Prove sharp 24-array retention for the QQ16 L2 cut

[RossRichardson]

PR2470's QQ16 L2 lead retains 32 post-F0 selected arrays while granting 200 live arrays immediately after B1. Eight retained arrays are redundant: the existing live future logger reconstructs y1_A. This package proves and attains exactly 24 retained rational-linear complete arrays for that fixed observation contract.

Retain x1_A, x1_T, y1_T; read live X2_U, Y2_U, Y2_A; reconstruct the post-F0 state in order, then apply the credited F0 inverse. For every finite common array dimension n>0, injectivity gives (200+q)n >= 224n. An explicit 24n-dimensional live-observation kernel proves the bound is sharp. Records may be arbitrary fixed rational-linear compression, and the lower bound permits a nonlinear decoder.

This is a changed information contract relative to PR2443: the extra 96 Y2_U live arrays remain material. It neither changes the 88-read result nor establishes physical storage/work savings. Native access, record retention/retirement, dirty cleanup, later controller cuts, precision and the complete supplier invoice remain open. No new kappa, supplier admission or formal-kernel proof is claimed.

Only research/qq16-l2-minimal-retention/ is added. Evidence includes:

• Six complete inverse identities over exact rational free-group operators, with all 224 input arrays and all 224 independently specified observation arrays. Actual R/K, selected Grams, the F0/B1 chronology and 224 registered inverse-route pairs are pinned and checked. Native semantics and phase geometry are inherited, not freshly rederived.
• 24 retained-coordinate omissions, eight other semantic faults, two equivalent-presentation controls, five behavioral test groups, and a deletion-sensitive ineffective-control guard. Nonzero free-operator faults are not described as actual-native counterexamples.
• A separate specialist's written proof and independently implemented noncommuting Q² matrix check: all 448 input and observation coordinates, both inverse orders, five concrete fault witnesses. No independent human review claimed.

Validation passed locally on Python 3.12.12:

python3.12 -I -B scripts/research_package.py --package research/qq16-l2-minimal-retention
make selected-record-check

The registered hook covers normal/optimized primary replay, the independent checker, and behavioral tests. Separate direct checks pass on Python 3.14.6; the independent checker also passes optimized mode. Metadata/pins, local links and whitespace checks pass. Selected-record integrity is not the selected cold replay. Hosted CI is separate and no pass is claimed here.

Predecessor credit: Sagar Thakrar's PR2470 (1b2eee3b) supplies L2 and the retention census; starship-s's PR2443 (545c05e1) supplies the ordered decoder; ywz65's PR2456 (665ba8d7) supplies the prior operator audit and chart-fault warning. Ali Romman/PR1969, Gareth Davidson/PR2432, commdata2338/PR2174 and the retained supplier lineage retain their credit. No predecessor executable is imported. Exact consulted heads/blobs/hashes are recorded.

Canonical scoped claim. The adjacent native-L2 claim explicitly excludes this information minimum and supplies a concrete next interface task; its claimed native work is not assumed verified here.

Base/main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4; selected-record SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Submission refresh leaves guidance and inputs unchanged. The overlap snapshot reports complete pagination for 678 open PRs (12:18:35 UTC) and 1194 discussion records (12:21:39 UTC), plus 1536 local records. Exact predecessor heads were reread unchanged. The documented search does not cover every code diff or establish novelty.

Prepared by Ross Richardson with substantial OpenAI Codex assistance in derivation, implementation, verification and writing; a separate recursive-interface specialist supplied the independent proof/matrix check. Apache-2.0; all frozen sources and selected records remain unchanged.