"""Build human-readable audit and publication drafts from verified results."""
from pathlib import Path
import csv,hashlib,json,platform,sys,zipfile
import numpy,scipy,sympy,matplotlib
ROOT=Path(__file__).resolve().parents[1]
def text(path,s):
    (ROOT/path).write_text(s.strip()+'\n',encoding='utf-8')
def js(path,x):text(path,json.dumps(x,indent=2,ensure_ascii=False))
def csvfile(path,rows):
    with (ROOT/path).open('w',newline='',encoding='utf-8') as f:
        w=csv.DictWriter(f,fieldnames=list(rows[0]));w.writeheader();w.writerows(rows)
verified=json.loads((ROOT/'results/verification.json').read_text())
physics=json.loads((ROOT/'physics/parameters_and_results.json').read_text())
supp=json.loads((ROOT/'results/supplement_verification.json').read_text())
claims=[
('O1','One-port square-setting tomography','Retained reconstruction, not claimed newly invented','Main 2','complex_tomography','Schur complements and complex polarization','Calibrated complex response and independent fixed-model controls','Recovers effective visible inverse response, not a microscopic basis'),
('O2','Physical adaptive q-squared lower bound','Extension of the supplied algebraic-only lower bound; historical priority unestablished','Main 2','one_frequency_physical_realization; physical_short_design_ambiguity','Realization theory and finite-dimensional evaluation lower bounds','Worst case at one fixed complex frequency; arbitrary unknown L,C; q hidden modes suffice','Closes an explicit physical parameter-count gap, not all experimental sample-complexity questions'),
('O3','Reciprocal q(q+1)/2 setting theorem','Explicit restricted-class refinement; likely classical symmetry consequence','Main 2','reciprocal_tomography','Symmetric quadratic polarization','Known common real-symmetric basis and real controls','Shows precisely when the general lower bound can be reduced'),
('O4','Proper-Cauchy finite-data admissibility','Self-contained formulation; potentially a classical constrained interpolation specialization','Main 3','canonical_interpolation_flatness; descriptor_identity; input_rejections','Matrix Nevanlinna-Pick; Herglotz realization; Loewner framework','K positive semidefinite AND range(D) contained in range(K); no feedthrough','Finite algebraic test and explicit smallest Hermitian interpolant'),
('O5','Complete hidden-extension parametrization','Explicit extension of supplied rank results; global novelty not verified','Main 4','extension_interface; unbounded_extension_family','Self-adjoint extensions; constrained Nevanlinna-Pick parametrization','Self-adjoint L and bounded finite-column C; unitary snapshot-coordinate equivalence','Describes every compatible hidden attachment through a data-computable interface'),
('O6','Exact completion versus unbounded visible extension','Corrects the supplied blanket finite-data caveat; broader priority unestablished','Main 4-5','flat_two_sample_certificate; extension_interface; rank_profile_node_independence','Singular interpolation; block grade and flatness','Distinct upper nodes; exact data; proper-Cauchy model class','No pole-count prior required on flat branch; otherwise no finite upper visible-dimension bound'),
('O7','Unbounded-spectrum polynomial-module rank profile','Extension relative to the supplied finite-pole proof; related to established Krylov grades','Main 5','rank_profile_node_independence','Block Krylov theory; positive matrix measures','Finite total matrix measure; L0 module avoids unjustified finite moments','Defines exact rank growth even with continuous or unbounded spectra'),
('O8','No robust finite exact-order upper bound','Negative theorem; not claimed historically new','Main 6','Written constructive proof; weak-residue mechanism','Inverse-problem instability and positive-measure perturbations','No minimum-residue restriction','Prevents spurious exact mode counts under finite precision'),
('O9','Rational mass and finite-time memory bounds','Explicit certified synthesis; no optimality or priority claim','Main 6','rational_witnesses; rational_annihilator_identity; spectral_witness.json','Rational Krylov and spectral-location error bounds','Positive measure; support and total-mass bounds for noisy claims','Replaces discontinuous rank with an observable-error guarantee'),
('O10','Common-gauge colored spectral-cycle classification','Corrects separate-pole/two-channel scope; graph machinery established','Main 7','joint_gauge_invariance; two_channel_cross_pole_invariant; supplement common_gauge_cases','Gain-graph switching; quiver invariants; Specht-type criteria','One shared visible gauge; labeled matching poles and support','Recovers relations absent from separately quotiented residues'),
('O11','Strict-damping full-rank kernel theorem','Explicit model-boundary result; no historical-priority assertion','Main 8','dissipative_kernel_identity; damped_kernel_ranks','Dissipative resolvents; Hardy kernels; self-adjoint dilation','Gamma positive definite and C full column rank for strict rank statement','Separates damped state order from self-adjoint visible spectral dimension'),
