Research: no single coordinate tap restores the QQ16 selected inputs

[commdata2338]

Change and mathematical scope

This takes the full-injectivity question that PR #2268 leaves open. With PR #2216's F0-to-B1 A-to-T shear and a paired tap from any one ordinary source port into a selected T field, some original selected inputs stay invisible through the complete retained QQ16 schedule. PR #2268's U2-to-T21 tap detects PR #2093's displayed witness, but it does not restore the expanded input space.

• New witness: coefficients c1 = 1, c16 = -1, c88 = -1 on ports 1, 16 and 88 (axes 21, 50, 478), with r_1 = r_16 + r_88, so R_U c = 0 and the tapped port 2 is identically zero. Its original X_A at the identity owner is (-1/2, 1/2, 0, 0, 1/2, 1/2, 0, 0), while every selected cut, completed-X descendant and forward history is zero through the full tail. The surviving ordinary value ends in final X_(0,U) with the former-Y native type, outside the observation contract.
• All single taps: this support is disjoint from PR Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093's {2, 8, 85}, so for any tapped source one of the two witnesses is zero there. All 96 × 8 = 768 source-to-T taps fail.
• Eight hidden dimensions per source: for each excluded source u, both parity classes of the remaining centre columns contain a nonsingular 8-by-8 minor (192 minors in all), so the invisible family spans all eight original A values at the identity owner. This is eight dimensions at one owner, not per owner.
• Fixed port sets: reading any fixed set of k <= 8 source ports leaves an invisible family of dimension at least 9 - k, because each further coordinate constraint lowers the image dimension by at most one. At least nine source ports are necessary in this coordinate-access model; nine are not proved sufficient.
• Status: a scoped proof with an exact finite certificate (registered as a negative result). PR Add a QQ16 ordinary-source tap witness repair #2268's positive result is reproduced unchanged. No supplier or κ change.

Remaining obligations. Nine-port sufficiency, dense ordinary queries such as B0 X_U, an earlier retained record, changed first maps or ordinary mixing, final-cut retention, native implementation, hosting, precision and all-size admission, and a full supplier replay are outside this result. It is not a per-owner transcript-width bound or a native-cost tariff. No proof assistant or independent human review.

Task and overlap

• Task ID / scope key: joint-query-controller (22e535909f1d243e7553), refined to QQ16/shear-plus-coordinate-tap/full-selected-input-kernel. Chooser nonce b3f7fda4b64212179063ec745ca2c0d8, track recursive-interfaces, priority revision 4; the card was the chooser's first suggestion, taken through PR Add a QQ16 ordinary-source tap witness repair #2268's explicit full-injectivity handoff (passing over connector-alphabet-change and coverage-law-change). No reroll.
• Base and exact heads: base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, rechecked unchanged at 05:27 UTC; contribution fb7d64cd4a51c49bc56920305b0aca64011a420c. Inspected heads: PR Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093 8b21a900eb520e4f11ea177b310f66316f8e8983, PR QQ16: add an F0-B1 selected-state shear #2216 b80e9ba43367fb8b20877a97da1cb677c34f9264, PR Add a QQ16 ordinary-source tap witness repair #2268 daf44bfc752a5e89127defa1cb296210708cf7e6, PR Independent audit: correct QQ16 shear native-frame claim #2252 6dd49c2b186e08ef1f3efd08f62e1add97ff04a3, PR research: rule out selected-only QQ16 boundary repairs #2306 4d6e08099c11ff06a8585d04ed59453dd5a62d7d, and this account's PR Prove QQ16 two-query recovery at a recorded first-pair cut #2174 f79470a7931f3943360c10d15b428e0e4e479c22. Only PR Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093's pinned source helper is vendored and used, under references/pr2093/; the other pending heads are context, not dependencies. Main inputs are pinned in SOURCES.json.
• Scope status: refined: ordinary source-coordinate reads are permitted at the complete F0/B1 cut; ordinary fields stay unchanged, later controls are homogeneous and selected-only, and no pre-F0 record, dense ordinary preprocessing or final former-Y read is granted.
• Nearest work: PR Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093 has one witness for unchanged feedback; PR QQ16: add an F0-B1 selected-state shear #2216 and PR Add a QQ16 ordinary-source tap witness repair #2268 repair particular directions. PR research: rule out selected-only QQ16 boundary repairs #2306 excludes selected-only interventions after F0 and allows no ordinary reads; this result allows fixed ordinary reads and picks defects that vanish on them. PR Independent audit: correct QQ16 shear native-frame claim #2252 and this account's PR Research: the QQ16 shear prefix needs exactly sixteen native lines #2328 (the shear's native-line cost) concern physical frames, not information. This account's PRs Bound QQ16 transcript capacity and rule out the full initial R2 query #2153, Prove QQ16 two-query recovery at a recorded first-pair cut #2174 and Rule out fifteen-coordinate QQ16 transcripts via the fourth moment #2189 study read-only transcripts or a recorded cut.
• Claim and final check: the claim is in discussion #2205. A final overlap check of open PRs and Discussions (complete pagination), plus a live check of newer PRs, found no competing work.

