| --- |
| license: cc-by-4.0 |
| task_categories: |
| - tabular-classification |
| - tabular-regression |
| tags: |
| - physics |
| - electromagnetics |
| - verification |
| - interval-arithmetic |
| - formal-methods |
| - counterexamples |
| - eda |
| - parasitic-extraction |
| pretty_name: Screening Ceiling — Certified Regions and Counterexamples |
| size_categories: |
| - n<1K |
| configs: |
| - config_name: regions |
| data_files: data/certified_regions.jsonl |
| - config_name: counterexamples |
| data_files: data/counterexamples.jsonl |
| --- |
| |
| # screening-ceiling |
|
|
|       |
|
|
| 📖 **[Documentation site](https://nickharris808.github.io/physics-lint/)** — the portfolio narrative, the concepts, a full walkthrough, and what all of this proves (and does not). |
|
|
| **A machine-certified impossibility result about coupling extraction, plus the |
| concrete layouts where a plausible extractor predicts impossible physics.** |
|
|
| Most ML-for-physics datasets are samples: here are some inputs, here are the |
| answers, fit something. This one is different in a way worth being precise |
| about. It carries a **universal claim** — a statement about *every* layout in a |
| continuous four-parameter family, established by interval branch-and-bound |
| rather than by sampling — together with **existential counterexamples** that |
| refute a specific competing method. |
|
|
| ## Why this exists |
|
|
| When conductors are packed together, every other conductor screens the field |
| between any two. So a pair's mutual capacitance inside an array is at most its |
| isolated-pair value: |
|
|
| ``` |
| k = |C_full| / |C_iso| ≤ 1 |
| ``` |
|
|
| Pairwise-superposition extraction — used throughout fast parasitic extraction — |
| assumes `k ≡ 1`. The certified claim here is that on a particular manufacturable |
| family it is **provably never right**, and quantifies by how much: |
|
|
| > For every layout in the family box, `k ≤ 0.909090909091`. A pairwise extractor |
| > therefore over-predicts the worst coupling by **at least 10.000002%** on |
| > *every* member of the family — not on average, not usually, always. |
|
|
| And the other direction: a second-order Born correction, the obvious cheap fix |
| when a full solve is too slow, does not merely stay inaccurate — on 27 layouts |
| here it predicts `k > 1`, which is **anti-screening**, a physical impossibility. |
|
|
| ## 30-second quickstart |
|
|
| No install, no dependencies, nothing from the repository that produced it: |
|
|
| ```bash |
| python3 verify.py |
| ``` |
|
|
| ``` |
| screening-ceiling independent re-derivation (stdlib only) |
| |
| claim k <= 0.909090909091 for every layout in the family |
| forced error pairwise over-predicts by >= 10.0000% |
| |
| regions 256 x 25 samples = 6400 layouts |
| worst sampled k 0.903974725909 (bound 0.909090909091) |
| margin to bound 0.005116183182 |
| violations 0 |
| worst at region 3.0.3.3 d0_um=55.7830 jog_mult=0.3838 pt_mult=1.0009 sep_mult=4.4492 |
| |
| counterexamples 27/27 re-derived and confirmed above the ceiling |
| |
| consistent: no sampled layout exceeds the bound, and every counterexample re-derives |
| |
| scope: A complete interval theorem about the frozen MONOPOLE-CLOSURE model only. The closure-vs-BEM/PDE model gap remains additive and unresolved. This witness does not establish Maxwell, BEM, driven-S, fabrication, or measured-silicon truth. |
| ``` |
|
|
| `verify.py` rebuilds the electrostatics from the published geometry using the |
| standard library alone — its own Gauss-Jordan inverse, its own potential matrix. |
| It does not import this dataset's producer, numpy, or anything else. |
|
|
| **Sampling cannot prove the universal claim.** That is what the interval |
| branch-and-bound in the source proof is for. What sampling *can* do is refute |
| it, and that is the useful thing to hand a skeptical reader: a cheap, |
| dependency-free way to try to catch us being wrong. |
