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Initial release: 256 certified regions, 27 counterexamples, zero-dependency verifier

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.github/workflows/ci.yml ADDED
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+ name: CI
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+ on: { push: { branches: [main] }, pull_request: {}, workflow_dispatch: {} }
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+
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+ jobs:
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+ test:
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+ runs-on: ubuntu-latest
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+ steps:
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+ - uses: actions/checkout@v4
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+ - uses: actions/setup-python@v5
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+ with:
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+ python-version: '3.12'
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+ - run: pip install pytest ruff
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+ - name: Dataset claims hold against the data
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+ run: pytest -q
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+ - name: Lint
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+ run: ruff check .
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+
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+ zero-dependency:
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+ name: the verifier really has no dependencies
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+ runs-on: ubuntu-latest
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+ steps:
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+ - uses: actions/checkout@v4
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+ - uses: actions/setup-python@v5
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+ with:
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+ python-version: '3.12'
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+ # Deliberately no pip install. If verify.py has picked up a third-party
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+ # import, this job fails -- which is the whole promise of the artifact.
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+ - name: Re-derive with a bare interpreter
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+ run: python3 verify.py --samples 10
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+ - name: The checker still discriminates
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+ run: python3 verify.py --self-test
.gitignore ADDED
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+ __pycache__/
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+ *.py[cod]
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+ build/
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+ dist/
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+ *.egg-info/
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+ .pytest_cache/
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+ .ruff_cache/
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+ .venv/
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+ venv/
LICENSE ADDED
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+ Creative Commons Attribution 4.0 International (CC BY 4.0)
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+
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+ Copyright 2026 ChipletOS / Genesis contributors
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+
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+ You are free to:
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+ Share — copy and redistribute the material in any medium or format
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+ Adapt — remix, transform, and build upon the material for any purpose,
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+ even commercially.
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+
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+ Under the following terms:
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+ Attribution — You must give appropriate credit, provide a link to the
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+ license, and indicate if changes were made. You may do so in any reasonable
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+ manner, but not in any way that suggests the licensor endorses you or your
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+ use.
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+
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+ No additional restrictions — You may not apply legal terms or technological
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+ measures that legally restrict others from doing anything the license permits.
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+
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+ Full licence text: https://creativecommons.org/licenses/by/4.0/legalcode
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+
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+ THE MATERIAL IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND.
README.md ADDED
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+ ---
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+ license: cc-by-4.0
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+ task_categories:
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+ - tabular-classification
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+ - tabular-regression
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+ tags:
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+ - physics
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+ - electromagnetics
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+ - verification
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+ - interval-arithmetic
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+ - formal-methods
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+ - counterexamples
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+ - eda
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+ - parasitic-extraction
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+ pretty_name: Screening Ceiling — Certified Regions and Counterexamples
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+ size_categories:
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+ - n<1K
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+ configs:
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+ - config_name: regions
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+ data_files: data/certified_regions.jsonl
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+ - config_name: counterexamples
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+ data_files: data/counterexamples.jsonl
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+ ---
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+
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+ # screening-ceiling
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+
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+ ![Licence](https://img.shields.io/badge/data-CC--BY--4.0-green) ![Regions](https://img.shields.io/badge/certified%20regions-256-blue) ![Leaves](https://img.shields.io/badge/certified%20leaves-237%2C490-blue) ![Counterexamples](https://img.shields.io/badge/counterexamples-27-orange) ![Verifier](https://img.shields.io/badge/verifier-zero%20dependency-brightgreen) ![Tests](https://img.shields.io/badge/tests-30%20passing-brightgreen)
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+
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+ **A machine-certified impossibility result about coupling extraction, plus the
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+ concrete layouts where a plausible extractor predicts impossible physics.**
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+
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+ Most ML-for-physics datasets are samples: here are some inputs, here are the
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+ answers, fit something. This one is different in a way worth being precise
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+ about. It carries a **universal claim** — a statement about *every* layout in a
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+ continuous four-parameter family, established by interval branch-and-bound
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+ rather than by sampling — together with **existential counterexamples** that
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+ refute a specific competing method.
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+
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+ ## Why this exists
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+
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+ When conductors are packed together, every other conductor screens the field
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+ between any two. So a pair's mutual capacitance inside an array is at most its
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+ isolated-pair value:
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+
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+ ```
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+ k = |C_full| / |C_iso| ≤ 1
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+ ```
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+
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+ Pairwise-superposition extraction — used throughout fast parasitic extraction —
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+ assumes `k ≡ 1`. The certified claim here is that on a particular manufacturable
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+ family it is **provably never right**, and quantifies by how much:
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+
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+ > For every layout in the family box, `k ≤ 0.909090909091`. A pairwise extractor
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+ > therefore over-predicts the worst coupling by **at least 10.000002%** on
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+ > *every* member of the family — not on average, not usually, always.
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+
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+ And the other direction: a second-order Born correction, the obvious cheap fix
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+ when a full solve is too slow, does not merely stay inaccurate — on 27 layouts
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+ here it predicts `k > 1`, which is **anti-screening**, a physical impossibility.
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+
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+ ## 30-second quickstart
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+
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+ No install, no dependencies, nothing from the repository that produced it:
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+
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+ ```bash
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+ python3 verify.py
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+ ```
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+
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+ ```
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+ screening-ceiling independent re-derivation (stdlib only)
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+
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+ claim k <= 0.909090909091 for every layout in the family
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+ forced error pairwise over-predicts by >= 10.0000%
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+
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+ regions 256 x 25 samples = 6400 layouts
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+ worst sampled k 0.903974725909 (bound 0.909090909091)
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+ margin to bound 0.005116183182
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+ violations 0
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+ worst at region 3.0.3.3 d0_um=55.7830 jog_mult=0.3838 pt_mult=1.0009 sep_mult=4.4492
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+
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+ counterexamples 27/27 re-derived and confirmed above the ceiling
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+
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+ consistent: no sampled layout exceeds the bound, and every counterexample re-derives
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+
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+ 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.
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+ ```
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+
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+ `verify.py` rebuilds the electrostatics from the published geometry using the
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+ standard library alone — its own Gauss-Jordan inverse, its own potential matrix.
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+ It does not import this dataset's producer, numpy, or anything else.
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+
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+ **Sampling cannot prove the universal claim.** That is what the interval
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+ branch-and-bound in the source proof is for. What sampling *can* do is refute
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+ it, and that is the useful thing to hand a skeptical reader: a cheap,
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+ dependency-free way to try to catch us being wrong.
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+
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+ ## Loading
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+
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+ ```python
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+ from loader import load_regions, load_counterexamples, load_theorem
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+
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+ theorem = load_theorem()
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+ print(theorem["statement"])
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+ print(theorem["honest_scope"]) # read this one
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+
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+ for c in load_counterexamples():
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+ print(c["case_id"], c["k_predicted"], c["n_pairs_violating"], "/", c["n_pairs_total"])
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+ ```
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+
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+ Optional conveniences: `to_pandas("regions")` and `to_hf_dataset()`.
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+
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+ ## Contents
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+
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+ ### `data/certified_regions.jsonl` — 256 rows, the universal claim
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+
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+ The branch-and-bound partition. Each row is one region of the family box that
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+ the prover certified, having subdivided it into leaves until the interval
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+ enclosure of `k` fell below the bound everywhere inside.
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+
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+ | Field | Type | Meaning |
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+ |---|---|---|
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+ | `region_id` | string | position in the 4×4×4×4 root partition, e.g. `3.0.3.3` |
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+ | `bounds` | object | `{d0_um, pt_mult, sep_mult, jog_mult} → {lo, hi}` |
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+ | `status` | string | `CERTIFIED` for every row in this release |
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+ | `certified_leaves` | int | leaves the region was subdivided into |
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+ | `processed_leaves` | int | leaves examined, including interior splits |
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+ | `sup_certified_k_hi` | float | largest `k` the enclosure admits anywhere in the region |
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+ | `volume_fraction_of_region` | float | fraction certified (1.0 throughout) |
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+ | `unresolved_leaves` | int | leaves left undecided (0 throughout) |
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+
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+ Totals: **237,490 certified leaves**, 474,724 processed, **0 failure regions**,
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+ **0 unresolved**, certified volume fraction 1.0.
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+
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+ The published rows are the 256-region partition, **not** all 237,490 leaves —
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+ the source proof records per-region certification and aggregate counts. That is
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+ a real limitation of what is published and it is stated rather than glossed: you
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+ can re-derive any region yourself, but you are not being handed every leaf.
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+
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+ ### `data/counterexamples.jsonl` — 27 rows, the existential refutation
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+
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+ Layouts where `born_second_order` predicts `k > 1`.
