | N/A - recovery of planted parameters, not held-out prediction |
-| Preprocessing leakage | Defense load standardized within-dataset; no split exists to leak across |
-| Metric computed from same code that fits | Separate module; metrics never influence the objective |
-## Checklist Summary
-| Category | Checked | Passed | Fixed | N/A |
-|---|---|---|---|---|
-| Code Correctness | 14 | 12 | 2 | 0 |
-| Data Leakage | 6 | 5 | 0 | 1 |
-| Experimental Design | 9 | 7 | 2 | 0 |
-| Reproducibility | 6 | 5 | 0 | 1 |
-| Result Authenticity | - | - | - | all (no results yet) |
-## Gate Decision
-**PASS - cleared to begin production sweeps.** All four issues are remediated and each fix was
-verified by re-running the affected component. Two conditions carry forward to the post-results
-gate: (1) oracle-mode results must be labelled as an upper bound, not a baseline; (2) the
-mis-specification sweep must actually be reported, not just implemented - it is the honest
-counterweight to a correctly-specified simulator.

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-# Review Report - LEDGER v2 Expansion
-**Review Mode**: Post-Results (v2)
-**Date**: 2026-08-17
-**Stage**: post-results review
-**Scope**: `RESEARCH_PLAN_V2.md`, the four v2 simulation sweeps (1,520 fits), the real-genome
-acquisition/annotation/audit pipeline, `RESULTS_V2.md`, and `paper/sections/results_v2.tex`.
-## Summary
-**Overall Status**: 🟢 PASS
-`src/evaluation/audit_v2.py` independently recomputes every headline v2 claim from the raw
-per-fit records and the real-data audit JSON: **73 of 73 reproduced**. Together with the Phase 0
-audit this is **131/131**. No fabrication, no leakage. Five substantive faults were found during
-v2 and all five were fixed or the affected work withdrawn *before* reporting; three of them would
-have produced confidently wrong science.
-## Integrity Verdict
-| Check | Verdict |
-|---|---|
-| Fabrication detected | **No** - 73/73 v2 claims recomputed (131/131 with Phase 0) |
-| Data leakage detected | **No** - latent Z used only in labelled oracle roles; real-data audit is host-side only |
-| All results traceable to code | **Yes** - `python -m src.evaluation.audit_v2` |
-| Statistical claims valid | **Yes** - 20 replicates/arm, paired tests, permutation nulls, BH correction |
-| Negative results reported | **Yes** - ST-A and ST-B both fail and are headline items |
-| Discarded work retained | **Yes** - see §"Withdrawn and discarded" |
-## Faults found during v2, and their disposition
-### 🔴 F1 - Threat manipulation drew from the main RNG stream (FIXED, work re-run)
-Enabling CRISIS physical coupling shifted every subsequent random draw, including the **planted
-susceptibility coefficients**: true α was −1.251 with the threat on versus −1.090 with it off. The
-arms therefore differed in more than the manipulation and the entire Threat B comparison was
-invalid. Fixed with a dedicated generator; all arms now verified to share planted α = −1.094. The
-confounded records are retained at `experiments/threat_crisis_CONFOUNDED_RNG.jsonl`.
-**This is the second occurrence of this exact failure mode** (the first was the v1 linkage code
-path, caught at the pre-training gate). Two independent instances in one project is a pattern, and
-the lesson is recorded: any simulator manipulation that consumes randomness must use a dedicated
-stream, and every arm's planted truth should be asserted equal as a test rather than assumed.
-### 🔴 F2 - A threat mechanism was biologically wrong (FIXED, work re-run)
-CRISIS de-repression was keyed on CRISPR *absence*. Under physical coupling embedded systems exist
-only in CRISPR⁺ hosts, so the functional term was identically zero and the `both` arm came out
-numerically identical to `physical` to three decimals. \citet{Shu2026CRISPRregulates} describe
-de-repression when CRISPR is *present but compromised* (mutation or anti-CRISPR); a compromised
-state is now modelled explicitly. The degeneracy was the symptom; the wrong biology was the cause.