|
|
| ## Loading |
|
|
| ```python |
| from loader import load_regions, load_counterexamples, load_theorem |
| |
| theorem = load_theorem() |
| print(theorem["statement"]) |
| print(theorem["honest_scope"]) # read this one |
| |
| for c in load_counterexamples(): |
| print(c["case_id"], c["k_predicted"], c["n_pairs_violating"], "/", c["n_pairs_total"]) |
| ``` |
|
|
| Optional conveniences: `to_pandas("regions")` and `to_hf_dataset()`. |
|
|
| ## Contents |
|
|
| ### `data/certified_regions.jsonl` — 256 rows, the universal claim |
| |
| The branch-and-bound partition. Each row is one region of the family box that |
| the prover certified, having subdivided it into leaves until the interval |
| enclosure of `k` fell below the bound everywhere inside. |
| |
| | Field | Type | Meaning | |
| |---|---|---| |
| | `region_id` | string | position in the 4×4×4×4 root partition, e.g. `3.0.3.3` | |
| | `bounds` | object | `{d0_um, pt_mult, sep_mult, jog_mult} → {lo, hi}` | |
| | `status` | string | `CERTIFIED` for every row in this release | |
| | `certified_leaves` | int | leaves the region was subdivided into | |
| | `processed_leaves` | int | leaves examined, including interior splits | |
| | `sup_certified_k_hi` | float | largest `k` the enclosure admits anywhere in the region | |
| | `volume_fraction_of_region` | float | fraction certified (1.0 throughout) | |
| | `unresolved_leaves` | int | leaves left undecided (0 throughout) | |
|
|
| Totals: **237,490 certified leaves**, 474,724 processed, **0 failure regions**, |
| **0 unresolved**, certified volume fraction 1.0. |
|
|
| The published rows are the 256-region partition, **not** all 237,490 leaves — |
| the source proof records per-region certification and aggregate counts. That is |
| a real limitation of what is published and it is stated rather than glossed: you |
| can re-derive any region yourself, but you are not being handed every leaf. |
|
|
| ### `data/counterexamples.jsonl` — 27 rows, the existential refutation |
|
|
| Layouts where `born_second_order` predicts `k > 1`. |
|
|
| | Field | Type | Meaning | |
| |---|---|---| |
| | `case_id` | string | e.g. `born2_n6_p100_s1` | |
| | `model` | string | `born_second_order` | |
| | `n_conductors` | int | 6, 8 or 12 | |
| | `nominal_pitch_um` | float | 60, 80 or 100 | |
| | `seed` | int | generator seed | |
| | `worst_pair` | [int, int] | indices of the worst-violating pair | |
| | `k_predicted` | float | predicted screening factor (> 1 for every row) | |
| | `n_pairs_violating` | int | pairs above the ceiling in this layout | |
| | `n_pairs_total` | int | ordered pairs in this layout | |
| | `xy_um` | [[float, float]] | conductor centres, micrometres | |
| | `radius_um` | [float] | conductor radii, micrometres | |
| | `eps_r` | float | relative permittivity (4.6) | |
|
|
| **2,060 violating pairs** across the 27 layouts, worst `k = 3.5141`. Full |
| coordinates are included deliberately: a counterexample you cannot rebuild is an |
| anecdote, not evidence. |
|
|
| ### `data/theorem.json` — the claim, its scope, its provenance |
|
|
| The statement, the family box, the certified totals, the exact geometry |
| definition, and the SHA-256 of the source proof witness. |
|
|
| ## Geometry |
|
|
| Four parallel circular conductors forming two tight pairs: |
|
|
| ``` |
| pitch = 1.6 · d0 · pt_mult |
| separation = pitch · sep_mult |
| jog = jog_mult · separation |
| |
| centres: (0,0) (pitch,0) (separation,jog) (separation+pitch,jog) |
| every conductor has diameter d0 |
| ``` |
|
|
| Family box: `d0 ∈ [25,60] µm`, `pt_mult ∈ [1.0,1.2]`, `sep_mult ∈ [2.5,4.5]`, |
| `jog_mult ∈ [−0.4,0.4]`. Self-term radius scale 1.0. |
|
|
| `loader.family_layout(...)` builds it for you. |
|
|
| ## Scope, honestly |
|
|
| **This is a theorem about the monopole-closure model, not about Maxwell.** The |
| closure is a zero-parameter analytic multiple-scattering model that matches a |