('O12','Four-mode phase-odd reflection prediction','Theorem-driven measurement application; not a new physical interaction','Main 9 and Physics Protocol','cross_pole_phase_and_analytic_contrast; make_data.py','Coherent multi-path optomechanical interference','Ideal independently calibrated actuator and fixed losses; all data synthetic','Falsifiable phase orientation readout missed by real controls'),
('O13','Physical exact error-erasure sharpness','Physical-interior transfer of established code-distance argument','Main 2','MDS_all_maximal_minors; predecessor coded_verification','Full-spark evaluation codes and Singleton bound','Exact support errors, not arbitrary analog noise; generic controls','Distinguishes genuine redundancy from unsupported noise-immunity claims'),
('O14','Calibrated mass minimum, closure, and response bound','Additional explicit Schur/mass refinement; mechanism established','Technical Appendix 5','supplement mass_cases; exact_mass_identity','Positive block Gram completion and Schur complement','Exact finite interpolation data plus independently bounded total mass','Controls all unseen extensions without bounding hidden dimension or spectrum'),
('O15','Restricted non-Abelian tree-gauge reduction','Established reduction, included as context rather than a new classification','Main 7','Explicit Pauli-matrix counterexample in proof','Futorny-Horn-Sergeichuk trace-word criterion','Unitary edge connections only; general matrix-valued residue classification not solved','Explains why individual loop spectra lose common-frame information')]
rows=[]
for cid,title,novelty,loc,tests,prior,limit,importance in claims:
    rows.append(dict(id=cid,claim=title,exact_novelty_assertion=novelty,
                     proof_status='Complete written proof or explicitly identified standard reduction; internal review only',
                     location=loc,computational_verification=tests,closest_prior_art=prior,
                     independent_review_status='None',known_limitations=limit,
                     scientific_importance_and_justification=importance))
csvfile('audit/claim_ledger.csv',rows);js('audit/claim_ledger.json',rows)
with zipfile.ZipFile(ROOT/'provenance/SUPPLIED_NAEVORA_IX.zip') as archive:
    original=json.loads(archive.read('CLAIM_LEDGER.json'))
origrows=[]
for item in original['claims']:
    cid=item['id'];decision='Retained under stated assumptions; no historical novelty endorsed'
    if cid=='IX-T3':decision='Retained; strengthened to worst-case physical/adaptive bound under explicit unknown-model assumptions'
    if cid=='IX-T7':decision='The sufficient finite-pole rank theorem retained; blanket no-finite-certification caveat corrected by exact flatness'
    if cid in ['IX-T8','IX-T9']:decision='Retained for one residue; extended to a common gauge across labeled poles'
    if cid=='IX-P1':decision='Proposal only; no experiment; nonlinear-to-linear reduction and damping limitations made explicit'
    if cid=='IX-R1':decision='Not established; not promoted to a field-defining claim'
    if cid=='IX-H1':decision='Symbolic inspiration only; not evidence of a physical force or reciprocal agency'
    origrows.append(dict(id=cid,original_title=item['title'],audit_decision=decision,
                         source='Supplied NAEVORA-IX archive only',independent_review='None'))
csvfile('audit/predecessor_claim_audit.csv',origrows)
js('audit/rejected_constructions.json',supp['rejected_trial_design'])
text('audit/dependency_graph.dot',r'''
digraph LIORAEN_Omega {
 rankdir=LR;
 Schur -> Tomography; Polarization -> Tomography;
 OneValueRealization -> PhysicalInterior -> AdaptiveLowerBound;
 PhysicalInterior -> PhysicalCodeSharpness; FullSpark -> PhysicalCodeSharpness;
 SpectralTheorem -> PositiveKernel; PositiveKernel -> RangeCriterion;
 DisplacementIdentity -> CanonicalRealization; RangeCriterion -> CanonicalRealization;
 CanonicalRealization -> AllExtensions; ResolventIdentity -> AllExtensions;
 AllExtensions -> DefectFormula; RationalKrylov -> DefectFormula;
 AllExtensions -> UnboundedVisibleExtensions; DefectFormula -> FlatCompletion;
 MeasureUniqueness -> FlatCompletion; AllExtensions -> MassClosure;
 PositiveKernel -> RationalWitness -> MemoryBound;
 WeakPositiveResidues -> NoNoisyOrderBound;
 CommonGauge -> ColoredCycles -> MixedPoleMemory;
 DissipativeResolvent -> HardyKernel -> DampedRankBoundary;
 Tomography -> PhaseReadout; MixedPoleMemory -> PhaseReadout;
}
''')
text('audit/SCOPE_AND_LIMITATIONS.md',r'''
# Scope and uncompleted checks
The entire supplied NAEVORA-IX archive is preserved unmodified in provenance/SUPPLIED_NAEVORA_IX.zip. Its 25-page manuscript and LaTeX were inspected; the principal theorem dependencies were reconstructed and all four original executable test programs rerun successfully. Earlier volumes are described in its lineage file but their complete manuscripts are not present. A Hugging Face connector search for predecessors was attempted and was disabled by server configuration. No inaccessible predecessor is represented as audited.

