[amaybaum]

States and dynamics research record. All results are internally reviewed research; none is native availability, probability selection, premise or access adoption, or full OI-to-QM equivalence.

• Head: 5fc698e0ea3f8ffa3b654728f22eb8a364c1ae5a.
• Everything is under verification/programmes/oi-qm/reconstruction/states-dynamics-audit-20261024/.
• Handoff and package index.``

Merge: not authorized.

Results

Finite-menu approximation (a2_efficiency_v6/)```

• A fully executed finite geometric controller: 1,536 labels and 96 initial fair bits, plus tables, clock/word and retained workspace.
• For its declared finite preparation/read/rotation menus and a total h=3 operation horizon, the complete public-record/decoded-output CQ error is at most 0.074764.
• It narrows, and does not replace, the broader all-menu theorem in finite-a2-v5/.
• Accepting review at 15b31612.

Depth extension (a2_depth_v7/)

• On the in-menu protocol "prepare X+, then read a, X, a, X, …", the executed controller and every memoryless-reset controller have complete-record TV from quantum theory tending to 1.
• A retained-seed reset escapes, as a protocol-specific sampler.
• Review rounds: two blocking, then one accepting at 26683436.
• REPORT.md was later edited in one bullet. dc210283 restates the lower bound in its adaptive-controller form and adds a line for the executed extension; 49e1a119 corrects that line from S = Σ d_t²/4 to S ≥ Σ d_t²/4. The checker and numbers are unchanged, and no retained review round covers that restatement.

Bounded persistent memory (a2_memory_v8/)````

• On that protocol, every controller with finite whole persistent state, a time-independent update and B fair fresh bits per slot has T(h) → 1, for any initial law.
• The obstruction is arithmetic: dyadic fresh randomness against a run law with ratio 4/5.
• The result does not cover non-dyadic sources. For a fair five-valued source a memoryless sampler gives T = 0, computed exactly through h = 12.
• Not determined:
  • the least memory growth that keeps T bounded below 1;
  • bounded private memory with unbounded public state;
  • time-dependent updates;
  • growing per-slot blocks.
• One exploration preceded the plan, which is pinned at 1dfec979.
• The last retained review round accepts 70faede0..3ca0d8ba. Two later commits are not covered by a review round:
  • 5beb12b7 makes the existing opt-in --verify-plan-commit mode read only local objects, and adds mutant MT4;
  • 57fd7e04 retains re-checks 5 and 6 and edits REPORT.md and PROVENANCE.json.

Exact reset-resource audit (a1_reset_v6/)`````

• The specified fixed-vector Montina iteration fails repeated use: Z+ then X then Z gives final Z+ 2/3 instead of 1/2, and full-record TV 1/6.
• Montina's two-time theorem is preserved.
• An explicit reversible bit lift restores invertibility only.
• Supplied independent pair renewal restores the full finite-adaptive record/state law. It is sufficient, not minimal or native.
• No native reset or resource minimum is claimed.
• Accepting review at bdd89785.

The scope of the following is unchanged:

• the KS architecture (history-architecture-v5/);
• the native code bridge (native-code-bridge-v6/);
• the operational-quotient and stopping-source packages.

Landing audit

A separate-agent internal §A.42 landing audit of bafb38d6 found the science, evidence, pins, replays and gate all passing. Its text findings are fixed:

• F1–F3 and F6–F8 in 9e51c02b, 8e07346c and 5fc698e0, which change only CURRENT-HANDOFF.md:
  • the handoff no longer restates WIP: native nonlinear processing and second-front source audit #910's or Composition and access: finite-depth composition contract, logical acceptance circuit and complete-record laws (research record) #912's results;
  • the stale replay paragraph becomes a package index;
  • the a2_depth_v7 report restatement is noted;
  • the 2d555f17 provenance citations are recorded;
  • wording.
• F4–F5 in this description.

Re-checks of 9e51c02b, 8e07346c and this description accept with nits. 5fc698e0 applies the last re-check's proposed wording verbatim.

What the audit checked:

• Merge. git merge-tree with main facb46a3 is clean. The landing adds 229 files, all in the research directory, and modifies or deletes none.
• Replay. All 20 checker/result.json pairs are byte-identical under python3 -I -B, normally and with -O.
  • The 11 reviewer scripts with retained outputs reproduce: 3 for a2_depth_v7, where review_checks differs only in timings, and 8 for a2_memory_v8.
  • All 22 SHA256SUMS files pass.
  • The full mutant campaigns and the reviewers' mutant runners, roughly 95 minutes plus 2–3 CPU-hours, were not rerun.
• Gate. On the scratch merge, 20 of 21 steps pass. lean-axioms needs lake, and this PR touches no Lean. Legacy-records: 303 intact; 52 V3 receipts hold.
• Reachability.
  • The tree cites 86 distinct 40-hex ids: 36 are blobs in the tree, and 49 are commits reachable after the merge, 5 of them already on main.
  • The remaining one, 2d555f17, is on the branch research/missing-component-20261020 of closed Research (WIP): the missing component for F2-reg, and measurement as an added condition #885. It is provenance, not support. The claims rest on their own checkers and, where they cite Lean, on declarations at de6fe293, which is on main.
  • All 9 review INPUT-HASHES.json files verify.
• Hygiene. No secrets, e-mail addresses other than noreply, IP addresses, local paths or binaries.

Landing instructions

• Land with an ordinary merge commit, main first and the head second, so the cited commit ids stay reachable.
• Keep Research (WIP): the missing component for F2-reg, and measurement as an added condition #885's branch research/missing-component-20261020.

Related: #910 (native construction, merged), #912 (complete-record composition), Issue #913 (wider gates), #923 (OI-PE-1, which cites a2_memory_v8/REPORT.md at bafb38d6 as context).

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

[amaybaum]

Follow-up to a2_depth_v7. The head is now 49e1a1191c9ea5c303883afd2d8d3c28a233f9e5, a fast-forward from 26683436. This update contains two separately reviewed strands; each was blocked once and then accepted by a focused re-review.

1. Review retention and handoff (e4604d1b, 408c74b6).
   • a2_depth_v7/review/ keeps the three separate-engine review rounds byte for byte: round 1 (blocking), round 2 (blocking) and round 3 (accepting).
   • Each round has its report and checker outputs, plus each mutant as a unified diff against that round's checker; only the diff headers are made relative. review/SHA256SUMS has 35 entries.
   • The reviewer reproduced all 24 mutant files from the diffs.
   • Round 2's report also cites a mutant generator (mk2.py) and per-run directories that are not retained; the retained diffs and mutant outputs supersede them.
   • CURRENT-HANDOFF.md gains the depth-extension section:
     • the full memoryless reset class: carrier, responses and an unconstrained preparation read;
     • the retained-seed reset, outside the class for B≥2;
     • two routes still open: controllers that carry randomness across slots, and growing per-slot blocks.
2. Formula (dc210283, 49e1a119). The lower-bound bullet in REPORT.md now reads "S = Σ_t c_t ≥ Σ_t inf_past d_t²/4", which is the adaptive form. For the executed extension, S ≥ Σ_t d_t²/4, which is the value the depth table uses. The theorem, its scope and every number are unchanged.

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