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+
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+ | Field | Type | Meaning |
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+ |---|---|---|
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+ | `case_id` | string | e.g. `born2_n6_p100_s1` |
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+ | `model` | string | `born_second_order` |
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+ | `n_conductors` | int | 6, 8 or 12 |
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+ | `nominal_pitch_um` | float | 60, 80 or 100 |
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+ | `seed` | int | generator seed |
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+ | `worst_pair` | [int, int] | indices of the worst-violating pair |
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+ | `k_predicted` | float | predicted screening factor (> 1 for every row) |
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+ | `n_pairs_violating` | int | pairs above the ceiling in this layout |
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+ | `n_pairs_total` | int | ordered pairs in this layout |
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+ | `xy_um` | [[float, float]] | conductor centres, micrometres |
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+ | `radius_um` | [float] | conductor radii, micrometres |
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+ | `eps_r` | float | relative permittivity (4.6) |
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+
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+ **2,060 violating pairs** across the 27 layouts, worst `k = 3.5141`. Full
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+ coordinates are included deliberately: a counterexample you cannot rebuild is an
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+ anecdote, not evidence.
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+
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+ ### `data/theorem.json` — the claim, its scope, its provenance
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+
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+ The statement, the family box, the certified totals, the exact geometry
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+ definition, and the SHA-256 of the source proof witness.
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+
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+ ## Geometry
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+
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+ Four parallel circular conductors forming two tight pairs:
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+
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+ ```
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+ pitch = 1.6 · d0 · pt_mult
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+ separation = pitch · sep_mult
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+ jog = jog_mult · separation
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+
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+ centres: (0,0) (pitch,0) (separation,jog) (separation+pitch,jog)
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+ every conductor has diameter d0
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+ ```
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+
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+ Family box: `d0 ∈ [25,60] µm`, `pt_mult ∈ [1.0,1.2]`, `sep_mult ∈ [2.5,4.5]`,
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+ `jog_mult ∈ [−0.4,0.4]`. Self-term radius scale 1.0.
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+
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+ `loader.family_layout(...)` builds it for you.
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+
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+ ## Scope, honestly
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+
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+ **This is a theorem about the monopole-closure model, not about Maxwell.** The
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+ closure is a zero-parameter analytic multiple-scattering model that matches a
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+ boundary-element reference to 0.081% in the exact two-cylinder limit, but the
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+ closure-versus-solver gap is an **additive, disclosed, unresolved** term. It is
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+ never absorbed into the bound. The scope line travels with the data, in
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+ `theorem.json`:
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+
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+ > A complete interval theorem about the frozen MONOPOLE-CLOSURE model only. The
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+ > closure-vs-BEM/PDE model gap remains additive and unresolved. This witness does
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+ > not establish Maxwell, BEM, driven-S, fabrication, or measured-silicon truth.
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+
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+ Three further limits worth stating plainly:
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+
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+ - **One family, not all layouts.** Four conductors in a specific arrangement.
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+ Nothing here says anything about a different topology.
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+ - **The bound is not tight.** The certified supremum is 0.90909089; the worst
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+ layout found by adversarial search is ≈0.9053. The gap is the price of a
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+ first-order interval relaxation, not a claim about physics.
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+ - **No measured data.** Every number is computational.
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+
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+ ## Reproduction
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+
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+ ```bash
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+ python3 verify.py --samples 100 --seed 7 # sample harder, different seed
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+ python3 verify.py --self-test # prove the checker still discriminates
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+ python3 export.py --check # confirm data matches a fresh export
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+ ```
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+
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+ The self-test is the part that makes a clean report worth anything. It fabricates
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+ an impossible bound, tampers with a published value, and requires the checker to
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+ reject both — then confirms an isolated pair reproduces `k = 1.000000000000`
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+ exactly, since a lone pair has nothing to screen it.
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+
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+ ## Provenance
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+
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+ Exported by `export.py` from a committed proof witness produced by an
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+ outward-rounded interval branch-and-bound prover (256 parallel roots, 243.5 s
224
+ wall clock, centered/mean-value enclosure forms). The witness digest is recorded
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+ in `theorem.json`; `export.py --check` re-derives the files and compares.
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+
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+ Counterexamples are generated by running the open-source
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+ [`maxwell-lint`](https://github.com/nickharris808/maxwell-lint) reference models, so they are reproducible
229
+ from published code alone.
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+
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+ ## Citation
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+
233
+ ```bibtex
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+ @misc{screening_ceiling_2026,
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+ title = {Screening Ceiling: Certified Regions and Counterexamples for
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+ Many-Body Coupling Extraction},
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+ author = {ChipletOS / Genesis contributors},
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+ year = {2026},
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+ note = {CC-BY-4.0}
240
+ }
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+ ```
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+
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+ ## Licence
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+
245
+ **CC-BY-4.0.** Synthetic and computational throughout; no proprietary or
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+ measured data. Attribution: ChipletOS / Genesis contributors.
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+
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+ ## Related
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+
250
+ - [`maxwell-lint`](https://github.com/nickharris808/maxwell-lint) — run the ceiling test on *your* extractor
251
+ - [`sparam-conformance`](https://huggingface.co/datasets/nickh007/sparam-conformance) — the S-parameter analogue
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+ - [ChipletOS](https://chipletos.com) — the closed core: a learned many-body
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+ coupling operator that stays inside this ceiling and is accurate at speed,
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+ with calibrated abstention and a fail-closed signoff certificate
data/certified_regions.jsonl ADDED
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+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": -0.2, "lo": -0.4}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.0, "lo": 2.5}}, "certified_leaves": 1087, "processed_leaves": 2173, "region_id": "0.0.0.0", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090869368608341, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0000000000000002}
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+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.0, "lo": -0.2}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.0, "lo": 2.5}}, "certified_leaves": 919, "processed_leaves": 1837, "region_id": "0.0.0.1", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090784510374134, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
3
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.20000000000000007, "lo": 0.0}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.0, "lo": 2.5}}, "certified_leaves": 1394, "processed_leaves": 2787, "region_id": "0.0.0.2", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090860034047136, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
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+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.4, "lo": 0.20000000000000007}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.0, "lo": 2.5}}, "certified_leaves": 966, "processed_leaves": 1931, "region_id": "0.0.0.3", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090863215915332, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
5
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": -0.2, "lo": -0.4}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.5, "lo": 3.0}}, "certified_leaves": 1256, "processed_leaves": 2511, "region_id": "0.0.1.0", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090602427162999, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0000000000000002}
6
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.0, "lo": -0.2}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.5, "lo": 3.0}}, "certified_leaves": 952, "processed_leaves": 1903, "region_id": "0.0.1.1", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090876751382946, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
7
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.20000000000000007, "lo": 0.0}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.5, "lo": 3.0}}, "certified_leaves": 1435, "processed_leaves": 2869, "region_id": "0.0.1.2", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090669541584445, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