-### 🔴 F3 - The planned sensitivity analysis was invalid (DISCARDED, documented)
-`RESEARCH_PLAN_V2.md` §2 specified a posited-offset robustness value. Implemented and tested: the
-fixed offset is absorbed by the other free exposure parameters, so α̂ moves non-monotonically
-(−1.063 → −0.978 over λ = 0 → 4) and no breakdown point exists. **Reporting a robustness value
-read off that curve would have been meaningless.** Superseded by direct estimation of λ. The code
-path is retained and labelled void; the plan section is marked superseded with the failure
-recorded rather than the specification quietly rewritten.
-### 🟡 F4 - A sweep was mechanistically redundant (WITHDRAWN before reporting)
-`threat_boundary` manipulates the same simulator knob as `threat_att_leak` at a different
-strength. The mechanism is identical - an element-borne system counted as chromosomal predicts
-exposure, and the estimator cannot distinguish attachment-site proximity from a misplaced prophage
-boundary. Reporting both would have presented one manipulation as two independent findings.
-Retained in code, unrun, labelled.
-### 🟡 F5 - Planted-truth value mixed two sweeps (FIXED)
-`RESULTS_V2.md` and the paper quoted "true α = −1.103" for a table combining rows from two sweeps
-whose seed ranges draw independent coefficients (−1.108 for `lambda_recovery`, −1.103 for
-`assumed_restriction`). Caught by the v2 audit as the single mismatch on its first run. Both values
-are now stated and each row is scored against its own sweep's truth.
-### 🟡 F6 - skani screening threshold was wrong for within-species use (FIXED)
-The first ANI run used `--sparse -s 95`, but within a single species essentially all 3.8M pairs
-clear a 95% screen, so nothing was pruned. Re-run at `-s 99` on the cohort. A design error that
-cost wall-clock, not correctness.
-## Statistical validity
-- **Replication**: 20 independent replicates per configuration throughout; each draws a fresh
-  phylogeny, defense repertoire, planted *g* and element panel.
-- **Pairing**: method comparisons paired on replicate seed.
-- **Permutation nulls on the real data**: essential and vindicated. Raw within-cluster partial R²
-  is 0.0717 against a null of 0.0513 - reporting the raw figure would have overstated the
-  violation more than threefold. In the 120-genome pilot the inflation was far worse (0.527 vs
-  0.432). Any within-cluster partial R² reported without such a null is uninterpretable.
-- **Multiple testing**: Benjamini-Hochberg applied to the 99 per-system tests, necessary because
-  the permutation p-values have a hard floor of 1/(n_perm+1) and several systems sit on it.
-- **Threshold sensitivity reported, not hidden**: the audit is run at two ANI thresholds that
-  **disagree**, and the disagreement is reported as the finding rather than the more convenient
-  threshold being selected. The degenerate 99.0% clustering (5 clusters, largest 1,177) is
-  reported as degenerate.
-- **A non-replicating preliminary result is disclosed**: the pilot CRISPR/ecology association
-  (excess R² 0.284, p = 0.008) vanished at n = 785 under 99.9% clustering. It was flagged as
-  underpowered when first observed, not after it failed.
-- **A marginal p-value is not over-read**: Test B moved from p = 0.020 (n = 725) to p = 0.051
-  (n = 785). Reported as marginal at that threshold rather than as significant.
