[DavidAriasC]

Change and mathematical scope

Masked decoders leave the odd-pair entries unconstrained, so the existing all-pairs copy-cost floor does not directly apply. This scoped research result classifies the entire complex connected component containing the standard P112 eight-term decoder: every point is a factor-basis change and reciprocal row scaling of an all-pairs decoder. Consequently every continuous path of exact eight-term masked solutions from that starting point retains copy cost at least 64.

Both factors may leave the root-coordinate space. The exact 6,720 × 1,792 Jacobian has rank 1,617 and nullity 175. A written open-and-closed orbit argument extends the tangent calculation to the whole component, including exclusion of escape through deficient-rank factors. This is stronger than the trivial local floor from support persistence.

No new κ or physical supplier is claimed. Disconnected components, discrete/approximate searches and decoders with nine or more terms remain open. The cost corollary inherits PR1077/968's geometric classification premise and separate-term pairing-rank convention. All physical/compiler, hosting, precision/tape and analytic obligations remain unchanged.

The research package and its path-scoped .github/workflows/p112-masked-tangent-audit.yml workflow are added. Start with README.md and PROOF.md; the selected frontier, upstream and frozen inputs are untouched.

Task and overlap

Base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe, verified as current main before submission. Task selector: complex-masked-decoder, nonce c4cb3fadd3712193711993a2fb0dac76; TASK.md records the bounded domain and method.

PR1191 (640b43bb13d3d476a2d83b74ef0d33f14d1b5711) proves one-sided root-linear masked rigidity for arbitrary term count. This result instead treats two unrestricted factors, eight terms and one connected component. PR1180 (75b408646d558147a4eb250fc407d1fbfcb8df4e) treats overcomplete all-pairs root-linear factors. Discussion1210 proposes an arbitrary-term root-star support census; it is complementary and remains provisional. Exact predecessor heads and source hashes are in SOURCES.json. The final overlap scan covered 820 open PRs including drafts through #1211 and all six active discussions.

Validation

Python 3.10+; standard library only:

python3 -I -B research/p112-masked-tangent-audit/verify.py
python3 -I -B research/p112-masked-tangent-audit/independent.py
python3 -I -B research/p112-masked-tangent-audit/test_package.py

Passed on macOS arm64 / CPython 3.14.7:

• Primary sparse F101 elimination checks a 1,617-square minor and 175 independent integer kernel directions; nine semantic controls pass.
• Separate symmetric/antisymmetric F3 bitset implementation obtains ranks 868 + 749, integer kernel dimensions 28 + 147, and six control groups.
• Five package tests cover optimized isolated relocation, read-only replay, corrupted evidence, changed/missing proofs and omitted source pins.
• PR1077's complete scoped verifier, selected-record integrity, five named selected-record tests and whitespace checks pass.

The proof and code received separate AI review; the identified source-inventory hardening is included. No Lean, full selected-supplier cold replay or independent human mathematical review is claimed. VALIDATION.md records commands and limits.

Hosted CI

The focused GitHub Actions run passed on Ubuntu 24.04 with Python 3.10 and 3.14, for PR head 8867cf20fbe0d3960f68bcffca118a5ac0624f7f. Both jobs passed the primary and independent certificates, optimized relocation/rejection controls, inherited complex-floor replay, selected-record integrity/regressions, and unchanged-tracked-files check. No test failures required mathematical or verifier changes.

These are fork-hosted results. Upstream fork workflows remain behind GitHub's maintainer-approval gate; they are not represented as passed. The unfiltered historical fork suites were canceled because they do not cover this package. Their workflows and tests were not changed.

Credit

DreamingOfClouds (PR717/595), themilkman216 (PR968), woklerx (PR1077 and complementary PR1180), Philipp / mightyOil (PR1191), Joel Pulikkan / GamingPuzzled (PR620), icekylinx (P112), and the retained supplier lineage retain attribution. Substantial OpenAI Codex assistance in research, mathematics, both implementations, review and writing. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 8867cf20fbe0d3960f68bcffca118a5ac0624f7f.

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

Reviewed scope: Exact 1617-rank masked Jacobian and 175-dimensional gauge orbit; inverse-function and closed-orbit arguments classify the coordinate connected component, retaining inherited floor64. Disconnected or overcomplete solutions 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.