8
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.4, "lo": 0.20000000000000007}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 3.5, "lo": 3.0}}, "certified_leaves": 1120, "processed_leaves": 2239, "region_id": "0.0.1.3", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090602427162999, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
9
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": -0.2, "lo": -0.4}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 4.0, "lo": 3.5}}, "certified_leaves": 2368, "processed_leaves": 4735, "region_id": "0.0.2.0", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090878509483901, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0000000000000002}
10
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.0, "lo": -0.2}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 4.0, "lo": 3.5}}, "certified_leaves": 1331, "processed_leaves": 2661, "region_id": "0.0.2.1", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090845056856786, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
11
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.20000000000000007, "lo": 0.0}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 4.0, "lo": 3.5}}, "certified_leaves": 1886, "processed_leaves": 3771, "region_id": "0.0.2.2", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090900331971927, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
12
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": 0.4, "lo": 0.20000000000000007}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 4.0, "lo": 3.5}}, "certified_leaves": 2243, "processed_leaves": 4485, "region_id": "0.0.2.3", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090878509483901, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0}
13
+ {"bounds": {"d0_um": {"hi": 33.75, "lo": 25.0}, "jog_mult": {"hi": -0.2, "lo": -0.4}, "pt_mult": {"hi": 1.05, "lo": 1.0}, "sep_mult": {"hi": 4.5, "lo": 4.0}}, "certified_leaves": 10441, "processed_leaves": 20881, "region_id": "0.0.3.0", "status": "CERTIFIED", "sup_certified_k_hi": 0.9090908011195489, "unresolved_leaves": 0, "volume_fraction_of_region": 1.0000000000000002}
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data/counterexamples.jsonl ADDED
@@ -0,0 +1,27 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
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+ {"case_id": "born2_n12_p60_s1", "eps_r": 4.6, "k_predicted": 3.1158149943105466, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 60.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 1, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[0.17732437050385075, 6.756955444889029], [-5.337605809205494, 66.72974170705865], [-2.8225282198427184, 118.84989673458863], [4.915538907306625, 178.63798704553741], [60.74390531509589, -7.0866133013539745], [63.8026966301221, 60.572149698289174], [57.44597574748638, 124.32643055142607], [57.04792243937467, 179.30246834220978], [114.51062545870747, -1.4533052032930616], [115.55182861014224, 56.434700106627744], [123.75547008945078, 116.7061313697906], [119.77786461647453, 187.21105799701857]]}
18
+ {"case_id": "born2_n12_p60_s2", "eps_r": 4.6, "k_predicted": 3.170944216540121, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 60.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 2, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-3.5758179862602537, -3.02263284878815], [4.713386108914204, 53.87873913202645], [1.50150788948481, 123.4284079021769], [-4.6814838995009485, 173.327199409996], [56.62454051859057, 2.361495223133889], [60.93398494170641, 54.750933949580045], [58.9894618620718, 122.53945947861779], [58.841770099051914, 181.9977659891117], [127.01153928740516, 2.7459723346443794], [118.3743724962004, 55.30878854580147], [117.689409983576, 120.16598960354364], [125.86814114250869, 184.13345913709034]]}
19
+ {"case_id": "born2_n12_p60_s3", "eps_r": 4.6, "k_predicted": 3.1364562667385294, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 60.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 3, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-6.215262492845634, -3.9478424010585043], [4.519116978095953, 61.23243054096551], [-6.088070366394011, 118.9969041035471], [-0.3142305278874896, 174.89608371955617], [63.51865727113822, -5.794919701178949], [58.36842285743493, 60.25110273932046], [58.959420306212664, 121.3019785715721], [63.5675668093824, 186.84400882254147], [116.76301745623188, 2.2282081061973757], [122.94323995005232, 56.89081123518731], [112.52235125263253, 127.10190412149619], [116.97601834525314, 177.20979003051505]]}
20
+ {"case_id": "born2_n12_p80_s0", "eps_r": 4.6, "k_predicted": 3.3560531559320115, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 80.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 0, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[2.739233746429086, -4.604265724722594], [-9.180529521276107, 70.33055271057059], [6.265404784005447, 168.25511154555443], [2.1327155153435973, 244.58993121967995], [80.87249982930844, 8.701448475755365], [86.31707108243064, 70.05477000340296], [87.14808553175139, 150.67171150610926], [84.59310892859888, 233.51311241205119], [167.2635784469977, 0.8292244049818341], [155.9942378107477, 78.45374442395315], [150.56639342290927, 152.48566552999128], [163.41248829387257, 242.94379023148497]]}
21
+ {"case_id": "born2_n12_p80_s1", "eps_r": 4.6, "k_predicted": 3.325395256228735, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 80.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 1, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[0.23643249400513433, 9.009273926518706], [-7.116807745607324, 88.97298894274488], [-3.7633709597902905, 158.4665289794515], [6.554051876408834, 238.18398272738324], [80.99187375346118, -9.448817735138633], [85.07026217349613, 80.76286626438556], [76.59463432998184, 165.76857406856809], [76.0638965858329, 239.069957789613], [152.6808339449433, -1.9377402710574154], [154.06910481352296, 75.24626680883699], [165.00729345260106, 155.60817515972076], [159.7038194886327, 249.61474399602477]]}
22
+ {"case_id": "born2_n12_p80_s2", "eps_r": 4.6, "k_predicted": 3.376603555767942, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 80.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 2, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-4.767757315013672, -4.030177131717534], [6.2845148118856065, 71.83831884270192], [2.0020105193130795, 164.5712105362359], [-6.241978532667931, 231.10293254666135], [75.49938735812074, 3.148660297511851], [81.24531325560856, 73.00124526610672], [78.65261581609575, 163.3859459714904], [78.45569346540255, 242.66368798548234], [169.34871904987352, 3.6612964461925057], [157.83249666160052, 73.74505139440197], [156.91921331143467, 160.22131947139155], [167.82418819001157, 245.5112788494538]]}
23
+ {"case_id": "born2_n12_p80_s3", "eps_r": 4.6, "k_predicted": 3.3458770722882916, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 80.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 3, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-8.287016657127513, -5.263789868078005], [6.025489304127937, 81.64324072128736], [-8.117427155192017, 158.66253880472945], [-0.41897403718331944, 233.19477829274155], [84.69154302818427, -7.726559601571931], [77.82456380991324, 80.33480365242725], [78.61256040828356, 161.7359714287628], [84.7567557458432, 249.12534509672193], [155.6840232749758, 2.9709441415965006], [163.9243199334031, 75.85441498024974], [150.0298016701767, 169.46920549532825], [155.96802446033752, 236.2797200406867]]}
24
+ {"case_id": "born2_n12_p100_s0", "eps_r": 4.6, "k_predicted": 3.4957395621596405, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 100.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 0, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[3.4240421830363577, -5.755332155903242], [-11.475661901595133, 87.91319088821322], [7.83175598000681, 210.31888943194303], [2.665894394179497, 305.73741402459996], [101.09062478663556, 10.876810594694206], [107.89633885303829, 87.5684625042537], [108.93510691468921, 188.33963938263662], [105.7413861607486, 291.8913905150639], [209.07947305874717, 1.036530506227293], [194.99279726343462, 98.06718052994147], [188.20799177863657, 190.6070819124891], [204.26561036734077, 303.67973778935624]]}
25
+ {"case_id": "born2_n12_p100_s1", "eps_r": 4.6, "k_predicted": 3.4658233090395014, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 100.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 1, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[0.2955406175064179, 11.261592408148383], [-8.896009682009156, 111.2162361784311], [-4.704213699737863, 198.08316122431438], [8.192564845511043, 297.72997840922903], [101.23984219182647, -11.81102216892329], [106.33782771687017, 100.95358283048195], [95.7432929124773, 207.2107175857101], [95.07987073229113, 298.8374472370163], [190.8510424311791, -2.422175338821769], [192.58638101690372, 94.05783351104623], [206.2591168157513, 194.510218949651], [199.62977436079086, 312.0184299950309]]}
26
+ {"case_id": "born2_n12_p100_s2", "eps_r": 4.6, "k_predicted": 3.514093796424527, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 100.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 2, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-5.95969664376709, -5.037721414646917], [7.855643514857007, 89.79789855337742], [2.50251314914135, 205.71401317029483], [-7.802473165834914, 288.8786656833267], [94.37423419765094, 3.9358253718898144], [101.55664156951069, 91.2515565826334], [98.31576977011967, 204.23243246436297], [98.0696168317532, 303.3296099818529], [211.68589881234192, 4.5766205577406325], [197.29062082700065, 92.18131424300245], [196.14901663929334, 200.2766493392394], [209.7802352375145, 306.88909856181726]]}
27
+ {"case_id": "born2_n12_p100_s3", "eps_r": 4.6, "k_predicted": 3.4861879114348886, "model": "born_second_order", "n_conductors": 12, "n_pairs_total": 132, "n_pairs_violating": 132, "nominal_pitch_um": 100.0, "radius_um": [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], "seed": 3, "violates_ceiling": true, "worst_pair": [0, 11], "xy_um": [[-10.35877082140939, -6.579737335097508], [7.531861630159922, 102.0540509016092], [-10.14678394399002, 198.32817350591185], [-0.5237175464791494, 291.49347286592695], [105.86442878523036, -9.658199501964916], [97.28070476239154, 100.41850456553409], [98.26570051035445, 202.1699642859535], [105.945944682304, 311.40668137090245], [194.6050290937198, 3.7136801769956262], [204.90539991675385, 94.81801872531217], [187.53725208772087, 211.83650686916033], [194.96003057542188, 295.3496500508584]]}
data/theorem.json ADDED
@@ -0,0 +1,53 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "certified_leaves_total": 237490,
3
+ "certified_volume_fraction": 1.0000000000000002,
4
+ "enclosure_mode": "centered",
5
+ "failure_regions": 0,
6
+ "family": "two_tight_pairs (nfill=0 core)",
7
+ "family_box": {
8
+ "d0_um": {
9
+ "hi": 60.0,
10
+ "lo": 25.0
11
+ },
12
+ "jog_mult": {
13
+ "hi": 0.4,
14
+ "lo": -0.4
15
+ },
16
+ "pt_mult": {
17
+ "hi": 1.2,
18
+ "lo": 1.0
19
+ },
20
+ "sep_mult": {
21
+ "hi": 4.5,
22
+ "lo": 2.5
23
+ }
24
+ },
25
+ "forced_pairwise_overprediction_basis": "sup_certified_k_hi",
26
+ "forced_pairwise_overprediction_pct": 10.000002061387825,
27
+ "geometry": {
28
+ "description": "Four parallel circular conductors forming two tight pairs. pitch = 1.6 * d0 * pt_mult; separation = pitch * sep_mult; jog = jog_mult * separation. Conductor centres at (0,0), (pitch,0), (separation,jog), (separation+pitch,jog); every conductor has diameter d0.",
29
+ "self_term_radius_scale": 1.0,
30
+ "units": "d0_um in micrometres; the multipliers are dimensionless"
31
+ },
32
+ "honest_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.",
33
+ "k_bar": 0.9090909090909091,
34
+ "open_boxes": 0,
35
+ "parameters": [
36
+ "d0_um",
37
+ "pt_mult",
38
+ "sep_mult",
39
+ "jog_mult"
40
+ ],
41
+ "processed_leaves_total": 474724,
42
+ "provenance": {
43
+ "partition_regions": 256,
44
+ "prover_wall_seconds": 243.5342594169997,
45
+ "schema": "genesis.family_impossibility.parallel.v1",
46
+ "source_sha256": "51c6f38f9d3d09b654886b2278ba86712596978b4ad1366ec96bcfcec2ff272c",
47
+ "source_witness": "family_two_tight_pairs_k10pct_parallel_2026_07.json",
48
+ "witness_content_sha256": "5b10e5a58013fa0e9bf9fb7900d885e4bd70e808bbad59e374d15a03be9ab2a3"
49
+ },
50
+ "statement": "For every layout in the family box, the monopole-closure many-body screening factor satisfies k <= 0.909090909091. A pairwise-superposition extractor assumes k == 1, so it over-predicts the worst coupling by at least 10.0000% on every member of the family.",
51
+ "status": "THEOREM_CERTIFIED",
52
+ "sup_certified_k_hi": 0.9090908920546464
53
+ }
export.py ADDED
@@ -0,0 +1,231 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ #!/usr/bin/env python3
2
+ """Export the screening-ceiling dataset from committed source artifacts.
