\n\nA formal specification is not a presentation. It is a contract that compiles.
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This project is the first attempt to treat interatomic potential validation as a theorem-driven engineering discipline. Rather than running every simulation and hoping the statistics converge, we formalize what it means to validate — and we lock that formalization into the build.
\n\n\nCurrent status (2026-06): the Projection Law proof chain now reports 77\nbuild-locked theorems, ~225 theorem/lemma declarations, seven paper theorems,\nzero
\nsorry, and a 2,891-joblake buildgreen. This page began as the\nearlier executable-vision snapshot; the inventory below is retained as lineage,\nwhile the counters have been updated to the current public proof surface.
In conventional materials informatics, a "claim" lives in a PDF. In this project, a claim lives in a Lean 4 module — and if the claim breaks, the build breaks.
\nOur vision file (Vision.lean) contains #guard statements that are evaluated at compile time:
#guard (hypothesisCount >= 6)\n#guard (computationallyProvenCount >= 10)\n#guard (epistemicGapCount >= 1)\nThese are not tests. They are epistemic minimums. A future commit cannot silently drop below 6 formally stated hypotheses, remove all computationally proven theorems, or close every epistemic gap without justification.
\nsyntheticFccCount — 72 FCC entries embeddedsyntheticBccCount — 42 BCC entries embeddednistScaffoldCount — 9 NIST scaffold rowsnistScaffoldAlMissing — NIST predictions are absentsyntheticFccIsSynthetic — all FCC entries carry synthetic provenancesyntheticBccIsSynthetic — all BCC entries carry synthetic provenancesyntheticFccNonEmpty / syntheticBccNonEmpty — datasets are non-emptynistScaffoldPredictionsMissing_bool — structural check on missing datanoSimpsonsDetected — Simpson's paradox is fabricated in synthetic BCCpooledRBelowMinus08 — pooled correlation < −0.8pooledWithinRBelowMinus09 — within-group correlation < −0.9nGroupsEqualsSeven — exactly 7 metal groupsnTotalEqualsTwentyOne — exactly 21 data pointsreversalMagnitudeAbove01 — reversal exceeds significance thresholdsyntheticBccEamPointsNonEmpty / syntheticBccAllPointsNonEmptyfccEamPRBounded — EAM PR ∈ (1.2, 1.3)fccLjPRBounded — LJ PR ∈ (1.1, 1.2)fccSwPRBounded — SW PR ∈ (1.1, 1.2)fccAllPRBounded — All FCC PR ∈ (1.3, 1.4)paperClaimHolds — hyper-ribbon claim satisfiedfccEamPRGreaterThanLj — EAM PR > LJ PRfccAllSatisfiesHyperRibbon — PR/n < 0.5 for full FCC setfccEamVectorCount / fccAllVectorCount — structural countsfccAllMoreThanEam — full dataset larger than EAM subsetsyntheticEamSatisfiesBound — EAM participation ratio ≤ min(params, observables)hypothesisBoardLength — exactly 6 hypotheses registeredcubicIrrepSum — cubic irrep dimensions sum to 4trueCausalGraphNoConfounder — nature: element → structure → error (no bypass)syntheticCausalGraphHasConfounder — synthetic data: element → error (confounder)printStatusBoardNonEmpty — status board rendersallPredictionsHaveTraces_empty — empty benchmark needs no tracesallPredictionsHaveTraces_nil_traces — nil trace list behaviorsyntheticEntryNeedsNoTrace — synthetic provenance needs no LAMMPS runactualExperimentIsNotNistBacked — our experiment lacks NIST provenanceactualExperimentUsesSyntheticData — all predictions are syntheticactualExperimentNotPreRegistered — no pre-registration record existssyntheticFccFailsNistIntegrity — synthetic FCC fails NIST integrity checksyntheticBccFailsNistIntegrity — synthetic BCC fails NIST integrity checksimpsonVerdictContainsFabricated — audit string contains "FABRICATED"hyperRibbonVerdictContainsConsistent — audit string contains "CONSISTENT"auditReportNonEmpty — report renderssimpsonPooledRNegative — pooled correlation is negativenistScaffoldIncomplete — NIST scaffold has no predictionsEvery theorem in the specification is fully proven — there are no sorry proofs. But not every claim is grounded in NIST-backed data. Five documented gaps in Validation.Experiment mark the boundary between what we can compute on synthetic data and what requires ground-truth LAMMPS traces:
These gaps are not bugs. They are features of honesty. They prevent the build from pretending to know what it does not know.
\nMost interatomic potential papers publish:
\nThis project publishes:
\n\n\nProof or reproducible trace. Everything else is marketing.
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