{"id":"t1-wander-gate","title":"T1 — The Convention-Wander Gate","subtitle":"Gate semantics for cross-engine barrier comparisons: |barrier_A − barrier_B| ≤ offset wander, so wander above the 40 meV gate downgrades a VASP-referenced verdict to convention-contaminated.","category":"references","tags":["t1","wander","gate","cross-engine","theorem-commons"],"source":"articles/docs/analysis/t1-wander-gate.md","lang":"en","words":1090,"readMinutes":5,"toc":[{"depth":2,"text":"1. Measured evidence — one failure, one win, same wander","id":"1-measured-evidence-one-failure-one-win-same-wander"},{"depth":2,"text":"2. Why the wander, not the mean","id":"2-why-the-wander-not-the-mean"},{"depth":2,"text":"3. Gate semantics","id":"3-gate-semantics"},{"depth":2,"text":"4. Why this is the theorem-commons loop working","id":"4-why-this-is-the-theorem-commons-loop-working"},{"depth":2,"text":"5. Future work — Lean formalization sketch","id":"5-future-work-lean-formalization-sketch"},{"depth":2,"text":"Reproduce","id":"reproduce"}],"html":"

T1 — The Convention-Wander Gate

Theorem line: T1 (first theorem contributed from our own campaign failure) ·\nScript: tools/analysis/t1_wander.py (stdlib-only) · Tests: tools/analysis/test_t1_wander.py ·\nWired into: gcp/sparse-dft-pilot/union_pilot.py assembly (per_path[].t1_gate, t1_summary) ·\nAmendment: docs/plans/2026-07-21-sparse-dft-pilot-amendment-01.md (§A1) · Recorded: 2026-07-21

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Per evaluated image of a NEB path, the cross-engine offset is\noffset(image) = E_GPAW(image) − E_VASP(image). T1 reports the offset mean\nand the offset wander (max − min) per path, and gates on the wander.

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1. Measured evidence — one failure, one win, same wander

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
PathAnchorsOffset wanderCross-engine barrier errorVerdict vs ≤40 meV gate
path-7, mp-770939_10_1_1_0_14 (images 0,1,2,4)139.4 meV118.8 meVFAIL
smoke path, mp-760344chgnet-guided set~122 meV32.2 meVWIN

Path-7 numbers are reproduced by the gate from the receipt\n(/tmp/z1-sparse-local/chgnet/path-7.json, imported as union checkpoints\nlupine.z1.union_pilot.anchor.v1): per-image offsets −14756.1, −14698.1,\n−14616.8, −14666.2 meV → wander 139.3758 meV, mean −14684.3 meV, driven by\nthe image pair (0, 2). The smoke-path figures are the recorded trigger\nevidence of amendment 01 (its anchor receipts predate the union checkpoint\nlayout; only /tmp/gpaw-pilot/run.py survives).

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The two rows are the whole argument: two paths, two opposite verdicts, the\nsame wander magnitude. Under a single VASP-referenced basis, the pilot's\nverdict measures where the engine-convention wander happens to land, not\nprotocol quality. Wander is necessary but not sufficient for a cross-engine\nfailure — the smoke path won because its wander landed off the\nbarrier-defining images. That is exactly why T1 is a gate with a\ncontamination flag, not a hard refusal.

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2. Why the wander, not the mean

A barrier is an energy difference between different structures:\nbarrier = max_i E(i) − min_i E(i). A constant offset — however large —\ncancels in every difference; the −14.7 eV mean above is barrier-irrelevant.\nOnly variation of the offset across images injects into the comparison, and\nthe worst-case injection over a path is bounded by the wander:

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|barrier_GPAW − barrier_VASP| ≤ wander = max offset − min offset\n
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(proof sketch in §5). With measured wander ~3× the 40 meV verdict gate, every\ncross-engine verdict on these paths was one unlucky landing away from\nflipping. Amendment 01 therefore splits the basis (same-engine primary,\nVASP-referenced secondary) and promotes T1 to its own experiment.

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3. Gate semantics

Default threshold is the frozen verdict gate, 40 meV\n(WIN_THRESHOLD_MEV in gcp/mlip-cell-runner/z1_sparse_dft.py).