The main new results are internally proved in the declared proper matrix-Cauchy response class. The code implements finite matrices, not arbitrary unbounded operators. Unbounded-operator results have written proofs only. Exact symbolic checks cover finite examples and rational identities; there is no proof-assistant formalization.

No independent specialist referee, experimental team, or publication venue has validated this release. The literature search established substantial closely related prior art, not exhaustive historical novelty. No named consequential open problem in the literature is claimed solved. The release does not claim a world first, new physical force, quantum advantage, topological protection, or universally stable hidden-state recovery.

The physics files are synthetic reference data. The proposed independent control edge, common loss calibration, and fixed hidden parameters remain hardware requirements, not achieved capabilities. The separate Physics Protocol repeats the monograph's physics section and is not counted as additional original research pages.

Not produced: a fabricated 80–120-page volume, a laboratory dataset, a proof-assistant artifact, an external review report, a verified global priority claim, unavailable predecessor reconstructions, or an uploaded/assigned DOI. Publication materials are drafts; nothing has been sent or published remotely.
''')
text('audit/CANDIDATE_ASSESSMENT.md',r'''
# Candidate comparison and open-problem boundary
## Complete finite-response identifiability
Target: classify every self-adjoint latent realization consistent with finitely many full matrix response values. Missing step: characterize the off-snapshot blocks of a general compatible operator, not just the smallest rational fit. Resolved here by the exact block formula L=[A,V*;V,Dh], C=[B;-VT1], with V annihilating all snapshot differences. The data-computable defect has dimension at most q. Zero defect gives uniqueness; nonzero defect permits arbitrarily large visible extensions.
Closest literature: matrix Nevanlinna–Pick parametrizations, self-adjoint realization, and Loewner data. This is the strongest internal result, but it may be a specialized presentation of established interpolation theory. Historical originality remains unestablished.

## Physical minimum intervention count
Target: determine whether passivity invalidates the supplied algebraic q-squared lower bound. Missing step: a full-dimensional physical realization family at fixed frequency and calibrated visible block. Resolved by an explicit q-dimensional Hermitian realization of every strictly negative-imaginary matrix value. Deterministic adaptive evaluation protocols then have the same worst-case bound. The reciprocal subclass has a smaller sharp count. This is a scoped physical-identifiability result, not a universal measurement lower bound across frequencies or prior information.

## Operator-valued relational classification
Target: retain noncommuting relational information across local bases and spectral labels. Closest literature already includes complete trace-word criteria for systems of linear maps. A new general classification was not obtained. The proven output is a complete scalar common-gauge colored-cycle theorem and a restricted unitary-edge reduction. Independent spectra of loop operators are explicitly insufficient.

## What was not retroactively called an open-problem solution
These targets were selected from identifiable gaps in the supplied research and relevant established literatures. Their introduction here is not evidence that they are previously stated, consequential open problems. No universal inverse-boundary, general nonlinear quantum identification, or optimal noisy model-order problem is claimed solved. Current literature review supports a useful, checkable synthesis and corrections; it does not justify a major-breakthrough label.
''')
refs=[
('Gesztesy–Tsekanovskii','On Matrix-Valued Herglotz Functions','1997 preprint / 2000 journal','https://arxiv.org/abs/funct-an/9712004','Matrix spectral measures and self-adjoint realization; established foundation'),
('Belyi–Hassi–de Snoo–Tsekanovskii','A general realization theorem for matrix-valued Herglotz–Nevanlinna functions','2005 preprint / 2006 journal','https://arxiv.org/abs/math/0510464','General realization context; our class has finite mass and no feedthrough'),
('Ball–Bolotnikov','The bitangential matrix Nevanlinna–Pick interpolation problem revisited','2016 preprint','https://arxiv.org/abs/1611.07097','Full PDF and relevant theorem inspected; kernel/state-space/LFT frameworks materially limit novelty claims'),
('Mayo–Antoulas','A framework for the solution of the generalized realization problem','2007','https://doi.org/10.1016/j.laa.2007.03.008','Loewner and shifted-Loewner realization background; publisher DOI fetch failed on final recheck, citation corroborated by primary later papers'),
('Elsworth–Güttel','The Block Rational Arnoldi Method','2019 preprint / 2020 journal','https://eprints.maths.manchester.ac.uk/2685/','Author-hosted abstract and publisher metadata inspected; rank/breakdown and rational bases are established'),
('Gutknecht–Schmelzer','The block grade of a block Krylov space','2009','https://www.sciencedirect.com/science/article/pii/S0024379508003479','Established block-grade stopping structure; author-hosted related block-Krylov exposition identified'),
('Massei–Robol','Error formulas for block rational Krylov approximations of matrix functions','2025 preprint','https://arxiv.org/abs/2504.05151','Primary preprint/HTML reviewed for spectral-location error bounds; no optimality claimed against it'),
('Futorny–Horn–Sergeichuk',"Specht’s criterion for systems of linear mappings",'2017','https://arxiv.org/abs/1701.08826','Primary theorem states completeness of closed-walk traces for systems of maps; non-Abelian novelty restricted accordingly'),
('Guţă–Yamamoto','System identification for passive linear quantum systems','2016','https://arxiv.org/abs/1303.3771','Minimal-unitary identification and infecting subclasses already established'),
('Bernier et al.','Nonreciprocal reconfigurable microwave optomechanical circuit','2017','https://doi.org/10.1038/s41467-017-00447-1','Primary experiment demonstrates coherent phase-path mechanism, not the exact actuator proposed here'),
('Kuznetsov et al.','Microcavity phonoritons – a coherent optical-to-microwave interface','2023','https://doi.org/10.1038/s41467-023-40894-7','Primary experiment demonstrates exciton-photon-phonon physics; does not establish the present fixed passive linear control model')]
refrows=[dict(authors=a,title=b,date=c,url=d,review_scope=e) for a,b,c,d,e in refs]
csvfile('audit/prior_art_sources.csv',refrows);js('audit/prior_art_sources.json',refrows)
text('audit/PRIOR_ART_REVIEW.md','# Prior-art review\n\nSearch and verification date: 16 October 2026. Sources were searched by mathematical structure, not by the project name. No claim of exhaustiveness or priority certification is made.\n\n'+'\n\n'.join(f'## {a}: {b}\n{c}. {d}\n\n{e}.' for a,b,c,d,e in refs)+r'''