-## Real-data pipeline audit
-| Check | Verdict |
-|---|---|
-| Data provenance recorded | Yes - NCBI Datasets v2 API, accession lists retained |
-| Only complete assemblies used | Yes - absence of an element in a draft would be a false negative |
-| Metadata coverage measured, not assumed | Yes - 83.2% / 94.3% / 92.5% / 100% |
-| Cohort selection reproducible | Yes - stratified by country × year-bin, seeded |
-| Annotation idempotent and resumable | Yes; per-genome failures logged separately |
-| Tool versions pinned | Yes - DefenseFinder 3.0.0, models CasFinder 3.1.0 / DF-models 3.1.0 |
-| Tool failure disclosed | Yes - `defense-finder update` HTTP 504 on first attempt, retried |
-| Known filter weakness quantified | Yes - replicon filtering catches only 1.79% vs ~20% literature MGE-borne rate |
-| Missing layer disclosed | Yes - AntiDefenseFinder produced no calls; anti-defense matrix empty, deferred |
-| Partial completion disclosed | Yes - annotation is partial by design, count stated, not represented as complete |
-## HT-D regression check (verified directly, not assumed)
-v2 added new mechanisms to the simulator (att-leak, CRISIS physical/functional, boundary error) and
-new terms to the model (free defense-load coefficient, fixed-offset path, CRISPR interaction). Each
-is gated behind a config flag that defaults to off, but "should be gated" is a claim that needs
-testing, so the default configuration was re-run and compared against the Phase 0 reference:
-| Quantity | Phase 0 reference | After all v2 changes |
-|---|---|---|
-| P(Z=1) | 0.3500 | 0.3500 |
-| P(Y=1\|Z=1) | 0.2176 | 0.2176 |
-| informative (Y=0,S=1) cells | 3,493 | 3,493 |
-| Spearman @ 2,500 steps | 0.738 | 0.738 |
-| RMSE @ 2,500 steps | 0.100 | 0.100 |
-| ρ₀ estimated / true | 0.306 / 0.300 | 0.306 / 0.300 |
-| ρ₁ estimated / true | 0.093 / 0.090 | 0.093 / 0.090 |
-Identical throughout, and the Phase 0 audit still returns **58/58**. HT-D holds by measurement.
-## Warnings carried forward
-1. **The audit is host-side only.** It cannot measure λ̂ itself, which needs the element layer. We
-   explicitly decline to convert the audit statistics into a λ-equivalent, because the simulated λ
-   and the real-data proxies are different quantities and a mapping would be invented. This
-   abstention should survive into any future draft.
-2. **CRISIS coupling remains unmitigated.** ST-A fails at 38% against an 80% bar. The nominated
-   absorber is actively harmful. The untested embedded-subset absorber is specified and must not
-   be described as validated.
-3. **Threshold-dependent conclusion.** The exclusion restriction is violated at 99.5% ANI and not
-   detectably at 99.9%. Power and lineage control trade off, and the two explanations cannot be
-   separated with this design. Both are stated.
-4. **AntiDefenseFinder not run**, so no interaction-block claim is possible from real data.
-## Checklist Summary
-| Category | Checked | Passed | Fixed/Withdrawn |
-|---|---|---|---|
-| Result authenticity (v2) | 73 | 73 | 0 |
-| Simulator correctness | 6 | 4 | 2 (F1, F2) |
-| Method validity | 3 | 2 | 1 discarded (F3) |
-| Experimental design | 5 | 4 | 1 withdrawn (F4) |
-| Reporting consistency | 4 | 3 | 1 (F5) |
-| Real-data pipeline | 10 | 10 | 0 |
-| Statistical validity | 7 | 7 | 0 |
-## Gate Decision
-**PASS.** Every v2 claim is traceable, the two failed soft thresholds are reported as failures
-rather than reframed, and the five faults found during execution were fixed or withdrawn before
-reporting with the discarded artefacts retained on disk. The most important property of this round
-is that three of the five faults (F1, F2, F3) would each have produced a confident and wrong
-result, and all three were caught by internal checks or by checking implementation against the
-source paper rather than by luck.

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-# Training Log - LEDGER
-**Project**: LEDGER - Latent Exposure Deconfounding for Gene-Element Receptivity
-**Field**: Computational microbial genomics / horizontal gene transfer
-**Started**: 2026-08-16
-**Hardware**: 4× NVIDIA A100 80GB (GPUs 1 and 3 used; GPUs 0 and 2 reserved for other users),
-32 CPU cores, 502 GB RAM. No scheduler.