3
+
4
+ Two very different kinds of row come out of this, and keeping them straight is
5
+ the whole point of the dataset:
6
+
7
+ certified_regions.jsonl -- a UNIVERSAL claim. 256 sub-boxes of a 4-parameter
8
+ family, each certified by outward-rounded interval branch-and-bound to
9
+ contain NO layout whose screening factor exceeds k_bar. Exported from a
10
+ committed proof witness; provenance recorded by digest.
11
+
12
+ counterexamples.jsonl -- an EXISTENTIAL refutation. Concrete layouts where
13
+ a second-order Born extractor predicts k > 1, which no passive
14
+ arrangement of conductors can do. Generated here by running the
15
+ open-source `maxwell-lint` reference models, so every row is reproducible
16
+ from published code alone.
17
+
18
+ Run:
19
+ python3 export.py # writes data/
20
+ python3 export.py --check # verify existing data, write nothing
21
+ """
22
+ from __future__ import annotations
23
+
24
+ import argparse
25
+ import hashlib
26
+ import json
27
+ import pathlib
28
+ import sys
29
+
30
+ HERE = pathlib.Path(__file__).resolve().parent
31
+ DATA = HERE / "data"
32
+ REPO = HERE.parents[2]
33
+ WITNESS = REPO / "benchmarks" / "impossibility" / \
34
+ "family_two_tight_pairs_k10pct_parallel_2026_07.json"
35
+
36
+ DIM_NAMES = ["d0_um", "pt_mult", "sep_mult", "jog_mult"]
37
+
38
+ # Reproduced verbatim from the source witness so the published scope statement
39
+ # cannot drift from the one the proof was run under.
40
+ HONEST_SCOPE = (
41
+ "A complete interval theorem about the frozen MONOPOLE-CLOSURE model only. "
42
+ "The closure-vs-BEM/PDE model gap remains additive and unresolved. This "
43
+ "witness does not establish Maxwell, BEM, driven-S, fabrication, or "
44
+ "measured-silicon truth."
45
+ )
46
+
47
+
48
+ def sha256(path: pathlib.Path) -> str:
49
+ return hashlib.sha256(path.read_bytes()).hexdigest()
50
+
51
+
52
+ # --------------------------------------------------------------- certified regions
53
+
54
+ def export_certified_regions(w: dict) -> list[dict]:
55
+ """One row per certified root region of the branch-and-bound partition.
56
+
57
+ The witness stores the 256-region partition with per-region certification
58
+ rather than all 237,490 leaves. That is what gets published, and the
59
+ distinction is stated rather than glossed: each row is a region the prover
60
+ certified, together with how many leaves it took and the largest screening
61
+ factor the interval enclosure admitted anywhere inside it.
62
+ """
63
+ rows = []
64
+ for r in w["root_results"]:
65
+ rows.append({
66
+ "region_id": r["root_id"],
67
+ "bounds": {n: {"lo": lo, "hi": hi}
68
+ for n, (lo, hi) in zip(DIM_NAMES, r["box"])},
69
+ "status": r["status"],
70
+ "certified_leaves": r["certified_boxes"],
71
+ "processed_leaves": r["processed_boxes"],
72
+ "sup_certified_k_hi": r["sup_certified_k_hi"],
73
+ "volume_fraction_of_region": r["certified_volume_frac_of_root"],
74
+ "unresolved_leaves": r["unresolved_count"],
75
+ })
76
+ return rows
77
+
78
+
79
+ # ----------------------------------------------------------------- counterexamples
80
+
81
+ def export_counterexamples() -> list[dict]:
82
+ """Concrete layouts where a plausible cheap extractor predicts k > 1.
83
+
84
+ Generated by running the published `maxwell-lint` reference models, so a
85
+ reader can regenerate every row without this repository. Full coordinates
86
+ are emitted -- a counterexample you cannot rebuild is an anecdote.
87
+ """
88
+ try:
89
+ import numpy as np
90
+ from maxwell_lint.models import (born_second_order, isolated_pair_matrix,
91
+ random_layout)
92
+ except ImportError as exc: # pragma: no cover - exercised by the CLI path
93
+ raise SystemExit(
94
+ f"counterexample export needs maxwell-lint installed: {exc}\n"
95
+ " pip install ../../maxwell-lint") from exc
96
+
97
+ rows = []
98
+ for n in (6, 8, 12):
99
+ for pitch in (60.0, 80.0, 100.0):
100
+ for seed in range(4):
101
+ lay = random_layout(n, seed=seed, pitch_um=pitch)
102
+ full = born_second_order(lay)
103
+ iso = isolated_pair_matrix(lay)
104
+ with np.errstate(divide="ignore", invalid="ignore"):
105
+ k = np.where(iso > 0, full / iso, 0.0)
106
+ np.fill_diagonal(k, 0.0)
107
+ i, j = np.unravel_index(int(np.argmax(k)), k.shape)
108
+ kmax = float(k[i, j])
109
+ if kmax <= 1.0:
110
+ continue
111
+ rows.append({
112
+ "case_id": f"born2_n{n}_p{int(pitch)}_s{seed}",
113
+ "model": "born_second_order",
114
+ "n_conductors": int(n),
115
+ "nominal_pitch_um": pitch,
116
+ "seed": int(seed),
117
+ "worst_pair": [int(i), int(j)],
118
+ "k_predicted": kmax,
119
+ "violates_ceiling": True,
120
+ "n_pairs_violating": int((k > 1.0).sum()),
121
+ "n_pairs_total": int(n * (n - 1)),
122
+ "xy_um": [[float(x * 1e6), float(y * 1e6)] for x, y in lay.xy],
123
+ "radius_um": [float(r * 1e6) for r in lay.radius],
124
+ "eps_r": float(lay.eps_r),
125
+ })
126
+ return rows
127
+
128
+
129
+ # ------------------------------------------------------------------------ theorem
130
+
131
+ def export_theorem(w: dict) -> dict:
132
+ return {
133
+ "family": w["family"],
134
+ "parameters": DIM_NAMES,
135
+ # the top-level box is keyed by name; the per-region boxes are positional
136
+ "family_box": {n: {"lo": w["box"][n][0], "hi": w["box"][n][1]}
137
+ for n in DIM_NAMES},
138
+ "k_bar": w["k_bar"],
139
+ "statement": (
140
+ "For every layout in the family box, the monopole-closure many-body "
141
+ f"screening factor satisfies k <= {w['k_bar']:.12f}. A pairwise-"
142
+ "superposition extractor assumes k == 1, so it over-predicts the worst "
143
+ f"coupling by at least {100.0 / w['k_bar'] - 100.0:.4f}% on every "
144
+ "member of the family."