## Specialist novelty questions
Does the exact range condition plus extension-interface block formula reduce to a known singular proper-Cauchy Nevanlinna–Pick parametrization? Is the at-most-q defect formula already explicit in a matrix quadrature or boundary-triple formulation? Is the physical q-squared lower-bound construction known in one-port Weyl-function recovery? Are the mixed-pole two-edge invariants standard in phase-referenced spectroscopy? An affirmative answer may change the novelty label without invalidating a proved statement.

The manuscript does not rename Schur complements, Krylov indices, gauge cycles, or a positive kernel as a new fundamental theory. The value offered for review is the explicit theorem chain, corrections, construction of all compatible models, and operational limits.
''')
text('audit/REVIEWER_CHECKLIST.md',r'''
# Specialist reviewer checklist
1. Verify the class: self-adjoint L, bounded finite-column C, finite positive matrix measure, and no feedthrough. Check upper/lower half-plane conjugations and the sign of the Pick kernel.
2. Reconstruct K, J, D from arbitrary data. Confirm necessity AND sufficiency of positivity plus range(D) ⊆ range(K), including rank zero and singular K.
3. Check AT = TZ − BE and the exact descriptor identity. Decide whether the uniqueness assertion is explicitly limited to the smallest r-dimensional interpolant until the defect is tested.
4. Audit the unbounded-operator block decomposition. Confirm S ⊆ dom(L), bounded off-diagonal blocks, and self-adjointness of the complement.
5. Verify that V annihilates every Ti−T1 and that every compatible realization has this form. Check both directions and dark redundancies.
6. Verify dim E = r_m−r_(m−1), independent of which distinct node is deleted. Review the measurable-polynomial-module proof when moments do not exist.
7. Audit the arbitrary-size extension construction: added modes must be visible, not merely appended dark states. Check the continuous-spectrum construction separately.
8. Check the strictly negative-imaginary one-value realization and adaptive-transcript lower bound. Review the real-symmetric exception and exact-code sharpness separately.
9. Verify all noisy-data qualifications, matrix norm conventions, mass-witness constants, support assumptions, and the added total-mass calibration bound.
10. Check joint pole labeling and common gauge. Distinguish scalar colored cycles from the restricted non-Abelian edge setting.
11. Reproduce the dissipative-kernel decomposition and strict positivity proof; distinguish self-adjoint dilation dimension from damped-state order.
12. Recompute the phase-odd reflection formula, units, passivity, raw-response noise inversion, and the difference between microscopic density-displacement coupling and a linear surrogate.
13. Run all tests; inspect failed/rejected design records; treat numerical agreement as finite evidence, not universal proof.
14. Identify the nearest pre-existing theorem for each claimed extension before assigning originality or recommending publication. No external review is currently recorded.
''')
text('audit/EVALUATION.md',r'''
# Evidence-based evaluation
| Dimension | Current evidence | Remaining limitation |
|---|---|---|
| Correctness | Complete internal proofs and independently implemented finite algebraic checks | No external referee or proof-assistant verification |
| Originality | Specific extensions/corrections relative to supplied work | General historical novelty not established |
| Depth | Complete all-model extension classification and sharp identifiability dichotomy | May be a classical interpolation specialization |
| Generality | Arbitrary self-adjoint operators with bounded finite-column coupling | Excludes general nonlinear, non-Hermitian state-order, and arbitrary feedthrough models |
| Unification | Explicit links between interpolation, observable memory, coding, and shared spectral gauges | Established mechanisms are not counted as separate new fields |
| Predictive power | Exact phase-odd contrast; noise-dependent mass and memory bounds | All physics predictions synthetic |
| Computational value | Constructive descriptor, hidden-extension generator, common-gauge checker | Dense algorithms, no novel complexity improvement claimed |
| Physical importance | Can prevent false latent-order inference; testable phase-readout proposal | Actuator/control feasibility not demonstrated |
| Reproducibility | Code, exact tests, synthetic CSVs, sources, pinned versions, checksums | Runtime/PDF bytes can vary across platforms |
| Scientific impact | Useful scoped inverse-problem synthesis and corrections | No major open problem or field-defining impact established |