-**Environment**: Python 3.10.14, PyTorch 2.5.1+cu124, NumPy 2.0.1, SciPy 1.15.3
-Every entry below corresponds to an actual process launch. Development smoke tests are logged
-separately from production sweeps and are marked as such.
----
-## Development runs (pre-gate, not used for any reported result)
-### DEV-001 - Simulator calibration check - 2026-08-16
-- **Purpose**: verify simulated marginals match calibration targets
-- **Result**: P(Z=1)=0.3492 (target 0.35); P(Y=1|Z=1)=0.2163 (target 0.22); P(Y=1)=0.0755;
-  CRISPR+ hosts 206/625 = 33.0%; informative (Y=0,S=1) cells = 3,964
-- **Invariant checks**: P(Z=1|S=1) = 0.9977 (expected ≈1, residual is the ε false-match rate);
-  P(Z=1|Y=1) = 1.0000 (must be exactly 1 by construction) - both PASS
-- **Status**: ✅ Completed
-- **Bug found and fixed**: `np.quantile` with a vector of quantiles returned a cross-product
-  instead of per-column thresholds (shape (12,12) instead of (12,)). Fixed to per-column.
-### DEV-002 - First estimator smoke test - 2026-08-16
-- **Config**: seed 1, 3000 Adam steps, lr 0.05
-- **Result**: oracle Spearman 0.755 / RMSE 0.080; LEDGER 0.760 / 0.090; naive (B3) 0.635 / 0.428
-- **Observation**: LEDGER essentially attains the oracle bound. `spearman_W` identical
-  (0.529-0.530) across all three methods - investigated rather than reported.
-- **Status**: ✅ Completed
-### DEV-003 - Metric ceiling investigation - 2026-08-16
-- **Finding**: with 86 zeros out of 96 entries in the planted W, the maximum attainable
-  Spearman on that block is **exactly 0.5302** (measured by scoring truth against itself with
-  ties broken randomly, 200 draws, sd 0.0000). All three methods were at the ceiling; the
-  metric had zero discriminative power.
-- **Action**: `spearman_W` removed; replaced with support-recovery AUROC/AUPRC, precision@k,
-  and Spearman restricted to true nonzeros. `spearman_ceiling()` now reported alongside every
-  tie-prone Spearman.
-- **Status**: ✅ Completed
-### DEV-004 - Receipt-channel necessity probe - 2026-08-16
-- **Hypothesis tested**: the receipt channel matters more when exposure metadata is noisy
-- **Config**: ecology observation noise ∈ {0, 1, 2, 4}
-- **Result**: receipt gain flat across all noise levels (ΔRMSE ≈ +0.011, ΔSpearman +0.001 to
-  +0.015). **Hypothesis rejected.**
-- **Interpretation**: identification comes from the *structural* exclusion restriction (f
-  contains no defense features at all), not from covariate quality. This redirected the study
-  toward the linkage regime and motivated the addition of sweep E1d.
-- **Status**: ✅ Completed
-### DEV-005 - Linkage probe - 2026-08-16
-- **Result**: under a linkage violation the marginal defense-load/presence association flips
-  from −0.542 to +0.454, reproducing the published confound. LEDGER 0.752/0.106,
-  no-receipt 0.661/0.127, naive 0.453/0.453.
-- **Status**: ✅ Completed - motivated E1d as a full sweep
----
-## 🔍 REVIEW CHECKPOINT 1 - Pre-Training Gate - 2026-08-16
-Outcome: **PASS after remediation of 4 issues.** See `REVIEW_REPORT_PRE_TRAINING.md`.
-Two issues were substantive: a divergent code path that would have invalidated the entire E1d
-sweep, and an unimplemented mis-specification stress test that the research plan's own risk
-table requires. Production sweeps were not launched until all four were fixed and re-verified.
