Prove an exact involutive Walsh lift of the historical selected complex supplier

[aliromman]

This enabling proof replaces the historical selected complex supplier's frames with exact involutive Walsh frames. For each old rank-r frame, Gamma_V = i^-r (H_V tensor H_V) satisfies Gamma_V^2 = I on arbitrary arrays. The actual routed centre queries then admit complementary factors whose cross-stage product is zero. This removes a coefficient-field obstruction to a reusable centre encoder.

The proof and finite invoice, centre application, complete replay receipt, and source manifest are pinned to the reviewed commit. The native proof and global binding establish the implementation interfaces.

The construction doubles the ambient dimension from 73 to 146 and every recursive child rank. It retains the 14336 productive families, complete borrowed-helper jobs, invocation order, owner assignment, and diagonal cover-group order. Its paid rank mass is 2082816 and its rank deficit is 10240. Every normalized recursive rank ratio is unchanged, so the pure complex moment and complete kappa calculation do not improve. The twofold lift passes the complete retained finite guards, including the 512-bit prefix and 48-bit local primitive bound. The fourfold comparison fails the local primitive guard.

The exact base and consumed dependency commit is bce54fb3f895cbe5cd4c0eb477c3afeed100190f. The input is the historical PR #1094 selection receipt, not a claim about today's selected frontier. The proof retains the all-size native, compiler, whole-call hosting, precision, fixed-tape, and analytic recurrence assumptions. The replay emits local native factors and a complete global operator schedule; it does not flatten an all-size instruction tape or prove the full multiplication theorem. Legal decoder access, changed-word mode hosting, and the complete cost of a cheaper centre supplier remain open.

From the repository root, with Python 3.10 or later, Git, and the pinned source commit present, run:

python3 -I -B research/involutive-walsh-lift/verify.py

The expected final line is:

PASS_INVOLUTIVE_WALSH_LIFT_PACKAGE

All seven stages passed, including cold replays into fresh output directories. Separate research agents checked the proofs and wrote independent exact reviewers. Coverage includes 1004 full frame adapters, 2896 full child operators, 224 endpoints, 36 helper normalizers, all 712 scalar input columns in both orientations, all 144 selected calls, 69120 complete helper jobs, 7526 idle suffixes, and 14336 productive endpoints. Negative controls reject a missing scalar phase, the singular even-line formula, a wrong helper route, a missing helper job, an incorrect bridge sign, and stale terminal or cover translations. Two exact rational moment engines agree. The final staged source and artifact hashes match the replay. Source assertions are required; do not run the driver with -O. The old frontier admission target was not rerun or modified. Independent human review has not yet occurred.

The source notices preserve the full lineage. The consumed local word and gauge are credited to @icekylinx in the gauge44 notice; the 16-replica assembly is credited to Hao Yan (@FanPUYen) in the t16 notice. The owner exchanges and invoice use @rohanarun's PR #1094, whose source README also credits Jeremy Kothe (@jeremykothe2) for PR #1087. Earlier author and license notices remain intact. New research, code, and verification used substantial OpenAI Codex assistance under the user's direction. New material uses the repository's Apache-2.0 license.

[Mister-Meeseeks]

Batch review at 3ae9a6f3ac74ded022ab3b4872a7357a621af6fb.

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

Reviewed scope: Written doubled-Walsh operator and cover proofs, complete native/global replays, and independent invoice checks preserve normalized recursive ranks and arbitrary helper jobs under inherited interfaces. The Gaussian-unit lift makes port phases involutions; changed centre decoding, mode hosting and its costs remain open, with no selected-bound improvement.

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.