Research theorem: common-flag rational-frame obstruction (no new kappa)

[navinor]

Result

Scoped negative theorem; no new kappa. In the fixed-width all-role rational-frame XOR interface, one common affine complete flag forces total paid rank s >= Wm. The resulting normalized child moment is at least one for every 0 < q < 1, even granting zero extra overhead. All physical edges, terminals, untouched roles and independently initialized scratch roles are charged.

This excludes arbitrary commuting rational frames, including Jordan blocks and nonsplit spectra, and also noncommuting upper-triangular frames. The proof uses characteristic-zero additive exponents in a characteristic-two Laurent fraction field, a rank perturbation telescope and triangular principal minors. It needs no routing hypothesis.

Only research/common-flag-frame-obstruction/ is added: proof/scope, exact finite evidence, standard-library checker, source pins, claim and verification handoff. The universal theorem is written separately from the finite checks.

Reproduce

python3 -I -B research/common-flag-frame-obstruction/verify.py
python3 -I -B research/common-flag-frame-obstruction/validate.py

Expected: PASS_COMMON_FLAG_OBSTRUCTION cases=14 tests=13 bound=s>=W*m kappa=unchanged, then PASS_COMMON_FLAG_CLI_CONTROLS with the control names.

Executed on Windows with CPython 3.14.7 and 3.12.14:

• All 14 exact circuit cases, 13 tests and 729 triangular-matrix differences pass. The existing repository scorer independently agrees on all per-edge ranks and all-role endpoint contracts.
• Optimized relocated replay, unchanged-input check, source/receipt corruption rejection, output overwrite protection and byte-identical regeneration pass.
• Existing finite-bit contract suite: 9 tests pass. Selected-record integrity check at the exact base passes. Staged whitespace check passes.

Full make verify, supplier cold replay, Linux execution and proof-assistant formalization were not run. Finite success does not formally verify the universal theorem or the full multiplication theorem. Details and commands are in VALIDATION.md.

Provenance and scope

OS-random assignment seed 42, structural-decoder track; three candidate scopes and the local claim are recorded in CLAIM.md. No pinned coordination issue exists. The final overlap snapshot covered 637 open PRs through #824, with no matching common-flag theorem found.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60, selecting PR 626/PR 543. During verification upstream advanced to 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261, selecting PR 741 with PR 589/PR 555 at 1661202643272239/1000000000000000000. Its selected record, assembly, actual construction and maintainer review were inspected. All four mathematical runtime sources are unchanged; frontier metadata is historical context rather than a replay dependency.

Credit Douglas Colkitt's commuting-projection/core work and the retained finite-bit/routing interface. Related pending work is attributed and distinguished in the README: DreamingOfClouds' PR 717 nonprojection-label question; Curtis-D's PR 791 idempotent-path penalties; littleBro's PR 705 and jeremydiviney's PR 800 Clifford criteria; davidgovea's PR 720 endpoint-target flag removal. This does not derive the older label-count inequality or close the unrestricted nonprojection question. No pending implementation is imported.

The theorem assumes all W inputs are independent, one common frame per linear XOR gate, all-role endpoint identity and one common affine full flag. Nontriangular frames, clean-input/dependent-copy models, changing width and complex Clifford interfaces remain outside scope. The verifier checks supplied flags, not general flag existence. No selected-supplier physical realization or inherited all-size/compiler/hosting/precision/analytic obligation is discharged.

Prepared for @navinor, with substantial OpenAI GPT-6 Astra assistance in derivation, implementation, testing and writing, including separately scoped AI proof and implementation reviews. Apache-2.0; no independent human review or literature-priority claim.

[Mister-Meeseeks]

100-PR batch review at 421db1ca2eb26056e82797f94b8c4eecd0120620.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Common-complete-flag rational-frame obstruction via a characteristic-two group-algebra telescope; unrestricted nontriangular frames remain open.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.