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The gate also reports the driver pair — the (min-offset, max-offset)\nimage pair whose difference is the wander — so a contaminated path names\nits own contaminated span (path-7: images 0↔2, which are also the\nbarrier-defining extrema of its sparse profile; the contamination sits\ndirectly on the barrier). Per-image drift vs a least-squares linear trend in\nimage index, and a Spearman rank monotonicity, are reported alongside as\ndiagnostics (path-7: slope ≈ +22.1 meV/image, ρ = 0.8 — the offset shallows\noverall along the reaction coordinate).

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In campaign.json (lupine.z1.union_pilot.campaign.v1, additive fields\nonly): per_path[].t1_gate = {wander_mev, verdict, driver_pair},\nt1_summary.paths_contaminated / contaminated_path_indices, and\nthresholds.t1_gate_mev. The gate is wired into union_pilot.py assembly as\na reported line item — it downgrades interpretation, never refuses a path.

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4. Why this is the theorem-commons loop working

T1 is the first theorem contributed from our own campaign failure. The loop\nran: a frozen preregistration produced a FAIL → the per-anchor receipts\nlocalized the cause to a protocol-external quantity (engine-convention\nwander) → an amendment split the basis so each verdict measures one thing →\nthe localized cause became a reusable gate that anyone comparing barriers\nacross engines can apply to their own receipts, before quoting a\ncross-engine number. The failure is now load-bearing: it defines the\nhypothesis (wander ≤ ε) under which cross-engine barrier comparisons are\ntrustworthy at tolerance ε, and it ships as a stdlib-only function with the\nmeasured counterexample pair encoded in its tests. Every future path in this\npilot — and any external GPAW↔VASP, or generally engine-A↔engine-B, barrier\ncomparison — gets flagged by the same gate instead of rediscovering the\ncontamination as a spurious verdict.

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5. Future work — Lean formalization sketch

The gate is the decidable hypothesis check of an elementary transfer theorem.\nState barrier f s = s.max' f − s.min' f over a nonempty Finset ι; the\noffset o : ι → ℝ is the cross-engine convention difference. Then:

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theorem barrier_transfer_of_bounded_offset_wander\n    {ι : Type*} (s : Finset ι) (hs : s.Nonempty)\n    (E o : ι → ℝ) {ε : ℝ}\n    (h : ∀ x ∈ s, ∀ y ∈ s, |o x - o y| ≤ ε) :\n    |barrier (fun i => E i + o i) s - barrier E s| ≤ ε := ...\n
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Proof idea (two inequalities, both one-liners from Finset.le_max' /\nFinset.min'_le): with x*/x⁻ the extrema of E + o,\nbarrier (E+o) − barrier E ≤ o x* − o x⁻ ≤ ε, because\nbarrier E ≥ E x* − E x⁻; with y*/y⁻ the extrema of E,\nbarrier E − barrier (E+o) ≤ o y⁻ − o y* ≤ ε. No library changes are needed\nfor the statement; the hypothesis is decidable on receipts because\nmax_{x,y} |o x − o y| = max o − min o = wander, i.e. the gate IS the\nhypothesis evaluated on data, with ε the verdict gate. Two honest\nboundary notes for the formalization: the converse is false (bounded wander\nis sufficient, not necessary — the smoke path's 32.2 meV win under 122 meV\nwander is the counterexample, since only the offset difference between the\nbarrier-defining pair enters the error), and a refined theorem bounding the\nerror by |o(argmax) − o(argmin)| alone would formalize that observation at\nthe cost of needing the extrema identified — which the sparse protocol is\nitself trying to estimate. The wander form is the version checkable before\ntrusting any verdict.

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Reproduce

# unit + real-receipt tests (receipt-cross-checks skip if /tmp files absent)\npython3 -m pytest tools/analysis/test_t1_wander.py -q\npython3 -m pytest gcp/sparse-dft-pilot/test_union_pilot.py -q\n\n# gate on the real path-7 anchor pool (offline assembly; no GPAW)\npython3 gcp/sparse-dft-pilot/union_pilot.py \\\n    --workdir /tmp/z1-union-local --local /tmp/z1-union-local/inputs \\\n    --paths 7 --assemble-only --no-import --out /tmp/campaign.json\n# -> path-7: wander=139.4 meV, t1_gate=contaminated, driver_pair=[0, 2]\n
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