| boundary-element reference to 0.081% in the exact two-cylinder limit, but the |
| closure-versus-solver gap is an **additive, disclosed, unresolved** term. It is |
| never absorbed into the bound. |
|
|
| That 0.081% comes from the boundary-element solver used to develop the closure, |
| which is **not part of this release** — so unlike every other figure on this |
| page, you cannot re-derive it from what is published here. It is quoted because |
| it bounds how much trust the closure has earned, and a reader is entitled to |
| know which numbers are checkable and which are taken on our word. |
|
|
| The scope line travels with the data, in `theorem.json`: |
|
|
| > A complete interval theorem about the frozen MONOPOLE-CLOSURE model only. The |
| > closure-vs-BEM/PDE model gap remains additive and unresolved. This witness does |
| > not establish Maxwell, BEM, driven-S, fabrication, or measured-silicon truth. |
|
|
| Three further limits worth stating plainly: |
|
|
| - **One family, not all layouts.** Four conductors in a specific arrangement. |
| Nothing here says anything about a different topology. |
| - **The bound is not tight.** The certified supremum is 0.90909089; the worst |
| layout found by adversarial search is ≈0.9053. The gap is the price of a |
| first-order interval relaxation, not a claim about physics. That 0.9053 is |
| the second figure on this page you cannot re-derive from the release — it |
| came from a differential-evolution search in the source prover. What you |
| *can* check here is weaker but points the same way: `verify.py` reports a |
| worst sampled `k` of 0.903974725909 at its defaults, and sampling harder |
| climbs toward that 0.9053 without ever reaching the bound — at `--seed 7`, |
| 25 / 100 / 400 samples per region give 0.902144353337, 0.903775408593, |
| 0.904308125283, with zero violations at each. |
| - **No measured data.** Every number is computational. |
|
|
| ## Reproduction |
|
|
| ```bash |
| python3 verify.py --samples 100 --seed 7 # sample harder, different seed |
| python3 verify.py --self-test # prove the checker still discriminates |
| python3 export.py --check # confirm data matches a fresh export |
| ``` |
|
|
| The self-test is the part that makes a clean report worth anything. It fabricates |
| an impossible bound, tampers with a published value, and requires the checker to |
| reject both — then confirms an isolated pair reproduces `k = 1.000000000000` |
| exactly, since a lone pair has nothing to screen it. |
|
|
| ## Troubleshooting |
|
|
| **`verify.py` reports violations** — that is the interesting outcome, and we |
| want to hear about it. Sampling cannot prove the bound but it can refute it, so |
| a genuine violation means the theorem is wrong. Before reporting, re-run with |
| `--self-test` to confirm the checker still discriminates: a checker that has |
| stopped working can produce either verdict. |
|
|
| **`ModuleNotFoundError: numpy` from `verify.py`** — it should never import |
| numpy. If it does, the file has been edited; the shipped version runs under |
| `env -i /usr/bin/python3` with nothing installed, and a test asserts it imports |
| no third-party module. |
|
|
| **`loader.to_pandas` or `to_hf_dataset` raises ImportError** — those two are |
| conveniences and do need `pandas` / `datasets`. Everything else, including |
| `verify.py`, is standard library only. |
| |
| **The Hub viewer shows two configs and you wanted one table** — `regions` and |
| `counterexamples` have different schemas and are deliberately separate. Pick the |
| config in the viewer's dropdown, or use `load_regions()` / `load_counterexamples()`. |
| |
| **`export.py --check` says the data does not match** — it re-derives the files |
| from the committed proof witness and compares. A mismatch means either the data |
| or the witness was edited. Counterexample regeneration also needs `maxwell-lint` |
| installed, since they are produced by running its reference models. |