-### DEV-006 - Post-fix verification - 2026-08-16
-- 25 lineages × 25 hosts confirmed; linkage sign flip −0.462 → +0.485 on the unified code path;
-  mis-specification leaves marginals stable (P(Y|Z) 0.218 → 0.225)
-- ρ recovery: estimated ρ₀ = 0.306 (true 0.300), ρ₁ = 0.093 (true 0.090)
-- `converged` flag corrected; now correctly reports False at 2,500 and 6,000 steps, True at
-  ~11,136. Recovery metrics stable from 2,500 steps (Spearman 0.738→0.739, RMSE 0.100→0.100).
-- **Status**: ✅ Completed - gate cleared
----
-## Production sweeps
-### RUN-001 through RUN-010 - Phase 0 identifiability sweeps - launched 2026-08-16
-- **Reference**: RESEARCH_PLAN.md §4.2
-- **Launch**: 10 concurrent processes, sharded across GPUs 1 and 3
-  - `e1` sharded 4 ways by replicate (reps 0-5, 5-10, 10-15, 15-20)
-  - `e1b`, `e1c`, `e1d`, `e5`, `ablations`, `misspec` one process each
-- **Config per fit**: 4,000 Adam steps, lr 0.05, patience 800, float64, l1_W 0.01, l2 1e-4
-- **Replicates**: 20 per configuration
-- **Total planned fits**: 3,260
-  (e1 1,600 · e1b 480 · misspec 400 · e1c 320 · e1d 300 · ablations 120 · e5 40)
-- **Observed throughput**: ~10 fits/min aggregate under contention (GPUs 0 and 2 were running
-  other users' jobs throughout)
-- **Output**: one JSON record per fit to `experiments/*.jsonl`
-- **Status**: ✅ **All 10 processes completed.** Realised record counts match plan exactly:
-  e1 1,600 (4 × 400 shards) · e1b 480 · e1c 320 · e1d 300 · misspec 400 · ablations 120
-- **Mean wall time per fit**: ~21 s under 10-way contention (GPUs 0 and 2 were occupied by
-  other users' jobs throughout)
-- **Convergence**: recorded per fit. At 4,000 steps most fits report `converged = False`,
-  meaning the objective was still creeping down when the budget expired. This is logged
-  honestly rather than suppressed: recovery metrics are stable from 2,500 steps onward
-  (Spearman 0.738 → 0.739, RMSE 0.100 → 0.100 between 2,500 and 12,000 steps), so the
-  reported coefficients are not sensitive to the remaining descent.
-### RUN-011 - E5 permutation controls, re-run - 2026-08-17
-- **Reason for re-run**: the original control failed its own threshold (mean Spearman 0.536,
-  support AUROC 0.951). Diagnosis showed the control was mis-specified, not the estimator.
-  See RESULTS.md Finding 4.
-- **Change**: added a *global* permutation arm (a genuine null, residual corr(D) = −0.007)
-  alongside the original within-lineage arm (residual corr(D) = +0.489), and scored both on
-  host-side coefficients only.
-- **Original 40 fits retained** at `experiments/e5_ORIGINAL_MISSPECIFIED_CONTROL.jsonl` rather
-  than deleted, so the failure remains inspectable.
-- **Result**: 80 fits. Global null mean |Spearman| = 0.075 → **HT4 PASSES**.
-- **Status**: ✅ Completed
-### RUN-012 - E5 unpermuted reference arm - 2026-08-17
-- **Reason**: the E5 figure's reference line was drawn from `spearman_all` in a different sweep
-  while the axis showed `spearman_host` - two different metrics on one axis.
-- **Action**: `src/training/run_e5_reference.py`, 40 fits on the same seeds, recording
-  `permutation="none"` and the same host-side metric.
-- **Result**: unpermuted reference Spearman(α, W) = 0.701. Recovery across the three arms
-  tracks residual signal monotonically: 1.000 → 0.701, 0.489 → 0.460, −0.007 → −0.054.
-- **Duration**: 559 s. **Status**: ✅ Completed
----
-## 🔍 REVIEW CHECKPOINT 2 - Post-Results Gate - 2026-08-17
-Outcome: **PASS.** See `REVIEW_REPORT_POST_RESULTS.md`. An independent audit script
-(`src/evaluation/audit.py`) recomputed every headline claim from the raw per-fit records:
-**58/58 reproduced**. No fabrication, no data leakage, all results traceable to code. Three
-warnings were found and fixed (metric-mismatched figure reference, inconsistent fit counts,
-stale single-seed numbers in narrative sections).
----
-## Final threshold outcomes
-| ID | Criterion | Observed | Target | Result |
-|---|---|---|---|---|
-| HT1 | Spearman at operating point | 0.746 (n=120) | ≥ 0.60 | ✅ PASS |
-| HT2 | RMSE reduction vs B3 | 77.4%, p = 2.0×10⁻²¹ | ≥ 30%, p < 0.01 | ✅ PASS |
-| HT3 | Sign-recovery accuracy | 1.000 | ≥ 0.80 | ✅ PASS |
-| HT4 | Global permutation null | 0.075 | < 0.15 | ✅ PASS |
-| ST2 | Receipt channel load-bearing | 0.002 | ≥ 0.20 | ❌ **FAIL** (reported) |
-| ST3 | Linkage flips association | −0.239 → +0.746 | sign flip | ✅ PASS |
-| ST4 | Beats B3 across grid | 20/20 cells | all cells | ✅ PASS |
-**No improvement cycles were triggered.** All hard thresholds passed on the first production
-run. The one failed soft threshold (ST2) is not a performance deficiency to be optimised away
-but a scientific finding about where identification actually comes from, and is reported as
-such.
-*Note on throughput*: a CPU benchmark during the run measured 127 steps/s with 4 threads
-(≈31 s per 4,000-step fit), roughly twice the per-process throughput of the contended GPUs.
-The sweeps were left on GPU rather than restarted, since they were already producing valid
-records and the remaining wall-clock fitted the compute budget; restarting would have
-discarded completed work for a modest gain.
----
-# v2 - Post-Phase-0 expansion (RESEARCH_PLAN_V2.md)
-**Started**: 2026-08-17
-## Real-data acquisition and annotation
-### RUN-V2-DATA - NCBI acquisition - 2026-08-17
-- Metadata for all 3,466 complete *P. aeruginosa* assemblies via NCBI Datasets v2 API
-- Exposure-covariate coverage measured: collection_date 83.2%, geo_loc_name 94.3%,
-  isolation_source 92.5%, bioproject 100.0%
-- 2,757 assemblies carry all three exposure covariates; **all 2,757 downloaded (18 GB)**
-- Stratified cohort of 1,200 selected by country × year-bin (60 countries, 423 BioProjects)
-- **Status**: ✅ Completed
-### RUN-V2-ANNOT - DefenseFinder 3.0.0 - 2026-08-17
-- Tool chain: mamba env (python 3.12, hmmer, ncbi-datasets-cli, skani) + pip
-  mdmparis-defense-finder 3.0.0; models CasFinder 3.1.0 + defense-finder-models 3.1.0
-- First `defense-finder update` failed with HTTP 504; retried successfully (logged, not hidden)
-- Throughput: ~40 s/genome at 4 workers. Run at 8×4 then rebalanced to 6×2 to share cores
-  with the simulation sweeps, then paused to let the crisis sweep finish.
-- **785 of 1,200 cohort genomes annotated** at the time of the final audit. Idempotent and
-  resumable; the remainder is unfinished, not failed.
-- AntiDefenseFinder produced no calls under default invocation, so the anti-defense matrix is
-  empty. Deferred: it is needed only for the interaction block (stage S5), not for the audit.
-- **Status**: ⚠️ Partial by design (785/1,200)
-### RUN-V2-ANI - skani lineage clustering - 2026-08-17
-- First attempt used `--sparse -s 95` over all 2,757 genomes. **Design error**: within a single
-  species nearly all 3.8M pairs clear a 95% screen, so almost nothing was pruned and the job was
-  projected at ~90 min. Killed and re-run with `-s 99` on the 1,200-genome cohort.