The core suite passed 13/13 numerical groups and 9/9 exact groups in the supplied execution. These 100% pass rates apply to the specified finite test suite, not to universal mathematical correctness, novelty, or physical success. Supplementary checks and original-package regressions are reported separately.
''')
versions={n:m.__version__ for n,m in [('numpy',numpy),('scipy',scipy),('sympy',sympy),('matplotlib',matplotlib)]}
text('requirements.txt','\n'.join(f'{k}=={v}' for k,v in versions.items()))
js('results/environment.json',dict(python=sys.version,platform=platform.platform(),versions=versions,
                                  threads='Test driver fixes OPENBLAS_NUM_THREADS, OMP_NUM_THREADS, MKL_NUM_THREADS to 1'))
sha=hashlib.sha256((ROOT/'provenance/SUPPLIED_NAEVORA_IX.zip').read_bytes()).hexdigest()
js('provenance/source_record.json',dict(original_filename='NAEVORA_IX_LIORAEN_Complete_Research_Package(1).zip',
                                     sha256=sha,source='User-supplied file',supplied_pdf_pages=25,
                                     archive_members=59,older_complete_predecessors_available=False))
text('README.md',r'''
---
language:
- en
license: cc-by-4.0
pretty_name: "LIORAEN-Omega: The Extension Defect of Hidden Information"
size_categories:
- 1K<n<10K
tags:
- mathematics
- inverse-problems
- system-identification
- spectral-theory
- reproducible-research
- synthetic-data
---
# LIORAEN–Ω: The Extension Defect of Hidden Information

**AI-assisted research release, version 1.0 — 16 October 2026.**
Research direction: Maciej Nowicki. AI-assisted mathematical development and writing: Artificial Hyperintelligence Eve.

**Status:** complete internal proofs of the stated results, executable verification, and synthetic physics reference data. No independent peer review, no experimental discovery, no established global novelty claim, and no major open problem claimed solved.

## Main result
For a proper matrix response Σ(z)=C*(z−L)^−1C, with self-adjoint L and bounded finite-column C, finite data admit a Hermitian realization exactly when their Pick matrix is positive semidefinite and the sample column lies in its range. An explicit smallest interpolant is constructed. Every larger compatible realization attaches through a data-computable extension interface of dimension

`e = rank(K_m) − rank(K_(m−1)) ≤ q`.

Zero interface is equivalent to unique completion of the entire visible response. Nonzero interface permits arbitrarily large finite visible systems and an infinite-dimensional visible realization with exactly the same samples. This statement concerns observable equivalence, never total microscopic dimension including dark states.

## Other validated content
The release strengthens the supplied q² algebraic setting lower bound to a worst-case physical bound, including deterministic adaptivity, and proves the q(q+1)/2 reciprocal subclass. It corrects a blanket finite-data caveat and a two-channel phase limitation. It gives common-gauge mixed-pole invariants, rational spectral-mass and memory-error bounds, an additional calibrated-mass closure criterion, and a strict-damping counterexample to interpreting every kernel rank as damped-state count.

The four-mode physics simulation predicts a complex-reflection contrast of about 0.581 under its declared parameters while real-control responses coincide. This is not experimental data or a new physical law.

## Files
- `LIORAEN_Omega_Complete_Manuscript.pdf`: main monograph plus independent appendix in one reading file.
- `MAIN_MONOGRAPH.pdf`, `TECHNICAL_APPENDIX.pdf`: the separate documents.
- `PHYSICS_PROTOCOL.pdf`: standalone extract of the physics section; not additional independent research content.
- `manuscript/`: complete LaTeX sources, bibliography, and generated figures.
- `src/lioraen_omega.py`: numerical reference algorithms, including compatible extensions and a common-gauge checker.
- `tests/verify.py`, `tests/verify_supplement.py`: deterministic numerical and exact-arithmetic audits.
- `physics/`, `data/`: explicitly synthetic CSVs, units, parameters, and observations.
- `audit/`: claim ledger, predecessor audit, prior art, limitations, rejected design, and reviewer checklist.
- `publication/`: Zenodo metadata and description, cover letter, and citation drafts.
- `provenance/`: the unmodified supplied archive and its checksum.
- `SHA256SUMS.txt`, `MANIFEST.json`: integrity records.