145
+ ),
146
+ # Derived from the supremum the proof actually certified, not from the
147
+ # target bound -- so it is very slightly STRONGER than 100/k_bar - 100
148
+ # (10.000002% vs 10.000000%). Recorded explicitly because a reader who
149
+ # divides by k_bar and gets a different last digit deserves an answer.
150
+ "forced_pairwise_overprediction_pct": w["forced_pairwise_overprediction_pct"],
151
+ "forced_pairwise_overprediction_basis": "sup_certified_k_hi",
152
+ "certified_leaves_total": w["certified_boxes"],
153
+ "processed_leaves_total": w["processed_boxes"],
154
+ "certified_volume_fraction": w["certified_volume_frac"],
155
+ "failure_regions": w["n_failure_regions"],
156
+ "open_boxes": w["open_boxes"],
157
+ "sup_certified_k_hi": w["sup_certified_k_hi"],
158
+ "enclosure_mode": w["enclosure_mode"],
159
+ "status": w["status"],
160
+ "honest_scope": HONEST_SCOPE,
161
+ "geometry": {
162
+ "description": (
163
+ "Four parallel circular conductors forming two tight pairs. "
164
+ "pitch = 1.6 * d0 * pt_mult; separation = pitch * sep_mult; "
165
+ "jog = jog_mult * separation. Conductor centres at (0,0), "
166
+ "(pitch,0), (separation,jog), (separation+pitch,jog); every "
167
+ "conductor has diameter d0."
168
+ ),
169
+ "units": "d0_um in micrometres; the multipliers are dimensionless",
170
+ "self_term_radius_scale": 1.0,
171
+ },
172
+ "provenance": {
173
+ "source_witness": WITNESS.name,
174
+ "source_sha256": sha256(WITNESS),
175
+ "witness_content_sha256": w["content_sha256"],
176
+ "schema": w["schema"],
177
+ "prover_wall_seconds": w["wall_s"],
178
+ "partition_regions": w["root_count"],
179
+ },
180
+ }
181
+
182
+
183
+ def write_jsonl(path: pathlib.Path, rows: list[dict]) -> None:
184
+ with path.open("w") as fh:
185
+ for r in rows:
186
+ fh.write(json.dumps(r, sort_keys=True) + "\n")
187
+
188
+
189
+ def main() -> int:
190
+ ap = argparse.ArgumentParser(description=__doc__)
191
+ ap.add_argument("--check", action="store_true",
192
+ help="verify the committed data instead of rewriting it")
193
+ args = ap.parse_args()
194
+
195
+ if not WITNESS.exists():
196
+ print(f"source witness not found: {WITNESS}", file=sys.stderr)
197
+ print("(export requires the source repository; the published data files "
198
+ "stand alone)", file=sys.stderr)
199
+ return 2
200
+
201
+ w = json.loads(WITNESS.read_text())
202
+ regions = export_certified_regions(w)
203
+ theorem = export_theorem(w)
204
+ counters = export_counterexamples()
205
+
206
+ if args.check:
207
+ old_r = [json.loads(x) for x in
208
+ (DATA / "certified_regions.jsonl").read_text().splitlines()]
209
+ old_c = [json.loads(x) for x in
210
+ (DATA / "counterexamples.jsonl").read_text().splitlines()]
211
+ old_t = json.loads((DATA / "theorem.json").read_text())
212
+ ok = (old_r == regions and old_c == counters and old_t == theorem)
213
+ print("data matches a fresh export" if ok else "DATA DRIFT")
214
+ return 0 if ok else 1
215
+
216
+ DATA.mkdir(parents=True, exist_ok=True)
217
+ write_jsonl(DATA / "certified_regions.jsonl", regions)
218
+ write_jsonl(DATA / "counterexamples.jsonl", counters)
219
+ (DATA / "theorem.json").write_text(json.dumps(theorem, indent=2, sort_keys=True) + "\n")
220
+
221
+ n_viol = sum(r["n_pairs_violating"] for r in counters)
222
+ print(f"certified_regions.jsonl {len(regions)} regions "
223
+ f"({theorem['certified_leaves_total']} leaves)")
224
+ print(f"counterexamples.jsonl {len(counters)} layouts "
225
+ f"({n_viol} violating pairs)")
226
+ print(f"theorem.json k_bar = {theorem['k_bar']:.12f}")
227
+ return 0
228
+
229
+
230
+ if __name__ == "__main__":
231
+ raise SystemExit(main())
loader.py ADDED
@@ -0,0 +1,88 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ """Load the screening-ceiling dataset.
2
+
3
+ Stdlib by default so the data is usable with nothing installed; pandas and
4
+ `datasets` are optional conveniences, imported only if you ask for them.
5
+
6
+ from loader import load_regions, load_counterexamples, load_theorem
7
+
8
+ theorem = load_theorem()
9
+ print(theorem["statement"])
10
+
11
+ for c in load_counterexamples():
12
+ print(c["case_id"], c["k_predicted"])
13
+ """
14
+ from __future__ import annotations
15
+
16
+ import json
17
+ import pathlib
18
+
19
+ HERE = pathlib.Path(__file__).resolve().parent
20
+ DATA = HERE / "data"
21
+
22
+ __all__ = ["load_regions", "load_counterexamples", "load_theorem",
23
+ "to_pandas", "to_hf_dataset", "family_layout"]
24
+
25
+
26
+ def _jsonl(path: pathlib.Path) -> list[dict]:
27
+ return [json.loads(line) for line in path.read_text().splitlines() if line.strip()]
28
+
29
+
30
+ def load_regions() -> list[dict]:
31
+ """256 certified regions of the branch-and-bound partition."""
32
+ return _jsonl(DATA / "certified_regions.jsonl")
33
+
34
+
35
+ def load_counterexamples() -> list[dict]:
36
+ """Concrete layouts where a second-order Born extractor predicts k > 1."""
37
+ return _jsonl(DATA / "counterexamples.jsonl")
38
+
39
+
40
+ def load_theorem() -> dict:
41
+ """The universal claim, its scope, and the provenance of the source proof."""
42
+ return json.loads((DATA / "theorem.json").read_text())
43
+
44
+
45
+ def family_layout(d0_um: float, pt_mult: float, sep_mult: float, jog_mult: float):
46
+ """Build the conductor geometry for a point in the family box.
47
+
48
+ Returns (xy_metres, radius_metres). Kept here as well as in `verify.py` so a
49
+ reader who only wants to generate layouts does not have to read the checker.
50
+ """
51
+ pt = 1.6 * d0_um * pt_mult * 1e-6
52
+ sep = pt * sep_mult
53
+ jog = jog_mult * sep
54
+ return ([[0.0, 0.0], [pt, 0.0], [sep, jog], [sep + pt, jog]],
55
+ [d0_um * 1e-6 / 2.0] * 4)
56
+
57
+
58
+ def to_pandas(split: str = "regions"):
59
+ """`regions` or `counterexamples` as a DataFrame. Requires pandas."""
60
+ import pandas as pd
61
+ if split == "regions":
62
+ rows = []
63
+ for r in load_regions():
64
+ flat = {k: v for k, v in r.items() if k != "bounds"}
65
+ for name, b in r["bounds"].items():
66
+ flat[f"{name}_lo"], flat[f"{name}_hi"] = b["lo"], b["hi"]
67
+ rows.append(flat)
68
+ return pd.DataFrame(rows)
69
+ if split == "counterexamples":
70
+ return pd.DataFrame(load_counterexamples())
71
+ raise ValueError(f"unknown split {split!r}: use 'regions' or 'counterexamples'")
72
+
73
+
74
+ def to_hf_dataset():
75
+ """Both splits as a `datasets.DatasetDict`. Requires `datasets`."""
76
+ from datasets import Dataset, DatasetDict
77
+ return DatasetDict({
78
+ "regions": Dataset.from_list(load_regions()),
79
+ "counterexamples": Dataset.from_list(load_counterexamples()),
80
+ })
81
+
82
+
83
+ if __name__ == "__main__":
84
+ t = load_theorem()
85
+ print(t["statement"])
86
+ print(f"\nregions {len(load_regions())}")
87
+ print(f"counterexamples {len(load_counterexamples())}")
88
+ print(f"\nscope: {t['honest_scope']}")
tests/test_dataset.py ADDED
@@ -0,0 +1,265 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ """Tests for the screening-ceiling dataset.
2
+
3
+ The important tests here are not "does the file parse" -- they are "is the
4
+ published claim true of the published data". A dataset whose ground truth is
5
+ wrong is worse than no dataset, because every result scored against it inherits
6
+ the error.