Validation

python3 -I -B scripts/research_package.py --package research/qq16-coordinate-tap-kernel --check-only
python3 -I -B scripts/research_package.py --package research/qq16-coordinate-tap-kernel
python3 -I -O -B research/qq16-coordinate-tap-kernel/verify.py

Linux x86_64, CPython 3.12.3, standard library. The registered replay (normal and optimized, plus three artifact-integrity tests) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 22 seconds and left the worktree unchanged.

PASS_QQ16_COORDINATE_TAP_KERNEL single_taps=768 A_defect=8 ports<=8_excluded controls=13 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/qq16-coordinate-tap-kernel outcome=negative-result

• The verifier binds 1,008 reconstructed route matrices to the actual QQ16 map registry, checks the 192 parity minors by rational row reduction, Bareiss determinants and explicit inverse products, synthesizes all 768 kernel vectors, and runs both sparse witnesses, the eight source-2-hidden basis inputs and an explicit eight-source example through the complete tail. PR Add a QQ16 ordinary-source tap witness repair #2268's 11 f_37 endpoint and 34/4/65 observation census are reproduced as a positive control.
• Thirteen controls reject, among others, a wrong tap sign, a changed chart axis, an absent route, a wrong later-pair binding, a singular minor, a corrupted inherited source and a receipt mismatch. A relocated replay preserves every package byte, and altered receipts or source code fail.
• I rechecked the witness against the centre matrix in research/joint-query/certificate.json.gz on main: r_1 = r_16 + r_88 = (0, 1, 1, 0, -1, 0, 0, -1), R_A X_A = -r_1, rank R_U = 8, and the two minors for excluded source 2 have determinants -16 and 32.

Credit

• Cinna Davis (@1337isnot1337): the shear (PR QQ16: add an F0-B1 selected-state shear #2216), the tap and the handoff (PR Add a QQ16 ordinary-source tap witness repair #2268). Adam Gall (@adamgall, PR Exhibit a QQ16 kernel invisible to nonzero-chart source queries #2093): the original witness and the vendored source reconstruction and F/B interpreter, which keep Adam Gall's attribution. Ali Romman (@aliromman, PR Add native joint centre-query transfers on sixteen selected ports #1969): the QQ16 maps, packet and retained schedule. @CubeJerry (PR research: rule out selected-only QQ16 boundary repairs #2306) and Charles Bethin (@cbethin, PR Independent audit: correct QQ16 shear native-frame claim #2252): the adjacent selected-only and native-frame results.
• The retained QQ16 and selected geometry lineage.

New work is Apache-2.0; retained notices are unchanged.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

See the package README and TASK.json. The smallest useful follow-up: specify one dense old-chart observation (not a coordinate read), test its complete ordered kernel and legal final retention, and price it only if no invisible defect survives. Whether nine source ports suffice is also open.

Workflow feedback (optional)

• What helped: PR Add a QQ16 ordinary-source tap witness repair #2268's DONE stated exactly which part was repaired and that full injectivity was open, which made the next test precise.
• Friction: a broad find_overlap.py --task joint-query-controller query returned over 1,600 matches, because of the nested-package term issue that this account's PR Tooling: derive find_overlap task terms from research package roots #2154 addresses; narrow QQ16/tap terms found the live thread.
• Suggestion: keep "witness detected" and "full kernel closed" as separate status lines in handoffs.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG