[GoGoKo699]

A one-band copy can satisfy every output-Pauli test while changing its carrier. This change derives the complete linear seed-space criterion: signed Walsh blocks give exact affine-support spaces and spectra, and a carrier fixed point enforces the full copied operator. A positive semidefinite defect matrix supplies quantitative certificates for specified walls.

The criterion is applied to an explicit uniform triple-axis joint-wall family. Its native word uses 3m T gates in one band, 18m Clifford gates, and 2m arbitrary helpers. Every core Pauli survives the tensor prefilter, but the complete seed space is zero for p >= 2. Full copy error is at least 1/sqrt(6) for every unitary seed, including arbitrary helper operators and identity spectators. This is a family-specific obstruction; no scalable seed/copy construction, unrestricted one-band exclusion, or improvement to R96 is claimed.

Thirteen exact tests cover Walsh support/spectra and literal T/T-dagger signs, complete versus output-only constraints, native joint walls and inverses, helper phases, and the four-address error certificate. The checkpoint and catalogues route to one proof home and retain the conditional 42-band construction target.

Validation on final head 39cbc0c5bc40ce1e881d38a84e9719128f5fa466, tree c4374c6947e736386e669dadbb9370089f831589:

• All ten required local commands passed. CPython 3.12.14 / NumPy 2.3.5: observed 2,009 tests in 1,393.722 seconds, followed by OK; total gate time 1,427.834 seconds. Worktree clean before and after.
• PR validation: Python 3.13.16 / NumPy 2.5.4 passed 2,009 tests in 1,955.551 seconds, all four fault-tolerant suites and all 16 job steps. Python 3.11.17 / NumPy 2.4.6 passed 2,009 tests in 2,383.719 seconds, all four fault-tolerant suites and all 16 job steps. Both complete PR logs explicitly list all 13 new tests as passing.
• Exact-head push validation: Python 3.11.17 / NumPy 2.4.6 passed 2,009 tests in 1,277.170 seconds; Python 3.13.16 / NumPy 2.5.4 passed 2,009 tests in 1,991.478 seconds. Both jobs completed all 16 steps successfully.
• Full presentation CI passed all nine steps and archived artifact 12806386827 (342,378,957 bytes). Its head binding was verified.
• Focused presentation: all six changed Markdown inputs byte-match the final tree; 214 unique expressions, 246 protected occurrences, zero failures. Visual inspection covered the proof opening, Walsh basis, native walls, robust proof at desktop/narrow widths, and narrow WORKSPACE. This is not a claim of manual inspection of every repository preview.

Exact-tree receipts:

• Base 97ade196941b6d8780556bbfa1585d311beee6f2; PR merge commit 8397cc919a9709310cd5b241e301f93a3d70cc9b has the identical final tree. Both complete PR logs explicitly check out that merge commit.
• Local gate: 2026-10-28 09:31:28.412227–09:55:16.247029 UTC; OPENBLAS_NUM_THREADS=1, OMP_NUM_THREADS=1.
• Local receipt SHA256: 95ac72654b3354aa67af18354fea913da651babf84cdf3a62e8365bb0a3c46bb.
• Complete local validation log SHA256: ab7d7981895d78f36a372cd148189413e81c8a86ea7f18eaddc37c701d50cb6a.
• Focused presentation report SHA256: 1a355359803efc2879b9de37ae20f95602d869360946d147b32078dd2f5740ea.
• Full presentation artifact SHA256: 2dd87954d82d38f6f2eac9119e80cf6b2102e51e5ff44e631fd9d8e2c0aa491e.

All five final-head checks were confirmed successful before merge.