[Superseded by #343 and #347] Audit finite gauge ambiguity beyond local query observability

[FlorianPfaff]

Scientific question

Can a locally supported physical query still vary over a finite unobserved gauge, and can decision-relevant common uncertainty cancel even when marginal intervals are broad?

This follows the partial-gauge and local-query work in #332 and #338. It is an analysis-only method extension and deterministic development control, not another provider adapter or a change to a target-side admission policy. It does not claim to repair a localized real-provider failure or advance a provider readiness stage.

Concrete counterexample

An exactly collinear x-axis overlap is invariant under rotation about x. For a probe initially at (0, 0.1, 0), the scalar query is y(phi) = 0.1 cos(phi). Its first twist derivative at zero vanishes, while its finite range is [-100, 100] mm.

The existing rank-six analytic factor gives direct local support 1, variance reduction 10/11, and worst variance ratio 1/11; the existing illustrative local gate admits the scalar query. This is not a bug in that explicitly local calculation and does not establish posterior undercoverage. It falsifies interpreting the local report as global finite-orbit invariance or a distribution-free decision certificate.

Method

Adds a NumPy-only experimental kernel for registered axial rotation groups and affine queries:

• exact finite-orbit query and pairwise-contrast bounds;
• correct aggregation inside a shared gauge group before taking amplitudes;
• sharp worst-case regret for actual affine action losses sharing the same angles;
• an attaining competitor/angle witness; and
• explicit support-motion and malformed-input checks.

The action check is analysis only: no action, belief selection, provider export, or production admission rule is changed. BayesianPhysTwin retains complete-belief selection and exact fallback ownership.

Controls

Control	Analytic result
Stationary off-axis y query	local twist derivative 0; finite range [-100, 100] mm
Off-axis probe, axial-coordinate query	exactly 40 mm for every angle
Equal-radius y difference, shared angle	exactly 0
Same points, separately variable angles	[-200, 200] mm; coincident axes do not authorize merging
Losses 0.1-y and 0.1+y	reference-selected action has 200 mm worst-case regret; exceeds illustrative 50 mm budget
Losses 0.05+y and 0.10+y	overlapping marginal intervals, but action 0 has exactly zero regret

Assumptions and novelty boundary

Sharpness is restricted to the declared product of full axial circles, fixed remaining transform parameters, and affine queries/losses. A rank-six factor, a near-collinear support, or a small Jacobian does not establish a finite likelihood symmetry. Smaller/coupled domains give conservative rather than necessarily sharp bounds. This is float64 evaluation of analytic formulas, not certified interval arithmetic.

Rodrigues' formula, harmonic support functions, group symmetry, and worst-case regret are classical. The documentation cites X-ICP and symmetry-reduced filtering and does not claim an exhaustive novelty result. The proposed contribution is the narrowly scoped finite-gauge/shared-lineage audit and its concrete negative and positive controls, not a new generic quotient theorem or a fourth manuscript.

Compatibility and evidence boundary

Exactly four additive files: kernel, reproducer, tests, and derivation/usage note. No stable API, existing result, calibration, exporter, workflow, protected dataset, source/target roster, runtime request, or claims.json change. No provider, target, BayesianPhysTwin, or Causal4D experiment executed. No new hardware acquisition is assumed. #333 remains separately governed and unqualified.

Validation before publication

• 27 standalone tests passed locally on Python 3.13.5 / NumPy 2.3.5.
• One existing-module integration test was explicitly deselected in the minimal offline copy; the committed test does not silently skip and must pass in the full repository CI.
• Independent quaternion reference, attained extrema/regret witnesses, shared cancellation, frame and axis-sign invariance, no-free-angle case, invalid inputs, and deterministic development output checked.
• Python compilation passed.
• Local Ruff/mypy were unavailable; exact-head hosted CI remains authoritative.

Draft pending exact-head CI and inspection. No auto-merge requested. Paper-facing development output will be retained separately without promoting an empirical claim.

[FlorianPfaff]

Validation completed for head 9f3cab5db1dcb09841ce53d448b9ce657379be69.

• Full hosted matrix passed: Python 3.10-3.14 plus declared runtime floors; build/install smoke jobs also passed.
• The Python 3.12 job 99171359127 in Tests run 33279210423 reports 1908 passed, 10 existing skips, 2 existing warnings. tests/test_axial_gauge_query.py executed all 28 tests, including the real local-gate integration; none of those tests were skipped.
• Fail-closed quality run 33279210438, provider preflight 33279210432, and security scanning 33279210425 all passed. The quality workflow checks changed Python with Ruff and the existing stable-interface list with mypy; this is not a claim of full new-module mypy coverage.
• CI checked out synthetic merge 19d4a2e70c17d2604f04d4c8296fd93eb0ac22ab. GitHub reports tree dbf050a408e3ad8603500d7b426aeb024138370c, identical to the PR head's tree.
• All four pushed files' Git-blob identities match the locally tested files.

Paper-side development output, source/output hashes, scope, and CI provenance are retained in BayesianPhysTwin-Paper PR #115. This supersedes the initial pending-CI paragraph, without promoting an empirical claim.

The attempted ready-for-review transition hit a connector GraphQL schema error (Repository.fullDatabaseId). No merge or auto-merge was requested.