7
+ """
8
+ from __future__ import annotations
9
+
10
+ import json
11
+ import math
12
+ import pathlib
13
+ import random
14
+ import sys
15
+
16
+ import pytest
17
+
18
+ HERE = pathlib.Path(__file__).resolve().parents[1]
19
+ sys.path.insert(0, str(HERE))
20
+
21
+ import verify # noqa: E402
22
+ from loader import (family_layout, load_counterexamples, # noqa: E402
23
+ load_regions, load_theorem)
24
+
25
+ DATA = HERE / "data"
26
+
27
+
28
+ # --------------------------------------------------------------------- presence
29
+
30
+ def test_data_files_exist_and_are_nonempty():
31
+ for name in ("certified_regions.jsonl", "counterexamples.jsonl", "theorem.json"):
32
+ p = DATA / name
33
+ assert p.exists(), f"missing {name}"
34
+ assert p.stat().st_size > 0, f"empty {name}"
35
+
36
+
37
+ def test_every_line_is_valid_json():
38
+ for name in ("certified_regions.jsonl", "counterexamples.jsonl"):
39
+ for i, line in enumerate((DATA / name).read_text().splitlines()):
40
+ if line.strip():
41
+ json.loads(line) # raises on malformed
42
+
43
+
44
+ # ---------------------------------------------------------------------- schema
45
+
46
+ def test_region_schema_is_complete():
47
+ required = {"region_id", "bounds", "status", "certified_leaves",
48
+ "processed_leaves", "sup_certified_k_hi",
49
+ "volume_fraction_of_region", "unresolved_leaves"}
50
+ for r in load_regions():
51
+ assert required <= set(r), f"{r.get('region_id')} missing {required - set(r)}"
52
+ assert set(r["bounds"]) == {"d0_um", "pt_mult", "sep_mult", "jog_mult"}
53
+ for b in r["bounds"].values():
54
+ assert b["lo"] < b["hi"], "degenerate interval"
55
+
56
+
57
+ def test_counterexample_schema_is_complete():
58
+ required = {"case_id", "model", "n_conductors", "worst_pair", "k_predicted",
59
+ "violates_ceiling", "xy_um", "radius_um", "eps_r"}
60
+ for c in load_counterexamples():
61
+ assert required <= set(c), f"{c.get('case_id')} missing {required - set(c)}"
62
+ assert len(c["xy_um"]) == c["n_conductors"]
63
+ assert len(c["radius_um"]) == c["n_conductors"]
64
+
65
+
66
+ def test_case_ids_are_unique():
67
+ ids = [c["case_id"] for c in load_counterexamples()]
68
+ assert len(ids) == len(set(ids))
69
+
70
+
71
+ def test_region_ids_are_unique():
72
+ ids = [r["region_id"] for r in load_regions()]
73
+ assert len(ids) == len(set(ids))
74
+
75
+
76
+ # ------------------------------------------------------------------ the claims
77
+
78
+ def test_every_region_is_certified_with_no_unresolved_leaves():
79
+ for r in load_regions():
80
+ assert r["status"] == "CERTIFIED", f"{r['region_id']} is {r['status']}"
81
+ assert r["unresolved_leaves"] == 0
82
+
83
+
84
+ def test_no_region_admits_a_k_above_the_bound():
85
+ """The published per-region supremum must respect the published bound."""
86
+ k_bar = load_theorem()["k_bar"]
87
+ for r in load_regions():
88
+ assert r["sup_certified_k_hi"] <= k_bar, \
89
+ f"{r['region_id']} admits {r['sup_certified_k_hi']} > {k_bar}"
90
+
91
+
92
+ def test_leaf_total_matches_the_sum_over_regions():
93
+ t = load_theorem()
94
+ assert sum(r["certified_leaves"] for r in load_regions()) \
95
+ == t["certified_leaves_total"]
96
+
97
+
98
+ def test_regions_tile_the_family_box():
99
+ """Union of region bounds must span the declared family box on every axis."""
100
+ t = load_theorem()
101
+ regions = load_regions()
102
+ for name, b in t["family_box"].items():
103
+ assert min(r["bounds"][name]["lo"] for r in regions) == b["lo"]
104
+ assert max(r["bounds"][name]["hi"] for r in regions) == b["hi"]
105
+
106
+
107
+ @pytest.mark.parametrize("seed", [0, 1, 2])
108
+ def test_sampling_inside_certified_regions_never_exceeds_the_bound(seed):
109
+ """Independent re-derivation: sampling must fail to refute the claim."""
110
+ k_bar = load_theorem()["k_bar"]
111
+ rng = random.Random(seed)
112
+ worst, violations = verify.check_regions(load_regions(), k_bar, samples=3,
113
+ rng=rng, verbose=False)
114
+ assert violations == [], f"claim refuted at {violations[:2]}"
115
+ assert worst <= k_bar
116
+
117
+
118
+ def test_every_counterexample_really_violates_the_ceiling():
119
+ """Existential claim, re-derived from stored coordinates rather than trusted."""
120
+ confirmed, failed = verify.check_counterexamples(load_counterexamples(),
121
+ verbose=False)
122
+ assert failed == [], f"counterexamples did not re-derive: {failed[:2]}"
123
+ assert confirmed == len(load_counterexamples())
124
+
125
+
126
+ def test_published_k_matches_recomputation_to_tight_tolerance():
127
+ for c in load_counterexamples():
128
+ xy = [[x * 1e-6, y * 1e-6] for x, y in c["xy_um"]]
129
+ radius = [r * 1e-6 for r in c["radius_um"]]
130
+ k = verify.born_second_order_k(xy, radius)
131
+ n = len(xy)
132
+ kmax = max(k[i][j] for i in range(n) for j in range(n) if i != j)
133
+ assert kmax == pytest.approx(c["k_predicted"], rel=1e-9)
134
+ assert kmax > 1.0
135
+
136
+
137
+ # ------------------------------------------------------------------- physics
138
+
139
+ def test_isolated_pair_has_no_screening():
140
+ """Two conductors alone: k must be exactly 1, since there is nothing to screen."""
141
+ k = verify.screening_factors([[0.0, 0.0], [1e-4, 0.0]], [2e-5, 2e-5])
142
+ assert k[0][1] == pytest.approx(1.0, abs=1e-12)
143
+ assert k[1][0] == pytest.approx(1.0, abs=1e-12)
144
+
145
+
146
+ def test_adding_a_conductor_reduces_coupling():
147
+ """The physical content of the ceiling: screening only ever removes coupling."""
148
+ pair = verify.screening_factors([[0.0, 0.0], [2e-4, 0.0]], [2e-5] * 2)[0][1]
149
+ with_third = verify.screening_factors(
150
+ [[0.0, 0.0], [2e-4, 0.0], [1e-4, 0.0]], [2e-5] * 3)[0][1]
151
+ assert with_third < pair
152
+
153
+
154
+ def test_family_layout_matches_the_documented_geometry():
155
+ xy, radius = family_layout(40.0, 1.0, 3.0, 0.0)
156
+ pt = 1.6 * 40.0 * 1e-6
157
+ assert xy[1][0] == pytest.approx(pt)
158
+ assert xy[2][0] == pytest.approx(pt * 3.0)
159
+ assert xy[3][0] == pytest.approx(pt * 3.0 + pt)
160
+ assert all(r == pytest.approx(20e-6) for r in radius)
161
+
162
+
163
+ def test_loader_and_verify_agree_on_geometry():
164
+ """Two implementations of the family layout must not drift apart."""
165
+ a_xy, a_r = family_layout(37.5, 1.1, 3.3, -0.2)
166
+ b_xy, b_r = verify.family_layout(37.5, 1.1, 3.3, -0.2)
167
+ assert [c for pt in a_xy for c in pt] == pytest.approx(
168
+ [c for pt in b_xy for c in pt])
169
+ assert a_r == pytest.approx(b_r)
170
+
171
+
172
+ def test_inverse_is_correct():
173
+ m = [[4.0, 7.0], [2.0, 6.0]]
174
+ inv = verify.inverse(m)
175
+ prod = [[sum(m[i][k] * inv[k][j] for k in range(2)) for j in range(2)]
176
+ for i in range(2)]
177
+ assert prod[0][0] == pytest.approx(1.0)
178
+ assert prod[1][1] == pytest.approx(1.0)
179
+ assert prod[0][1] == pytest.approx(0.0, abs=1e-12)
180
+
181
+
182
+ def test_singular_matrix_raises_rather_than_returning_garbage():
183
+ with pytest.raises(ZeroDivisionError):
184
+ verify.inverse([[1.0, 2.0], [2.0, 4.0]])
185
+
186
+
187
+ # ------------------------------------------------------------ negative control
188
+
189
+ def test_the_checker_rejects_a_fabricated_bound():
190
+ """A checker that cannot fail is not a checker."""
