Frozen research checkpoint: adaptive correction block v1 (preserved 2026-09-06)

Snapshot ID zeta-adaptive-freeze-v1. This directory is storage. Thomas paused the research and asked for the evidence to be preserved; nothing here was reviewed, promoted or extended by the pass that imported it, and importing a package does not promote its mathematics.

The narrative is provenance/FREEZE.md, written by the originating session and copied here unchanged. Read that first. This file says where the bytes are, what was checked mechanically, and what remains unreviewed.

The archive

archive/zeta_adaptive_freeze_v1.zip is the downloaded package, committed unchanged as a binary. archive/SHA256SUMS carries its hash.

Verify from the repository root:

cd hunts/prime_pair_error/frontier/2026-09-06/adaptive_freeze_v1/archive
shasum -a 256 -c SHA256SUMS

tests/test_adaptive_freeze_archive.py pins the hash and byte count independently of the sidecar, so the file, the sidecar and this README cannot drift apart silently. It also runs the archive's own verifier on a scratch extraction and byte-compares every imported file against its archive member.

Layout

adaptive_freeze_v1/
  README.md            this file, written in the repository
  archive/             the outer ZIP, unchanged, plus its SHA256SUMS sidecar
  provenance/          the archive's own top-level files, copied byte for byte

provenance/ holds nine files exactly as the archive carries them: FREEZE.md, CLAUDE_HANDOFF.md, README.md (the snapshot's own, not this one), FILE_MANIFEST.json, ARCHIVE_CONTENTS.json, IMPORT_MAP.json, REPO_STATE.json, LOCAL_VALIDATION.json and verify_freeze.py.

Their paths are relative to the archive root, not to this directory. IMPORT_MAP.json names original_archives/... and latest_extracted/..., which exist inside the ZIP and not beside it; verify_freeze.py expects to run against an extraction of the ZIP, with --root pointing at the extracted zeta_adaptive_freeze_v1/. That layout is described here rather than repaired, because rewriting an inventory to match a new location edits the evidence. REPO_STATE.json likewise records the PR states observed when the snapshot was sealed; the live states at import time are in the table below.

The archive carries 17 original research ZIPs. Three of them are already committed elsewhere in this tree and are byte-identical to the copies inside: zeta_frontier_handoff_2026-09-06.zip (../archive/), factorial_certificate_pilot.zip (../factorial_certificate_pilot/archive/) and zeta_research_checkpoint_2026-09-06.zip (../checkpoint/archive/). The overlap is deliberate. Do not deduplicate or recompress the originals.

The three imported packages

provenance/IMPORT_MAP.json names three destinations, all one level up beside the earlier imports. Each was extracted from the nested original ZIP inside the committed archive, so the imported bytes are the original package bytes:

No destination existed before this import, so nothing was overwritten and no difference had to be resolved. No vocabulary substitution was needed either: none of the 52 files carries the reserved word, so the imported copies are byte-identical to the originals with no documented edit. Each package's own SHA256SUMS.json lists every one of its files except itself, and all three verify. Two of the three manifests key size as bytes and one (repair_cost_rule) keys it as size; both conventions are read, neither is rewritten.

The recorded outputs in these directories are the originals. Rerun the scripts into new output files rather than over them.

Chronology since PR #198

The lineage, as provenance/FREEZE.md §3 records it:

reviewed combined-weight baseline (#199)
  -> reviewed joint candidate (#200)
    -> support-obstruction diagnostic (separate direction test)
      -> repair-cost rule, accepted direct steps at 20 and 21
        -> adaptive correction block, 23 corrections and 82 repairs

1. Reviewed baseline. The earlier cumulative checkpoint landed as PR #198, merged at 9ec3b6b3b86c25e256ce605f5116fbda3cbc7689. The baseline review in PR #199, head 96ce564c89a38a89a4a28da61d28d335679d4efb, reports the all-cutoff construction survives without mathematical repair.
2. Reviewed joint candidate. PR #200, head 85a42e7c0c7dad8163dcab8d239bac5bb6fe1b38, reports SURVIVES for the coordinated nine-amplitude candidate. The reviewer found a missing kappa(D)>0 assertion in the producer script, checked it with margin, and added the assertion in the independent checker rather than in the candidate. The candidate bytes are unchanged.
3. Support obstruction. joint_support_analysis/ records that the inherited repair dictionary forces the amplitude at 20 to vanish, leaving W(20)=3. That is a statement about the constrained construction, not a general impossibility theorem.
4. Repair-cost rule. repair_cost_rule/ bounds the greedy repair bill by the initial deficits and applies corrections to the final majorant directly. Two steps, at 20 and then 21, lower the leading constant to 1.04590351044777010....
5. Adaptive block. adaptive_correction_block/ selects 23 masked reciprocal-carry corrections from a 39-variable block, uses 82 positive repairs, and records a new leading constant of 1.03411910424755277....

