[thu-nmrc]

Two native FULL calls cannot complete pure rank-17 jobs on all main inputs, even when all 224 native main owners mix jointly across ports and arbitrarily many independent dirty identity workspace fields are available. The theorem covers any number m of main pairs, including the actual m=112 bank. No new kappa or supplier is claimed.

PR #4920's full-routing theorem covered exactly two main owners; its dirty-scratch theorem used a separated address algebra. This closes the released #4902 stabilization handoff and also removes the separate pairwise-routing restriction.

The new middle-grade projection (Fourier grades 1 through 16) forces all interstage main/workspace cross blocks to vanish. Workspace then occupies the entire allowed low-grade rank. A whole m-column main block must vanish, contradicting invertibility. The proof retains arbitrary outer owner mixing, role-dependent rank-eight factors, independently partitioned stages and noncommuting query letters. It even grants arbitrary dense m-by-m query blocks over the ambient group algebra. No reduced outer main block is assumed invertible and no transverse factor is commuted past a query.

The precise class is invertible controls over a fixed finite columnwise full monomial Clifford algebra, including central/fresh routing. Every dirty workspace input is arbitrary and must return unchanged. Source helpers remain autonomous and unavailable for mixing. Owned-zero COPY/CLEAR, native prefix observations, productive helper resources, altered interfaces, additional paid operations and approximate/noncolumnwise endpoints remain distinct resources. The actual112-port main ABI is inherited explicitly; no fresh native632 replay is asserted.

research/two-full-dirty-stability/PROOF.md contains the all-width argument. A separate agent review pins final manuscript SHA256 5c9331d51246ec9f3c6aabcb11b25eb6e438a3db4aee15cb61a9d24f55bfdf2f and finds no remaining blocker. Finite corroboration includes:

• Phase-correct sparse projective Clifford group algebra: 12 original orientation/workspace cases, six joint-bank cases with different stage partitions, 972 grade-band bimodule fixtures and actual17-axis 8/8/16/17 thresholds. Width-one matrix-sum relations are not treated as formal identities.
• Separately implemented free-word checks: 72 cross-row, 72 cross-column and 36 main-column identities, plus 36 dense-query multipair cases covering m=1,2,3 and s=0,1,2.
• A transformed-workspace boundary where the middle-grade elimination hypothesis fails; this is a scope control, not a positive endpoint.

Finite checks corroborate the written proof; they do not machine-check its universal quantifiers.

Validation at exact head 40bb94aebbf591a99e2f48533f16efe8914fb1e2:

• All six registered Python3.12 normal/optimized commands pass, standard-library only and read-only by default.
• Committed-byte preflight and official19-file export/integrity checks pass. All six commands pass from that Git-free export with PATH=/nonexistent, preserving every exported byte.
• Twelve actual source/manuscript/receipt corruptions reject across normal and optimized modes in the final exported bundle.
• Fresh main ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c has identical live inherited inputs; scientific base/catalogue remains a5df48c55ea806d7952b65acc9c76d878ff09b13.
• Source-ancestry preflight is unavailable in this shallow clone. Native632, compiler/precision/tape/outer and proof-kernel checks were not rerun; source interfaces and tensor separation remain explicit inherited premises.

Credit Chris R / Clear1nsight and the #4920/#4928 authors, JoyboyBrian's released handoff, Cinna Davis / 1337isnot1337, Cao Yifan / intqwq, Dugongue, zxv, Jacob Alan Sussman and the retained native/Clifford/compiler lineage. New intermediate-grade decoupling, stability and joint-bank extension prepared for @thu-nmrc with substantial OpenAI Codex assistance and separate algebra/review agents. Apache-2.0. Agent review is not independent human or kernel acceptance.

Request: substantive review of the middle-grade decoupling, regular-module rank reduction and joint-bank zero-column block. Archive merge and scientific adoption remain separate; no selected-frontier or core-contributor status is asserted.