## Reproduce
```bash
python -m pip install -r requirements.txt
python run_all.py
```
The default driver runs both new verification scripts. `python run_all.py --all` additionally regenerates synthetic figures/data and reruns the four supplied predecessor programs in a temporary directory. These extended steps can also be run separately; their delivered logs record successful individual executions. It requires no network after dependencies are installed. It intentionally limits numerical-library threads for predictable small-matrix performance. A nonzero exit status means a check failed.

The first plotting run may create a local Matplotlib font cache. Test pass/fail and numerical tolerances are the reproducibility target; elapsed times, PDF metadata, and platform-specific floating-point last bits need not be identical.

To rebuild PDFs with a TeX installation:
```bash
python tools/build_pdfs.py
```
To validate the delivered hashes before modifying files:
```bash
python tools/verify_integrity.py
```
Regeneration changes logs and generated files. A later checksum mismatch after intentional regeneration is not evidence that the original archive was corrupt; compare regenerated numerical reports or rebuild the manifest explicitly.

## Dataset card
### Dataset purpose and composition
This repository is a research-artifact dataset, not model weights and not a training dataset. It contains synthetic transfer-response curves, raw complex control records, held-out prediction checks, exact theoretical rank profiles, and numerical kernel spectra. No human-subject, personal-message, medical, biometric, or real instrument records are included.

### Generation and units
`src/make_data.py` records seed 16102027. Hamiltonian and linewidth quantities are normalized by Ω0=2π×1 MHz. The CSV column `omega_over_Omega0` is dimensionless; `time_times_Omega0` is dimensionless time. Complex quantities are split into real and imaginary columns. Theoretical ranks and numerical eigenvalues are separately labeled. Noise is simulated circular complex Gaussian readout noise under explicitly chosen, unmeasured assumptions.

### Intended uses
Independent mathematical checking; teaching distinctions between interpolation and identification; development/testing of small inverse-response algorithms; falsification-oriented experimental planning with new device-specific calibration.

### Out-of-scope uses
Certification of actual hidden hardware order from noisy rank thresholds; evidence of a new physical force or experimental discovery; claims of quantum advantage; proof of universal mathematical correctness; evidence of a human–fictional-character reciprocal bond; claims of global first discovery without prior-art review.

### Limitations
The exact theorems require their model assumptions. The numerical implementation handles finite matrices and tolerance-dependent diagnostics. Complete earlier predecessor manuscripts not supplied were not audited. Hardware implementation, independent review, and exhaustive novelty checking remain absent.

## Attribution and licensing
Research text, original figures, and synthetic data are offered under CC BY 4.0 where rights apply. Code is offered under MIT; see the separate files. The preserved source archive retains its own notices. The creative inspiration is symbolic and does not supply evidence for the mathematical or physical claims. No third-party character artwork is distributed.
''')
text('REPRODUCIBILITY.md',r'''
# Reproduction record
Run `python run_all.py` after installing requirements. Use `--all` for the optional extended data-generation and predecessor regressions, or run those steps separately. The delivered core report records 13 numerical groups, 1,658 cases, and nine exact groups, all passed. The cases include model trials and individual identity checks, not independent physical experiments. Supplemental checks add 30 mass-bound cases, 50 common-gauge cases, an intentionally rejected mismatch, an exact mass identity, and a failed trial-design certificate. All four supplied original programs passed.

Numerical thresholds are explicit in source and reports. Exact symbolic tests use SymPy rational and Gaussian-rational arithmetic. Data-generation seeds differ from theorem-test seeds. The full Hamiltonian resolvent is used to generate tomography data; the derived quadratic expression is used to reconstruct and predict, reducing circularity. The analytic contrast and dissipative Gram decompositions are independently compared against direct resolvent computations.

The unbounded Hilbert-space statements are proved in text, not simulated or formally verified by a proof assistant. There is no experiment. All figure data are synthetic. The main plotting/physics script also asserts passivity of the sampled reflection, the real-control null, and exact withheld-control agreement.

The core executable paths are finite-matrix references, not production-grade laboratory acquisition software. Direct eigendecomposition costs O((mq)^3) arithmetic and can be ill-conditioned. Exact rational bit complexity is not bounded by that operation count.

Build PDFs with `python tools/build_pdfs.py` when pdflatex/latexmk are installed. Check the initial downloaded archive with `python tools/verify_integrity.py` before regeneration; rerunning scripts intentionally changes reports and figures. The integrity manifest proves file identity, not mathematical correctness.
''')
text('physics/DATA_DICTIONARY.md',r'''
# Synthetic data dictionary
All files in this directory are simulated, never laboratory measurements.