Review status: the last three stages are unreviewed

This is the load-bearing line. The reviews in #199 and #200 apply only to the earlier objects they name. Neither covers the support-obstruction diagnostic, the repair-cost rule or the adaptive block. The producing session's own checks.json says so in its own status string: "PASS: separate-code self-check, not an independent-agent or human review".

PR states observed at import time on 2026-09-06, by query rather than read from the snapshot, with the head commits preserved so the refs survive independently of GitHub:

This preservation pass changed none of them, and archiving a reference does not authorize merging it. The same table, as the snapshot recorded it when sealed, is in provenance/REPO_STATE.json.

What was checked, and what was not

Checked mechanically in this pass, all byte-level:

• The download's size and SHA-256 match the values supplied with the handoff, before extraction.
• The ZIP carries no absolute path, no .. traversal, no symlink and no encrypted member.
• The shipped verify_freeze.py, run on a scratch extraction, reports PASS with 85 payload files, 17 original archives, 558 recursive archive member occurrences and 52 extracted files.
• All 52 imported files equal both the archive's own extraction and the member of the corresponding nested original ZIP.
• The four nested dependency links in LOCAL_VALIDATION.json hold: the adaptive block's input ZIP is the standalone repair-cost ZIP, whose input is the standalone support-analysis ZIP, whose inputs are the standalone joint-candidate and route-test ZIPs, byte for byte in each case.
• The three originals also committed elsewhere in this tree are identical to the copies inside the archive.

Not checked, and not claimed: the mathematics. The adaptive package records 99,999 prefix checks, 90,082 residue-table cases, 1,088,718 full-period cells and 1,532 factorial prime-exponent identities. Those are the producing session's recorded counts. This pass did not rerun them, and byte integrity is not a proof review.

Limitations recorded with the block

Kept here because a preserved result that loses its caveats is worse than an unpreserved one:

• The reported reduction of about 25.7% is a fraction of one construction's leading excess C-1. It is not a percentage of RH solved, and a fixed leading constant greater than one is not the required square-root-scale error bound.
• No package in this freeze establishes a certificate family with the necessary uniform refinement rate. The RH-sufficient target named in the source notes is B(N) <= N + O_epsilon(N^(1/2+epsilon)) for every epsilon, at all sufficiently large cutoffs.
• The full-envelope improvement is claimed for every integer N >= 10^6. At N = 10^4 the actual factorial expression improves but the conservative envelope worsens, and that unfavorable comparison is retained rather than dropped.
• The two shields are different quantities and must not be merged. The old double-lift shield stays 701/36; the newer direct corrections accumulate a single-lift shield of 3281/108. Replacing both by one combined coefficient would change the construction.
• Nothing here improves the completed upper bound on total CHHL E(N), and no novelty, optimality, prime-counting record or formal verification is claimed.

Rejected trials and alternatives, retained

• A third step at 20, after the accepted steps at 20 and 21, fails the sufficient test: the particular greedy construction increases the leading coefficient. It was run as a negative-control diagnostic and is not retained in the accepted state, but the diagnostic itself is preserved in repair_cost_rule/. Failure of the sufficient test is not a proof that all repairs there are impossible.
• The direction test in joint_support_analysis/ introduces new repair locations and reaches about 1.0469800114, but its complete conservative envelope is not better at every small cutoff. It is not the baseline the adaptive block was built on. Both it and the obstruction are preserved.
• An envelope-oriented alternative to the selected block is kept beside it as adaptive_correction_block/alternative_envelope_candidate.json (H = 289/12, actual C ~ 1.0342645), against the selected gain-policy block (H = 2633/108, actual C ~ 1.0341191). All 1,065 exploratory scout rows are kept in scouting_scores.json. The source calls the search exploratory; optimizer success is not treated as proof of feasibility or optimality.

Registration

The snapshot ID and the hash inventories register an artifact version and nothing more. This is not a Palomar entry, a journal submission, a novelty claim or an RH announcement, and no such submission is authorized by it. The Git tag research/adaptive-block-v1 marks the verified preservation commit; it is a storage marker, not a release.

The open question at the pause

Whether profitable correction blocks keep existing with controllable coefficient and shield growth as the remaining excess shrinks. One accepted block does not establish that rate. No new search, optimizer run or formalization pass was started here, and the next independent review should cover the post-#200 support, repair and adaptive chain against its own stated obligations.