| |
| **You want every certified leaf, not the 256 regions** — they are not published. |
| The source proof records per-region certification plus aggregate counts, so the |
| 237,490 leaves are attested but not enumerated here. That is a real limit of |
| this release and is stated rather than glossed. |
| |
| ## Provenance |
| |
| Exported by `export.py` from a committed proof witness produced by an |
| outward-rounded interval branch-and-bound prover (256 parallel roots, 243.5 s |
| wall clock, centered/mean-value enclosure forms). The witness digest is recorded |
| in `theorem.json`; `export.py --check` re-derives the files and compares. |
| |
| Counterexamples are generated by running the open-source |
| [`maxwell-lint`](https://github.com/nickharris808/maxwell-lint) reference models, so they are reproducible |
| from published code alone. |
| |
| ## Citation |
| |
| ```bibtex |
| @misc{screening_ceiling_2026, |
| title = {Screening Ceiling: Certified Regions and Counterexamples for |
| Many-Body Coupling Extraction}, |
| author = {ChipletOS / Genesis contributors}, |
| year = {2026}, |
| note = {CC-BY-4.0} |
| } |
| ``` |
| |
| ## The rest of the toolkit |
| |
| Eight artifacts that answer one question in different places: **is this |
| model physically possible?** Each is a grader — it can tell you a model is |
| wrong; none can tell you one is right. |
| |
| | | | |
| |---|---| |
| | [`sparam-lint`](https://github.com/nickharris808/sparam-lint) | Is an S-parameter model physically possible? Five laws + a negative control. | |
| | [`maxwell-lint`](https://github.com/nickharris808/maxwell-lint) | Does a coupling extractor predict impossible physics? Screening ceiling k ≤ 1. | |
| | [`abstain-bench`](https://github.com/nickharris808/abstain-bench) | Does a model know when to shut up? Abstention recall, never pooled with accuracy. | |
| | [`sparam-conformance`](https://huggingface.co/datasets/nickh007/sparam-conformance) | 11 labelled networks with verified ground truth. Grades the graders. | |
| | [`screening-ceiling`](https://huggingface.co/datasets/nickh007/screening-ceiling) ← you are here | A certified impossibility result + 27 counterexamples. Zero-dependency verifier. | |
| | [`physics-lint-action`](https://github.com/nickharris808/physics-lint-action) | The same checks, in your CI. | |
| | [`physics-lint-mcp`](https://github.com/nickharris808/physics-lint-mcp) | A physics oracle your AI agent can call. | |
| | [**Try it in your browser**](https://huggingface.co/spaces/nickh007/physics-lint) | All three checks, no install, runs client-side. | |
| |
| These tools **grade** a model. Producing one that is passive *by |
| construction* — so it cannot fail these laws whatever its parameters — and |
| accurate at speed in the many-body regime, with calibrated abstention and a |
| fail-closed signoff certificate, is the commercial core: |
| **[ChipletOS](https://chipletos.com)**. |
| |
| ## Licence |
| |
| **CC-BY-4.0.** Synthetic and computational throughout; no proprietary or |
| measured data. Attribution: ChipletOS / Genesis contributors. |
| |
| ## Related |
| |
| - [`maxwell-lint`](https://github.com/nickharris808/maxwell-lint) — run the ceiling test on *your* extractor |
| - [`sparam-conformance`](https://huggingface.co/datasets/nickh007/sparam-conformance) — the S-parameter analogue |
| - [ChipletOS](https://chipletos.com) — the closed core: a learned many-body |
| coupling operator that stays inside this ceiling and is accurate at speed, |
| with calibrated abstention and a fail-closed signoff certificate |
| |
| ## Contributing |
| |
| One non-negotiable rule here: the verifier must import nothing from this project, so a skeptic can read it in one sitting and run it with nothing installed. [`CONTRIBUTING.md`](CONTRIBUTING.md) has the detail. Each sibling repository states its own, and they differ — that is deliberate, and it is why each is trustworthy on its own terms. |
| |