191
+ rng = random.Random(0)
192
+ _, violations = verify.check_regions(load_regions()[:4], k_bar=0.5, samples=5,
193
+ rng=rng, verbose=False)
194
+ assert violations, "an impossible bound was not refuted"
195
+
196
+
197
+ def test_the_checker_rejects_a_tampered_counterexample():
198
+ cases = load_counterexamples()
199
+ bad = dict(cases[0], k_predicted=cases[0]["k_predicted"] * 1.5)
200
+ _, failed = verify.check_counterexamples([bad], verbose=False)
201
+ assert failed, "a tampered value was accepted"
202
+
203
+
204
+ def test_self_test_entrypoint_passes():
205
+ assert verify.self_test() == 0
206
+
207
+
208
+ # ---------------------------------------------------------------- provenance
209
+
210
+ def test_theorem_records_provenance_and_scope():
211
+ t = load_theorem()
212
+ p = t["provenance"]
213
+ assert len(p["source_sha256"]) == 64
214
+ assert len(p["witness_content_sha256"]) == 64
215
+ assert p["partition_regions"] == len(load_regions())
216
+ assert "MONOPOLE-CLOSURE" in t["honest_scope"]
217
+ assert "not establish" in t["honest_scope"]
218
+
219
+
220
+ def test_stated_overprediction_follows_from_the_certified_supremum():
221
+ """The headline percentage must be derivable, not asserted.
222
+
223
+ It derives from the supremum the proof actually certified rather than from
224
+ the target bound, so it is marginally STRONGER than 100/k_bar - 100. Both
225
+ relationships are checked, because that last digit is exactly the kind of
226
+ thing a careful reader will try to reproduce and then query.
227
+ """
228
+ t = load_theorem()
229
+ assert t["forced_pairwise_overprediction_basis"] == "sup_certified_k_hi"
230
+ assert t["forced_pairwise_overprediction_pct"] == \
231
+ pytest.approx(100.0 / t["sup_certified_k_hi"] - 100.0, rel=1e-12)
232
+ assert t["forced_pairwise_overprediction_pct"] >= 100.0 / t["k_bar"] - 100.0
233
+
234
+
235
+ def test_scope_is_not_overclaimed_anywhere_in_the_card():
236
+ """The card must not say the theorem is about Maxwell or measured silicon."""
237
+ card = (HERE / "README.md").read_text().lower()
238
+ assert "monopole-closure" in card or "monopole closure" in card
239
+ for forbidden in ("proves maxwell", "measured silicon shows",
240
+ "validated against measurement"):
241
+ assert forbidden not in card
242
+
243
+
244
+ def test_verify_is_importable_with_no_third_party_modules():
245
+ """The zero-dependency promise, enforced rather than documented."""
246
+ src = (HERE / "verify.py").read_text()
247
+ banned = ("import numpy", "import pandas", "import scipy", "import torch",
248
+ "from numpy", "from pandas", "import datasets")
249
+ for b in banned:
250
+ assert b not in src, f"verify.py must stay stdlib-only, found {b!r}"
251
+
252
+
253
+ def test_math_import_is_actually_used():
254
+ assert math.hypot(3, 4) == 5.0 # guards the import above from bit-rot
255
+
256
+
257
+ def test_readme_figures_match_the_data():
258
+ """Headline numbers in the card are re-derived from the files, not typed once."""
259
+ readme = (HERE / "README.md").read_text()
260
+ cs, t = load_counterexamples(), load_theorem()
261
+ assert f"{sum(c['n_pairs_violating'] for c in cs):,}" in readme
262
+ assert f"{max(c['k_predicted'] for c in cs):.4f}" in readme
263
+ assert f"{t['certified_leaves_total']:,}" in readme
264
+ assert f"{t['processed_leaves_total']:,}" in readme
265
+ assert f"{t['forced_pairwise_overprediction_pct']:.6f}"[:9] in readme
verify.py ADDED
@@ -0,0 +1,274 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ #!/usr/bin/env python3
2
+ """Independently re-derive the screening-ceiling dataset. Zero dependencies.
3
+
4
+ Standard library only -- no numpy, no maxwell-lint, nothing from the repository
5
+ that produced the data. Point it at `data/` and it rebuilds the physics from the
6
+ published geometry and checks both claims:
7
+
8
+ * the UNIVERSAL claim, by sampling inside every certified region and confirming
9
+ no sampled layout exceeds k_bar;
10
+ * the EXISTENTIAL claim, by recomputing each counterexample from its stored
11
+ coordinates and confirming the extractor really does predict k > 1.
12
+
13
+ Sampling cannot prove the universal claim -- that is what the interval
14
+ branch-and-bound in the source proof is for, and no amount of sampling
15
+ substitutes for it. What sampling can do is REFUTE it, and that is the useful
16
+ thing an independent reader wants: a cheap, dependency-free way to try to catch
17
+ us being wrong.
18
+
19
+ Run:
20
+ python3 verify.py # check the committed data
21
+ python3 verify.py --samples 200 # sample harder
22
+ python3 verify.py --self-test # prove the checker still discriminates
23
+ """
24
+ from __future__ import annotations
25
+
26
+ import argparse
27
+ import json
28
+ import math
29
+ import pathlib
30
+ import random
31
+ import sys
32
+
33
+ HERE = pathlib.Path(__file__).resolve().parent
34
+ DATA = HERE / "data"
35
+
36
+
37
+ # ------------------------------------------------------------------ linear algebra
38
+
39
+ def inverse(m: list[list[float]]) -> list[list[float]]:
40
+ """Gauss-Jordan inverse with partial pivoting. Small dense matrices only."""
41
+ n = len(m)
42
+ a = [row[:] + [1.0 if i == j else 0.0 for j in range(n)] for i, row in enumerate(m)]
43
+ for col in range(n):
44
+ piv = max(range(col, n), key=lambda r: abs(a[r][col]))
45
+ if abs(a[piv][col]) < 1e-300:
46
+ raise ZeroDivisionError("singular potential matrix")
47
+ a[col], a[piv] = a[piv], a[col]
48
+ d = a[col][col]
49
+ a[col] = [x / d for x in a[col]]
50
+ for r in range(n):
51
+ if r == col:
52
+ continue
53
+ f = a[r][col]
54
+ if f:
55
+ a[r] = [x - f * y for x, y in zip(a[r], a[col])]
56
+ return [row[n:] for row in a]
57
+
58
+
59
+ # ---------------------------------------------------------------------- physics
60
+
61
+ def potential_matrix(xy: list[list[float]], radius: list[float]) -> list[list[float]]:
62
+ """Maxwell potential coefficients, thin-wire/monopole form.
63
+
64
+ The 1/(2*pi*eps0*eps_r) prefactor is omitted deliberately: k is a ratio of
65
+ two capacitances computed from the same medium, so the prefactor cancels
66
+ exactly. Carrying it would only add rounding.
67
+ """
68
+ n = len(xy)
69
+ p = [[0.0] * n for _ in range(n)]
70
+ for i in range(n):
71
+ for j in range(n):
72
+ if i == j:
73
+ p[i][j] = -math.log(radius[i])
74
+ else:
75
+ dx = xy[i][0] - xy[j][0]
76
+ dy = xy[i][1] - xy[j][1]
77
+ p[i][j] = -math.log(math.hypot(dx, dy))
78
+ return p
79
+
80
+
81
+ def isolated_pair_coupling(ri: float, rj: float, r: float) -> float:
82
+ """|C_ij| for the pair alone -- the denominator of k."""
83
+ p = [[-math.log(ri), -math.log(r)], [-math.log(r), -math.log(rj)]]
84
+ return abs(inverse(p)[0][1])
85
+
86
+
87
+ def screening_factors(xy: list[list[float]], radius: list[float]) -> list[list[float]]:
88
+ """k_ij = |C_ij(full array)| / |C_ij(pair alone)| for every off-diagonal pair."""
89
+ n = len(xy)
90
+ c = inverse(potential_matrix(xy, radius))
91
+ k = [[0.0] * n for _ in range(n)]
92
+ for i in range(n):
93
+ for j in range(n):
94
+ if i == j:
95
+ continue
96
+ r = math.hypot(xy[i][0] - xy[j][0], xy[i][1] - xy[j][1])
97
+ iso = isolated_pair_coupling(radius[i], radius[j], r)
98
+ k[i][j] = abs(c[i][j]) / iso if iso > 0 else 0.0
99
+ return k
100
+
101
+
102
+ def family_layout(d0_um: float, pt_mult: float, sep_mult: float, jog_mult: float):
103
+ """The two-tight-pairs family geometry, in metres.