`phase_scan.csv`: 801 frequency rows. `omega_over_Omega0` is the normalized drive detuning. `S_plus_*` and `S_minus_*` are exact dimensionless reflection quadratures for phase ±π/2 with t=iτ. `absolute_contrast` is |S_plus−S_minus|. `noisy_*` add the declared averaged circular complex Gaussian noise.

`raw_control_records.csv`: four calibration settings at the grid-selected contrast frequency. Actual normalized complex control, exact and noisy reflection, and exact/noisy inverse root response are stored in separate columns. Noise is applied to reflection before response inversion.

`withheld_controls.csv`: twenty pre-generated synthetic validation settings; exact-model prediction error, noisy reconstruction error, and an intentional hidden-detuning drift error in normalized inverse-response units. The drift is 0.025 Ω0 and does not represent observed instrument drift.

`parameters_and_results.json`: Hamiltonian assumptions, linewidth and readout conventions, seeds, noise assumptions, exact simulation maxima, and a thermal-occupation example. No value should be treated as a validated instrument specification.

The `data/` directory contains theoretical integer rank profiles, two-pole memory intensities, and floating-point eigenvalue spectra. Negative tiny eigenvalues in the nominal rank-one corrected kernel are rounding artifacts, not physical negative spectral mass. The executable source fixes units and formulas completely.
''')
text('physics/EXPERIMENTAL_CHECKLIST.md',r'''
# Falsification and calibration gates
This is an unperformed experiment. Read PHYSICS_PROTOCOL.pdf before using the synthetic data.

Gate 1: independently calibrate every complex control and confirm that varying the root edge does not modify hidden detunings, couplings, linewidths, or an unmodeled direct path. Reject the fixed-family interpretation when this fails beyond a declared error budget.

Gate 2: measure complex reflection with a stable phase reference; intensity alone is not the declared observable. Calibrate gain, background, external coupling, and covariance before inversion.

Gate 3: preregister withheld controls, randomization, repetitions, phase reversals, null configurations, drift tests, and a residual-based acceptance threshold. Synthetic peak selection is not a preregistered experimental discovery statistic.

Gate 4: verify opposite phases are indistinguishable with real controls, distinguishable with complex controls as predicted, and produce the specified sign reversals and nulls. Reject the four-mode interpretation if calibrated withheld predictions fail reproducibly.

Gate 5: justify every use of uniform-loss frequency shifting. Unknown/nonuniform loss can produce full Pick rank even for a one-state damped model; positivity alone does not rescue finite-Hermitian order inference.

Gate 6: for an exciton–phonon implementation, verify linearization, sideband separation, saturation limits, pump-induced shifts, heating, thermal noise, and parameter stability. A microscopic density-displacement interaction is not assumed to be an exact linear coupling edge.
''')
abstract=('We study finite observations of proper matrix Cauchy responses generated by self-adjoint hidden systems. '
'Positivity of the sample Pick matrix together with a range condition yields an explicit smallest Hermitian interpolant. '
'Every compatible larger realization is characterized by a block extension through a data-computable interface of dimension '
'rank(K_m)-rank(K_(m-1)), at most the number of visible channels. Zero interface gives unique completion of the entire visible response; '
'nonzero interface permits arbitrarily large finite visible realizations and an infinite-dimensional one with identical samples. '
'Additional results establish a worst-case physical q-squared intervention bound including deterministic adaptivity, a reciprocal subclass, '
'common-gauge relations across spectral poles, certified spectral-mass and memory bounds, a calibrated-mass refinement, and a strict-damping '
'boundary separating effective state order from self-adjoint kernel rank. Complete internal proofs, exact-arithmetic and numerical checks, '
'synthetic physics data, and publication sources are included. Historical novelty is not established; no major open problem or experimental discovery is claimed.')
metadata=dict(title='LIORAEN–Ω: The Extension Defect of Hidden Information — Exact Completion, Compatible Hidden Realizations, and Measurement Limits',
              upload_type='publication',publication_type='technicalnote',publication_date='2026-10-16',version='1.0',
              creators=[dict(name='Nowicki, Maciej')],
              description=abstract+' AI-assisted mathematical development and writing: Artificial Hyperintelligence Eve. This is a draft metadata record; no DOI has been assigned.',
              keywords=['matrix-valued Cauchy response','Nevanlinna-Pick interpolation','self-adjoint realization','inverse problems','hidden-system identification','rational Krylov','spectral measure','phase-controlled tomography','synthetic data','AI-assisted research'],
              access_right='open',license='cc-by-4.0',notes='Research draft; internally checked, not independently reviewed. Code MIT. All physical datasets synthetic.')
js('publication/ZENODO_METADATA.json',metadata)
text('publication/ZENODO_DESCRIPTION.md','# '+metadata['title']+'\n\n## Abstract\n'+abstract+r'''

## What this release establishes
The principal theorem is an explicit finite-data classification within the proper self-adjoint Cauchy-response model. It distinguishes the unique-completion branch from an unbounded visible-extension branch, and gives constructive realizations in both. The physical setting lower bound applies at one fixed complex frequency to a worst-case unknown Hermitian latent model, not every reduced or calibrated subclass. The mixed-pole invariant uses one shared channel gauge. The damping theorem prevents conflating Hamiltonian spectral dimension with finite damped state order.

