[GoGoKo699]

Complete lookup remains the missing operation after the relative-involution repair. This change derives complete-action obstructions for joint bank mixing and auxiliary acceptance, and identifies a surviving construction whose lookup-dependent phase still needs native synthesis. R96 and the general resource frontier are unchanged.

• Either order of an affine bank permutation and a full Fourier layer has complete error at least √2 in the repaired word, for arbitrary X-diagonal pulses and computational-diagonal middles. At the original native product angles, no computational-monomial dressing gives exact lookup; this separate exact statement supplies no uniform approximate gap.
• A bank-only, fixed-address source with two Clifford mixing stages and arbitrary diagonal stages can have error below one only through an aligned rank-one exception. An explicit complete construction realizes the exception but does not pay for its middle phase. Two Hadamard masks in one common affine frame fail. The theorem does not cover active helper registers or address motion.
• The existing Bell charge conjugation gives exact norm transfer for arbitrary auxiliary effects, including coherent nondiagonal effects. Address-independent acceptance has the sharp Gram-error floor 1/4. A separate held-address, phase-free coset-permutation result explains why expansion alone cannot read the charge.

Proofs are in the coupled-encoder and Bell-source documents. Fifteen new exact tests cover native echoes and inverses, both affine/Fourier orders, correlated X phases, nonlinear monomial rigidity, the rank-one exception on every p=3 bank column, and coherent auxiliary effects. The 220-line workspace checkpoint and route/evidence catalogues preserve the scope and identify the unpaid native operation.

Starting main: 4598492c870b81666f8b149a4c8ccd8efcd8d0b2.
Reviewed head: 5291b3550a1e934fb6ab6c46bb0982c415838747.
Reviewed tree: 076b2c225d9fc6d1917bcecda2b27e63a31b0377.

Validation on the reviewed tree:

• Internal proof and scope audit passed; all 15 new exact tests passed.
• All ten required local commands passed (Python 3.12.14 / NumPy 2.3.5; 1,123.223 seconds). Gate receipt SHA256: e612c54b7bd568a49115fb9e58452c330c3d0ad55102bc9a2da8a7a252a36789.
• PR validation and push validation passed both Python 3.11 and 3.13 jobs. The successful exact-head log confirms 1,731 tests, OK.
• Full presentation CI passed: 370 documents, 5 diagrams, zero failures, covering desktop/narrow SVG and native MathML. Downloaded artifact 12581285106 matches SHA256 d04ff7a36db7f751748b0d625205fd340c34253ab924ca6b10ea6ee89c5ace3e; its parsed report SHA256 is 293c0e58b4eb200395c876f9bf0ef8b0e8c9be90dd7a1a574e18330496a6861c.
• Focused local rendering of both changed proof documents and the presentation guide passed, with visual inspection. Report SHA256: e0ecd3d52b30509b5e0c57d611a440ae6d279876e28854af16f0a31978a79c40. Duplicate full local render attempts were interrupted under memory pressure and are not counted as passes; the complete presentation receipt is the successful CI artifact above.
• Navigation checks, the 220-line checkpoint guard, and git diff --check passed.

These are scoped analytic results with finite regression evidence, not an unrestricted native-depth improvement.

Merged as a7a7cd213cf6df366a4c4e26261628caa645b03c. The merged main tree is exactly the reviewed tree 076b2c225d9fc6d1917bcecda2b27e63a31b0377; the local main checkout is synchronized and clean.