Quantify QQ16 information loss after the extra B2 query

[RossRichardson]

This adds an independent quantitative bound on QQ16 information loss after the proposed extra B2 query: at least ceil(32|G|/7) original A-input directions remain hidden, at least four sevenths of the entire 8|G|-dimensional A space. No new kappa is claimed.

The final overlap refresh found Adam Gall's concurrent PR #2093, head 8b21a900eb520e4f11ea177b310f66316f8e8983, which already proves qualitative insufficiency with an explicit three-port witness invisible to every nonzero chart. We credit that result. This package contributes the large missing-dimension bound for the B2-only repair and a code-disjoint trace-based verification method; it does not extend that dimension bound to all eight nonzero-chart observations. PR2093's pinned proof was inspected; its executable was not imported or rerun.

Adding the complete pre-F0 ordinary query B2 X_U does not make the fixed QQ16 controller able to restore every original selected input. This follows Cinna Davis's PR #2079, which correctly separates the old eight-direction witness family and leaves full recoverability open. The new source-bound rank argument supplies a residual family in ker B1 intersect ker B2 with nonzero B0 h.

For the actual three query operators on finite regular cover G, the checked traces are tr K=1152|G| and tr K^2=64512|G|. Thus rank[B0;B1;B2]>=144|G|/7 and the missing A-input space has dimension at least ceil(32|G|/7). A written ordered F0/B1 proof maps the new family to the predecessor's erased-selected state. All retained observations, including the added query, vanish although the original A value is nonzero.

The favorable screen grants the entire read-only query and its retention for free. It still fails the restoration obligation, so there is no proposed native implementation or moment gain. This dimension is not a paid recursive-child rank.

Scope and evidence

Only research/qq16-extra-query-residual/ is added. The fixed local pair, ordinary tail, native endpoint interpretation and stated observation cuts are retained. Later homogeneous selected-only controls cannot read ordinary banks. The full initial R2 X, changed maps, source mutation and further observations are different interfaces.

• Primary exact route/Gram checker: retained R certificate plus transvection routes; collision-aware coefficient matrices and the inherited formal h tail.
• Code-disjoint oracle: backward scalar covectors on all 712 input positions and orthonormal axis swaps. Full R/U96-route hashes, all three 192I coefficient matrices and both moments agree.
• Fixed receipts, explicit C3xC3 illustrative residual witness, six behavioral groups, source drift and typed/trace-preserving corruption checks. Removing actual oracle guards makes their controls fail. Normal and optimized package relocation preserve evidence.
• Independent agent mathematical review is bound to exact scientific-file hashes. No independent human or formal-kernel review is claimed.

Reproduce with the standard-library registered replay:

python3.12 -I -B scripts/research_package.py --package research/qq16-extra-query-residual

Observed locally on CPython 3.12.12: PASS_QQ16_EXTRA_QUERY_RESIDUAL, all six behavioral groups, PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result, selected-record integrity and staged whitespace checks. Hosted CI status is separate and will be reported from the published head.

Not checked: full cover enumeration, a compact uniform witness/precision bound, fresh full native-tail or supplier cold replay, physical cost, complete supplier admission or a new kappa. The new argument is a written all-parameter rank/existence proof with finite source checks; inherited tail semantics remain explicitly identified.

Provenance and next step

Scientific and upstream checkpoint base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Selected SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. The final overlap refresh at 19:19–19:22 UTC covered 369 open PRs and 753 Discussion/comment records with complete pagination and no warnings; PR2093 was then inspected at its exact head. Task metadata records the scoped continuation decision. Text search is not a novelty certificate. Selected sources and frozen upstream inputs are unchanged.

Credit Ali Romman PR #1969 (a6e6ad3936f67b8f63b5b68c5e75d540610a65e7) and the retained geometry/compiler/centre-encoding lineage for the QQ16 maps and original witness. Cinna Davis PR #2079 (49df8190b158e3028e702b2c6b798117006f7249) supplies the extra query audited here. Adam Gall's adjacent PR #2086 (68dcf180ce3918a9ee1998bfc5455f42516c6009) changes the first A logger without an extra observation; this contribution instead requires simultaneous B1/B2 kernel loss. Substantial OpenAI Codex assistance; new work Apache-2.0 with predecessor notices retained.

Claim and final handoff: #2074 (comment) . The next useful test is a full R2X or additional B0X_U observation against the complete A/T restoration kernel before native costing. Detecting this residual family alone would still not close a controller.