Prove QQ16 shear plus an old-chart read still loses selected inputs

[starship-s]

Change and mathematical scope

The QQ16 paired A-to-T shear plus a retained dense old-chart record q0 = B0 X_U^initial still cannot restore all original selected inputs. This package proves that at least ceil(32N/7) selected-defect dimensions remain invisible on a finite regular cover of size N, even when all implementation costs are granted free.

The new step intersects the actual three-query image with the graph {(0, -11Lc, Mc)} for the changed first pair. Every resulting input has zero q0, selected outputs after B1, completed-X descendants and five forward histories. The surviving ordinary value reaches only the excluded former-Y hole. The proof keeps operator order and uses the credited second-moment rank estimate, which the verifier rechecks against main's packet.

Scope: a written obstruction with exact source and regression checks. No new κ, native-cost claim, supplier admission or selected-frontier change. Earlier retained selected values, different queries, changed ordinary schedules and later ordinary reads remain outside the observation contract. No compact actual-cover witness or recursive precision bound is supplied.

Task and overlap

• Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; priority revision 4.
• Task: joint-query-controller, refined scope QQ16/shear-plus-initial-B0-read/ordered-graph-kernel; chooser nonce 7dcbcbed93c608a2c89c3e8330a31a30.
• Canonical claim. Exact predecessor heads, source pins and scope are in research/qq16-shear-old-chart-kernel/TASK.json and SOURCES.json.
• This takes Research: no single coordinate tap restores the QQ16 selected inputs #2326's dense-observation handoff. Rule out one mixed affine helper for the QQ16 interface #2122 concerns mixed records with the unchanged first pair; this proof includes QQ16: add an F0-B1 selected-state shear #2216's intervening shear. Bound QQ16 transcript capacity and rule out the full initial R2 query #2153 supplies the existing rank method. Prove QQ16 two-query recovery at a recorded first-pair cut #2174 grants two records and a privileged cut, so its positive theorem is not contradicted.
• Concurrent Prove the sharp 66-port threshold for a QQ16 witness family #2354 addresses the common-axis family's fixed-coordinate threshold, not this new kernel family. Its head is recorded in the task card.
• Final refresh: 572 open PRs and 1,087 Discussion records, complete pagination and no warnings; all 22 targeted matches inspected. Main and relevant predecessor heads were unchanged at 2026-10-15 06:39 UTC. This is bounded overlap coverage, not a novelty certificate.

Validation

python3.12 scripts/research_package.py --package research/qq16-shear-old-chart-kernel
python3.12 -I -O -B research/qq16-shear-old-chart-kernel/verify.py

CPython 3.12.13, standard library. Registered normal and optimized replays passed:

• actual Grams and three sets of 96 distinct relative owner routes;
• exact trace values 1152N, 64512N, rank estimate 144N/7 and residual bound 32N/7;
• four rational basis fixtures, including noncommuting selected sections, plus an exact sharp intersection fixture;
• all 17 retained tail events with explicit zero-source checks;
• six rejection-control groups: Gram corruption, route collision, shear sign, -10 in place of -11, reversed noncommuting factors and an omitted bridge.

A Git-free relocated optimized replay preserved all 11 copied files, and a corrupted copied input was rejected. Metadata/pins, Markdown links and whitespace checks passed. Separate Astra/max agent reviews found no blocking math/spec or verifier-quality issue.

Hosted CI has not executed: the registered-package run at head e5d4d78dcfdd55d323fcbc60df477b9f25c7abff reports action_required and has no jobs. No hosted test pass is claimed.

The finite rational fixtures are not actual-cover witnesses. The quantified claim follows from the written proof. Full native/supplier cold replay, proof-assistant verification and independent human review were not performed.

Credit

Ali Romman and the retained QQ16 lineage (#1969); Ross Richardson (#2104); commdata2338 (#2153, #2174, #2326); Cinna Davis (#2122, #2216); Adam Gall (#2093); and the parallel #2354 investigation. Existing notices and frozen sources are unchanged. New material is Apache-2.0.

Substantial AI assistance: Hermes (gpt-6-astra-900k) for the derivation, proof and verification specification; Codex (gpt-6-luna) for the initial verifier implementation; Codex (gpt-6-astra, max) for separate mathematical/spec and standards reviews. No independent human review is claimed.

Open next questions

The package README and task card give two bounded follow-ups: test one different dense record against its complete ordered kernel, or reconstruct the privileged post-B1 cut needed by #2174 from legal final records. Either must pass the algebraic test before native access, retention and a full invoice can justify construction work.