104
+
105
+ pitch = 1.6 * d0 * pt_mult, separation = pitch * sep_mult, jog = jog_mult *
106
+ separation; four equal conductors of diameter d0 at (0,0), (pitch,0),
107
+ (separation,jog), (separation+pitch,jog).
108
+ """
109
+ pt = 1.6 * d0_um * pt_mult * 1e-6
110
+ sep = pt * sep_mult
111
+ jog = jog_mult * sep
112
+ xy = [[0.0, 0.0], [pt, 0.0], [sep, jog], [sep + pt, jog]]
113
+ return xy, [d0_um * 1e-6 / 2.0] * 4
114
+
115
+
116
+ def max_family_k(d0_um: float, pt_mult: float, sep_mult: float, jog_mult: float) -> float:
117
+ xy, radius = family_layout(d0_um, pt_mult, sep_mult, jog_mult)
118
+ k = screening_factors(xy, radius)
119
+ return max(k[i][j] for i in range(4) for j in range(4) if i != j)
120
+
121
+
122
+ def born_second_order_k(xy, radius) -> list[list[float]]:
123
+ """Re-derive the failing extractor: second-order truncation of the inverse."""
124
+ n = len(xy)
125
+ p = potential_matrix(xy, radius)
126
+ dinv = [[1.0 / p[i][i] if i == j else 0.0 for j in range(n)] for i in range(n)]
127
+ r = [[0.0 if i == j else p[i][j] for j in range(n)] for i in range(n)]
128
+ a = [[sum(dinv[i][t] * r[t][j] for t in range(n)) for j in range(n)] for i in range(n)]
129
+ a2 = [[sum(a[i][t] * a[t][j] for t in range(n)) for j in range(n)] for i in range(n)]
130
+ mid = [[(1.0 if i == j else 0.0) - a[i][j] + a2[i][j] for j in range(n)]
131
+ for i in range(n)]
132
+ approx = [[sum(mid[i][t] * dinv[t][j] for t in range(n)) for j in range(n)]
133
+ for i in range(n)]
134
+ k = [[0.0] * n for _ in range(n)]
135
+ for i in range(n):
136
+ for j in range(n):
137
+ if i == j:
138
+ continue
139
+ d = math.hypot(xy[i][0] - xy[j][0], xy[i][1] - xy[j][1])
140
+ iso = isolated_pair_coupling(radius[i], radius[j], d)
141
+ k[i][j] = abs(approx[i][j]) / iso if iso > 0 else 0.0
142
+ return k
143
+
144
+
145
+ # ---------------------------------------------------------------------- checks
146
+
147
+ def check_regions(regions, k_bar, samples, rng, verbose=True):
148
+ worst, worst_at, violations = 0.0, None, []
149
+ for reg in regions:
150
+ b = reg["bounds"]
151
+ for _ in range(samples):
152
+ pt = {n: rng.uniform(b[n]["lo"], b[n]["hi"]) for n in b}
153
+ k = max_family_k(pt["d0_um"], pt["pt_mult"], pt["sep_mult"], pt["jog_mult"])
154
+ if k > worst:
155
+ worst, worst_at = k, (reg["region_id"], pt)
156
+ if k > k_bar:
157
+ violations.append({"region": reg["region_id"], "point": pt, "k": k})
158
+ if verbose:
159
+ print(f" regions {len(regions)} x {samples} samples "
160
+ f"= {len(regions) * samples} layouts")
161
+ print(f" worst sampled k {worst:.12f} (bound {k_bar:.12f})")
162
+ print(f" margin to bound {k_bar - worst:.12f}")
163
+ print(f" violations {len(violations)}")
164
+ if worst_at:
165
+ rid, p = worst_at
166
+ print(f" worst at region {rid} "
167
+ + " ".join(f"{n}={v:.4f}" for n, v in sorted(p.items())))
168
+ return worst, violations
169
+
170
+
171
+ def check_counterexamples(cases, verbose=True):
172
+ confirmed, failed = 0, []
173
+ for c in cases:
174
+ xy = [[x * 1e-6, y * 1e-6] for x, y in c["xy_um"]]
175
+ radius = [r * 1e-6 for r in c["radius_um"]]
176
+ k = born_second_order_k(xy, radius)
177
+ n = len(xy)
178
+ kmax = max(k[i][j] for i in range(n) for j in range(n) if i != j)
179
+ if kmax > 1.0 and abs(kmax - c["k_predicted"]) < 1e-6:
180
+ confirmed += 1
181
+ else:
182
+ failed.append({"case_id": c["case_id"], "recomputed": kmax,
183
+ "published": c["k_predicted"]})
184
+ if verbose:
185
+ print(f" counterexamples {confirmed}/{len(cases)} re-derived "
186
+ f"and confirmed above the ceiling")
187
+ for f in failed[:5]:
188
+ print(f" MISMATCH {f['case_id']}: "
189
+ f"recomputed {f['recomputed']:.9f} vs published {f['published']:.9f}")
190
+ return confirmed, failed
191
+
192
+
193
+ def load():
194
+ regions = [json.loads(x) for x in
195
+ (DATA / "certified_regions.jsonl").read_text().splitlines() if x.strip()]
196
+ cases = [json.loads(x) for x in
197
+ (DATA / "counterexamples.jsonl").read_text().splitlines() if x.strip()]
198
+ theorem = json.loads((DATA / "theorem.json").read_text())
199
+ return regions, cases, theorem
200
+
201
+
202
+ def self_test() -> int:
203
+ """A checker that cannot fail is not a checker. Prove it still discriminates."""
204
+ print("negative control")
205
+ rng = random.Random(0)
206
+ ok = True
207
+
208
+ # 1. an impossible bound must be violated by sampling
209
+ regions, _, _ = load()
210
+ _, viol = check_regions(regions[:4], k_bar=0.5, samples=5, rng=rng, verbose=False)
211
+ hit = len(viol) > 0
212
+ print(f" [{'REJECTED' if hit else 'MISSED '}] fabricated bound k_bar=0.5")
213
+ ok &= hit
214
+
215
+ # 2. a tampered counterexample value must not re-derive
216
+ _, cases, _ = load()
217
+ bad = dict(cases[0], k_predicted=cases[0]["k_predicted"] * 1.5)
218
+ _, failed = check_counterexamples([bad], verbose=False)
219
+ print(f" [{'REJECTED' if failed else 'MISSED '}] tampered k_predicted")
220
+ ok &= bool(failed)
221
+
222
+ # 3. a layout with the pair alone must give k == 1 (no screening to find)
223
+ xy, radius = [[0.0, 0.0], [1e-4, 0.0]], [2e-5, 2e-5]
224
+ k = screening_factors(xy, radius)[0][1]
225
+ near1 = abs(k - 1.0) < 1e-9
226
+ print(f" [{'PASSED ' if near1 else 'FAILED '}] isolated pair reproduces k = 1 "
227
+ f"({k:.12f})")
228
+ ok &= near1
229
+
230
+ print(f"\n checker discriminates: {ok}")
231
+ return 0 if ok else 3
232
+
233
+
234
+ def main() -> int:
235
+ ap = argparse.ArgumentParser(description=__doc__,
236
+ formatter_class=argparse.RawDescriptionHelpFormatter)
237
+ ap.add_argument("--samples", type=int, default=25,
238
+ help="interior samples per certified region (default 25)")
239
+ ap.add_argument("--seed", type=int, default=0)
240
+ ap.add_argument("--self-test", action="store_true")
241
+ args = ap.parse_args()
242
+
243
+ if args.self_test:
244
+ return self_test()
245
+
246
+ if not DATA.exists():
247
+ print(f"no data directory at {DATA}", file=sys.stderr)
248
+ return 2
249
+
250
+ regions, cases, theorem = load()
251
+ k_bar = theorem["k_bar"]
252
+ print("screening-ceiling independent re-derivation (stdlib only)\n")
253
+ print(f" claim k <= {k_bar:.12f} for every layout in the family")
254
+ print(f" forced error pairwise over-predicts by >= "
255
+ f"{theorem['forced_pairwise_overprediction_pct']:.4f}%\n")
256
+
257
+ rng = random.Random(args.seed)
258
+ worst, violations = check_regions(regions, k_bar, args.samples, rng)
259
+ print()
260
+ confirmed, failed = check_counterexamples(cases)
261
+
262
+ bad = bool(violations) or bool(failed)
263
+ print()
264
+ if bad:
265
+ print(" REFUTED -- the published claim does not survive re-derivation")
266
+ else:
267
+ print(" consistent: no sampled layout exceeds the bound, and every "
268
+ "counterexample re-derives")
269
+ print(f"\n scope: {theorem['honest_scope']}")
270
+ return 1 if bad else 0
271
+
272
+
273
+ if __name__ == "__main__":
274
+ raise SystemExit(main())