Extend QQ16 full-input obstruction to Clifford+T coefficients

[ywz65]

Normalized Hadamards and eighth-root phases do not repair PR2546's fixed complete-input QQ16 decoder. This contribution extends its credited full-input ideal-(5) obstruction from Gaussian-dyadic coefficients to Z[zeta_8,1/2], using an explicit unital reduction to F25. The same 224 granted observations vanish under this reduction while required original x_port1 equals one. The proof covers fixed finite affine-linear circuits, including the explicit normalized Clifford+T gate alphabet, without assuming the specialization preserves complex conjugation.

The source witness and minor census remain credited to Nick Petalas's PR2546 (3aff4ccbfaa1005e5093e95535e4d99aa3813e54); starship-s's PR2443 (545c05e17243c962b112b91e7f84b4c1a41de7b8) supplies the arbitrary-input two-cut contract. Both exact source documents are retained and hash-bound. The original H0 inverse remains a passing control. No information-loss claim over Q, selected-only obstruction, complete native alphabet binding, physical retention, supplier bill or new kappa is asserted.

Validation: native CPython 3.12.7 registered replay and CPython 3.14.5 direct optimized replay passed the exact witness, seven named gate controls/56 inverse columns, six mathematical failure boundaries and four Git-free export/corruption groups. Independent AI-assisted review used no candidate executable imports: all 390,625 cyclotomic residue products, 24 field inverses, a separate Q(i,sqrt2) gate implementation and full 224x224 observation maps passed; the original and alternative read maps have mod5 ranks 224 and 223 respectively, and the required output raises the latter to 224.

python3.12 -I -B scripts/research_package.py --package research/qq16-clifford-ring-obstruction

Fresh canonical main remains 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4, checked 16:23 UTC with both source heads unchanged. Overlap coverage combines the dated complete Discussion cache with fresh latest 100 open PRs and targeted PR2546 comments; it is not exhaustive. Our earlier canonical claim records completion and preserves its original scope. A newer independent claim also proposes native P/X/D/PH/C alphabet binding; that additional binding is invited as a complementary followup, and the shared ring extension is not counted twice.

Prepared by ywz65 with substantial OpenAI Codex assistance in mathematics, implementation, prose and checks. No independent human or proof-assistant certification is claimed. New work is Apache-2.0; predecessor notices remain intact.