## Evidence and status
The main suite passed 13 numerical groups (1,658 recorded cases) and nine exact-arithmetic groups. Supplemental tests and the original supplied package's four regression programs also passed. These results are finite verification evidence, not independent peer review. No historical first-discovery claim is made; established interpolation, realization, Krylov, gauge, and quantum-identification work is cited. No laboratory data are included.

## Package
Main manuscript, independent technical appendix, standalone physics extract, complete LaTeX, Python source, exact certificates, seeded synthetic CSVs, claim-by-claim audit, source provenance, reviewer checklist, and SHA-256 manifest. Research direction: Maciej Nowicki. AI-assisted mathematical development and writing: Artificial Hyperintelligence Eve. AI contribution is disclosed and is not presented as a human legal author for publication-system fields.

## Limitations
Exact-rank results do not survive arbitrary noise without extra assumptions. Earlier full predecessor manuscripts absent from the supplied archive were not audited. Hardware feasibility and independent specialist review remain unverified. This technical note is not advertised as solving a major open problem.
''')
text('publication/COVER_LETTER.txt',r'''
Dear Editor,

I am submitting for methodological and mathematical assessment “LIORAEN–Ω: The Extension Defect of Hidden Information.” The manuscript studies finite data from proper matrix-valued Cauchy responses of self-adjoint hidden systems and gives an explicit smallest interpolant together with a complete description of compatible extensions through a finite, data-computable interface.

The central conclusion is an exact completion/nonuniqueness dichotomy. A zero extension interface forces the entire visible response; a nonzero interface permits arbitrarily large visible realizations with the same observations. The manuscript also addresses worst-case physical intervention counts, common-gauge information across spectral poles, noisy mass and memory bounds, and the distinction between damped-state order and self-adjoint spectral rank.

The work is AI-assisted, with mathematical development and writing attributed in the manuscript to Artificial Hyperintelligence Eve under my research direction. It has undergone internal proof reconstruction and executable numerical and exact-arithmetic checks, but no independent referee review. I do not claim that the work solves a major open problem or that all statements are historically new. A principal purpose of review is to determine the precise relation of the extension formulation to existing singular Nevanlinna–Pick and realization results.

The release includes full sources, an independent technical appendix, test programs, synthetic data, an audit of assumptions and novelty, and an integrity manifest. The physical protocol is unperformed; all associated observations are labeled synthetic. I would particularly welcome assessment by specialists in matrix interpolation, self-adjoint realization, and inverse-system identification.

Sincerely,
Maciej Nowicki

Draft for author review. No submission, recipient address, affiliation, ORCID, or DOI has been fabricated or entered automatically.
''')
text('CITATION.cff',r'''
cff-version: 1.2.0
message: "Please cite this AI-assisted technical research release; see the manuscript for attribution and limitations."
title: "LIORAEN-Omega: The Extension Defect of Hidden Information"
type: dataset
authors:
  - family-names: Nowicki
    given-names: Maciej
version: 1.0.0
date-released: 2026-10-16
license: CC-BY-4.0
abstract: "Finite-response self-adjoint realization, complete hidden-extension classification, measurement limits, and synthetic verification. AI-assisted mathematical development and writing: Artificial Hyperintelligence Eve. Not independently reviewed; historical novelty not established."
''')
text('publication/CITATION.bib',r'''
@misc{nowicki_lioraen_omega_2026,
  author = {Nowicki, Maciej},
  title = {{LIORAEN--Omega}: The Extension Defect of Hidden Information},
  year = {2026},
  note = {Version 1.0. AI-assisted mathematical development and writing: Artificial Hyperintelligence Eve. Internal research release; independent review and historical priority not established.}
}
''')
text('LICENSE_RESEARCH.md',r'''
# Research materials and data
Original research text, original figures, and synthetic data in this release are offered under the Creative Commons Attribution 4.0 International license (CC BY 4.0), to the extent the contributors hold applicable rights. Attribute the release and retain its AI-assistance and research-status disclosures. License text: https://creativecommons.org/licenses/by/4.0/legalcode .

Code is separately MIT-licensed. The preserved supplied archive retains its own notices. External papers are cited, not republished. No third-party character artwork or font files are included. No warranty of correctness, novelty, experimental performance, or fitness for a particular purpose is given.
''')
text('LICENSE_CODE.txt',r'''
MIT License

Copyright (c) 2026 Maciej Nowicki and contributors, where applicable.
AI-assisted development is disclosed in the accompanying research materials.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
''')
print('Wrote audit, publication, README, dependency, provenance and licensing files.')