Prove the sharp 66-port threshold for a QQ16 witness family

[kyzer1023]

Change and mathematical scope

The QQ16 coordinate-tap handoff in #2326 left the sharp threshold for its common-axis witness family open. This package proves that exactly 66 fixed ordinary source-port reads are needed to eliminate that family. Fewer than 66 always leave an original selected A-input defect invisible; the complement of a specified 30-port, common-axis group attains the threshold for this family.

The new step is a certificate for the complete owner array: the map c -> B0 h, with h_p(d)=c_p bit_0(d b_p), has rank 74, and its restriction to ker(R_U) has rank 66. A 74-by-74 integer minor has determinant 36317027395115679744; a matching group-rank upper bound makes the rank exact. Evaluations use identity and actual registered stage-1 owner routes. No formal independence assumption about bit functions is needed.

This is a scoped proof with exact finite evidence. The 66 dimensions are across the entire owner array, not per owner. The threshold is for eliminating this witness family, not full controller recovery or a native-cost tariff. No supplier, selected-source or kappa change. Even free implementation cannot repair the family with fewer permitted coordinate reads; physical access, retention, hosting, precision, all-size admission and the complete supplier invoice remain open.

Task and overlap

• Task joint-query-controller, refined scope; key 0e34adbc1dd119161c3a, chooser nonce 19ff9482038bcc5873e8a54d230d4e65, recursive-interfaces, priority revision 4. Metadata: research/qq16-owner-separation/TASK.json.
• Canonical base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; contribution 308ebc7405303bb7ed91b012bb705949c6091a16.
• Direct predecessor Research: no single coordinate tap restores the QQ16 selected inputs #2326 at fb7d64cd4a51c49bc56920305b0aca64011a420c; common-axis family from Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093 at 8b21a900eb520e4f11ea177b310f66316f8e8983; QQ16 maps from Add native joint centre-query transfers on sixteen selected ports #1969 retained on main. No pending Python package is imported or vendored.
• After seeing EdDiboi's active parity-subspace investigation, I explicitly chose complementary full-owner evaluations. The exact certificate and attaining set were shared during the investigation. This is not a claim to discovering the family or the threshold question.
• Final overlap refresh covered 564 open PRs and 1,078 Discussion records with complete pagination at the recorded 06:13/06:16 UTC checkpoints. Main and the predecessor head were unchanged. Coverage excludes arbitrary code diffs; no-match is not proof of novelty.

Validation

python3.12 -I -B scripts/research_package.py --package research/qq16-owner-separation
python3 -I -O -B research/qq16-owner-separation/verify.py

Native Windows, CPython 3.12.14: registered normal and optimized replays pass, including 12 rejecting controls and three isolated integrity tests. CPython 3.14.6 reproduces the same exact receipt. The checker authenticates the sources, binds 1,008 routes, verifies rational ranks and the integer determinant, checks the attaining 66-tap and failing 65-tap cases, and replays the reduced 19-event ordinary trajectory. Altered receipts and manifests reject without rewriting evidence. Package metadata/source checks and git diff --check pass.

Expected: PASS_QQ16_OWNER_SEPARATION rank=74 defect=66 sharp_family_taps=66 controls=12 no_new_kappa.

Not run: full supplier cold replay, native child execution, proof-assistant formalization or independent human review. Local tests do not assert a hosted-CI pass.

Credit

commdata2338 (#2326), Adam Gall (#2093), Ali Romman (#1969), Cinna Davis (#2216/#2268), the concurrent EdDiboi investigation, and the retained construction/compiler lineage are credited in the README. New material is Apache-2.0; frozen source notices are unchanged. Substantial OpenAI Codex assistance was used for derivation, implementation, verification and writing; this is author-checked evidence.

Open next questions

The README and TASK.json give the precise follow-ups: test the attaining coordinate set against other full-controller input families, or test a dense old-chart record with an explicit retention contract. The latter now has a separate active claim; the coordinate-family theorem does not settle it.