Research: all-depth QQ16 cover-map parity floor at B1 cut

[1337isnot1337]

Scope and result

Scoped all-depth obstruction; no new kappa. At the exact post-B_1_2 QQ16 cut, the eight Y_A output frames each have 18 odd Z4 terms, while the existing private fields C0..C7 return in the zero frame. Every registered cover map applies an invertible binary owner transform and adds only coefficient 2. Modulo two, the payload shift vanishes and the owner transform preserves odd-support size. Therefore every finite composition of cover maps leaves all eight frames at odd-support weight 18; this rules out depth-one, depth-two, depth-three, and longer map-only normalization.

In the declared one-term native-line model, one rank-one correction changes at most one parity bit. Reaching the private zero frames requires at least 18 corrections per output, or 144 rank-one line calls total. This exceeds by 72 times the favorable budget of at most two extra rank-one-equivalent operations after the rank-eight output charge. The bill also includes 288 associated full-cover map operations, eight scalar copies priced at 32 real primitives, and up to eight terminal clear primitives (zero additional clears if the existing next core follows). Further map implementation, hosting, source routing, and precision charges cannot lower the line floor.

This extends the released one-map / one-term result in PR #2197 with an all-depth invariant. It is limited to the pinned eight frames, registered invertible cover maps, and one-term Z4 corrections. Alternate field layouts and multi-term native operations remain open. No full controller, supplier admission, or selected-bound change is claimed.

Exact evidence and reproduction

The source-pinned verifier reconstructs the eight port frames from the native recipes, checks all 3,650 owner maps for rank 73, applies every map to every port frame (29,200 checks), and validates a two-map positive control. Negative controls demonstrate that an odd coefficient shift could cancel a parity bit and that a singular owner map violates the invariant's hypothesis.

python3 -I -B research/qq16-map-parity-floor-seed-ed361f3c/verify.py
python3 scripts/research_package.py --package research/qq16-map-parity-floor-seed-ed361f3c --check-only

Both commands pass locally under CPython 3.14.7. The registered package replay requests Python 3.12, which is unavailable locally.

Pins and predecessor attribution

• Seed ed361f3c876dd81e664556c9f95bd36e; recursive-interfaces, joint-query-controller, priority revision 4.
• Scientific base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.
• Selected-result SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Catalogue SHA-256 d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7.
• Map/frame input SHA-256 a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7.
• Predecessor PR #2197, head 0a6f487ddff27cde0369e225f9ccb328ca2d8043, identifies the one-map obstruction and releases the depth-two/three question. This package proves the parity floor for every composition depth using the map law in the selected source certificate.
• PR #2174 supplies the conditional two-query decoder; merged PR #1969 supplies retained QQ16 map and private-field conventions.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in scope selection, proof development, exact verifier implementation, and packaging. Apache-2.0.