-- Final: 358,414 pairs recorded. Single-linkage clustering at three thresholds:
-  99.9% → 344 clusters (153 singletons, largest 72); 99.5% → 184 (59, 213);
-  **99.0% → 5 clusters, largest 1,177 - degenerate**, single-linkage chains the whole species.
-- **Status**: ✅ Completed
-## Simulation sweeps
-### RUN-V2-001 - lambda_recovery - 360 fits - ✅
-Is the exclusion-restriction violation estimable? λ̂ vs λ_true: slope 1.032, R² 0.9993, max
-|α̂ bias| 2.9%. **HT-A PASS.**
-### RUN-V2-002 - assumed_restriction - 540 fits - ✅
-The realistic failure mode Phase 0 never tested: data carry linkage, estimator assumes the
-restriction. α̂ attenuates to 79% at λ=4; Spearman 0.741 → 0.360.
-### RUN-V2-003 - threat_att_leak - 400 fits - ✅
-Lateral-transduction leak. Estimation holds α̂ within 1-7% of truth where assuming costs 44%.
-λ̂ rises monotonically with the leak. **HT-B PASS.**
-### RUN-V2-004 - threat_crisis - first attempt DISCARDED, re-run - ✅
-- **Discarded**: the physical-coupling manipulation drew from the main RNG stream, so enabling it
-  shifted every later draw including the planted coefficients (true α = −1.251 with the threat
-  on vs −1.090 with it off). Arms differed in more than the manipulation; comparison invalid.
-  Retained at `experiments/threat_crisis_CONFOUNDED_RNG.jsonl` rather than deleted.
-- **Also fixed before re-running**: de-repression had been keyed on CRISPR *absence*, which made
-  the "both" arm numerically identical to "physical" (embedded systems exist only in CRISPR+
-  hosts under physical coupling, so the functional term was identically zero). Shu et al.
-  describe de-repression when CRISPR is *present but compromised*; now modelled explicitly.
-- Re-run with a dedicated RNG; all arms verified to share planted α = −1.0896.
-- Added a second mitigation arm (CRISPR-status main effect + CRISPR×defense-load interaction).
-- **ST-A FAILS**: neither mitigation recovers the loss; the CRISPR-term variant makes the
-  functional arm worse.
-### RUN-V2-005 - threat_boundary - WITHDRAWN, NOT RUN
-Implemented, then withdrawn before reporting: it manipulates the same simulator knob as
-threat_att_leak at a different strength, so reporting both would present one manipulation as two
-findings. Retained in code, unrun and labelled.
-### Discarded method - posited-offset sensitivity analysis
-`RESEARCH_PLAN_V2.md` §2's Cinelli-Hazlett-style robustness value was implemented
-(`FitConfig.f_defense_load_fixed`) and found invalid: the fixed offset is absorbed by the other
-free exposure parameters, so α̂ moved non-monotonically (−1.063 → −0.978 over λ = 0 → 4) and no
-breakdown point exists to read off. The code path is retained and documented as void. Superseded
-by direct estimation, which is strictly more informative.
-## v2 threshold outcomes
-| ID | Criterion | Observed | Result |
-|---|---|---|---|
-| HT-A | Violation recoverable | slope 1.032, R² 0.9993, bias 2.9% | ✅ PASS |
-| HT-B | Spearman ≥ 0.60 at leak 0.25 or fragility flagged | 0.621 / 0.698; λ̂ flags it | ✅ PASS |
-| HT-C | Audit on ≥ 500 real genomes | 785 genomes, 2 ANI thresholds | ✅ PASS |
-| HT-D | Phase 0 thresholds still hold | unchanged | ✅ PASS |
-| ST-A | CRISIS mitigation recovers ≥ 80% | ~0%; one variant worse | ❌ FAIL |
-| ST-B | Real violation below tolerance | violated where powered (49/99 systems) | ❌ FAIL |
-| ST-C | Throughput ≥ 2,000 genomes | 2,757 downloaded, 785 annotated | ⚠️ PARTIAL |
----
-# v3 - Real element/spacer layers and the first real-data fit (RESEARCH_PLAN_V3.md)
-**Date**: 2026-08-17
-### RUN-V3-SPACERS - MinCED spacer extraction - ✅
-1,200 genomes, 12-way parallel, 80 seconds. **27,620 spacers.** QC against DefenseFinder Cas
-calls: CAS+ genomes median 40 spacers (611/611 with ≥10); CAS− median 0 (only 20% have any).
-Two independent methods agree on which genomes carry CRISPR.
-### RUN-V3-ELEMENTS - element layer from spacers - ✅ (second attempt)
-- **First attempt DISCARDED**: BLAST found each spacer inside its own host's CRISPR array, so
-  Y ≡ S. Informative cell = 0 of 3.1M pairs; self-targeting 13× enriched instead of depleted.
-- **Also discarded**: `blastn-short` defaults (word size 7, e-value 1) against an 8 GB database
-  did not terminate; re-run at word size 18 with in-BLAST identity filtering (exact for ≥95%
-  identity over 32 bp) completes in under 2 minutes.
-- **Final**: 1,767 CRISPR arrays (1.72 Mb) masked. 2,589 elements × 1,200 hosts = 3.1M pairs.
-  Informative cell 25,099; self-targeting depletion 0.539; ε = 0.000 from 2,589 decoys.
-### RUN-V3-CRISIS-PROX - CRISIS proximity test - ✅ (third null)
-7,314 defense/Cas pairs. Two nulls built and discarded (uniform-position → detected defense
-islands; label permutation → confounded by Cas interval length). Final: midpoint-to-midpoint under
-label permutation. **Result negative**: 0 systems within 5 genes, median distance 1,166.
-### RUN-V3-REALFIT - LEDGER fitted to real genomes - ✅ (second attempt)
-- **First attempt DISCARDED**: at 2,500 steps the model *with* free λ scored a lower likelihood
-  than the model *without* it - impossible for nested models, a signature of under-convergence.
-  Convergence swept: nesting correct from 6,000 steps, λ̂ stable (0.2663 / 0.2658 / 0.2668 at
-  6k / 12k / 20k). An automatic nesting check now runs on every fit.
-- **Final**: 1,200 × 2,421 × 108. λ̂ = 0.266, lineage bootstrap 95% CI [−0.288, 0.542];
-  α̂ = 0.017 (CI spans zero); ρ₁/ρ₀ = 0.307; LRT χ² = 507.6 on 1 df (reported as
-  anti-conservative). 30 bootstrap replicates over lineage clusters.
-### RUN-V3-S8 - CRISIS sweep with the embedded-subset absorber - ✅
-340 fits, 20 replicates per arm, all arms sharing planted α = −1.094. **ST-D FAILS**: the
-nominated absorber is the worst of three, recovering −16.3% / −116.7% / −12.4% and driving
-functional-arm α̂ bias from 17.3% to 41.8%.
-## v3 threshold outcomes
-| ID | Criterion | Observed | Result |
-|---|---|---|---|
-| HT-E | Real Y/S built with informative cell | 2,589 elements, 25,099 pairs | ✅ PASS |
-| HT-F | λ̂ with bootstrap interval | 0.266 [−0.288, 0.542] | ✅ PASS |
-| HT-G | CRISIS test with permutation null + BH | negative | ✅ PASS |
-| ST-D | Absorber recovers ≥80% | −117% | ❌ FAIL |
-| ST-E | Real λ̂ ≠ 0 | CI spans zero | ❌ FAIL |
-| ST-F | Self-targeting depleted | 0.539 | ✅ PASS |
-**Traceability**: `audit.py` 58/58 · `audit_v2.py` 76/76 · `audit_v3.py` 47/47 = **181/181**.