Updated 2026-10-18 (NS-1 / NS-38 historical recovery remains OPEN; for the scoped standalone paper manuscript/standalone_weil_certificates_and_obstructions_v4.tex and the 274-page standalone monograph manuscript/standalone_weil_certificates_and_obstructions_monograph_v4.tex [with v1–v3 preserved], all unrecovered historical v1.27–v1.34 diagnostic files are omitted and replaced by the archived certificates and analytical proofs mapped below).
| Evidence group | Status | Available evidence or remaining gap |
|---|---|---|
v1.25 complete even λ=4 certificate: g2_simultaneous |
RESTORED | 58 original files, including frozen witnesses, verifiers and saved complete residual ingredients, restored from the original v1.26 bundle. These files also match the original v1.25 bundle. |
v1.26 complete odd λ=4 certificate: g2_odd_complement |
RESTORED | 51 original files, including complement and directional witnesses, verifiers, saved reports and the exact shared-head check. |
| λ=5 disproof evidence through v1.28 | OPEN (historical originals unrecovered; omitted from scoped standalone paper) | Historical g2_lambda5_transfer ($N=16$) and g2_block_metric files remain unarchived. For the scoped standalone paper, the $\lambda=5$ comparison closures use only the archived replacement certificates NS-44 (prop:v152-tail-comparison, $\lambda=5$ 10^-8 D tail comparison failure in both parities) and NS-45 (prop:v152-block-comparison, $\lambda=5, N=25$ dyadic block-norm comparison failure in both parities), indexed in v1.52 at 320/448 bits. |
| v1.31–v1.34 concentration evidence and diagnostics | OPEN (historical originals unrecovered; omitted from scoped standalone paper) | Historical scripts and finite-grid diagnostics (g2_schatten_no_go, g2_nested_commutator degree-four check, g2_primitive_transport finite tables) remain unarchived; the v1.31 report is a partial recovery only. The scoped standalone paper omits those unarchived diagnostics and relies only on the analytical proofs in manuscript/fixed_space_prime_action_v1.tex (prop:v131-concentration, prop:v132-schatten, prop:v132-flat-top, prop:v133-leakage, prop:v133-noncommute degree-two proof, prop:v134-disjoint, prop:v134-primitive), the 192/320-bit Arb and 128/256-bit digamma-series replacement certificates for prop:v132-global-index ($\beta_{\log 4}(1) < -3/5$) in bounds-six-agent-2026-09-30-v1, and the archived cofinal scalar drawdown divergence (cor:v137-scalar-no-go) in v1.37. |
The original v1.26 ZIP and its complete extracted snapshot are available. All 468 extracted files match the archive byte-for-byte. Final proof gates using the saved ingredients, witness bindings and exact rational shared-head equality were replayed successfully. The full residual assemblies were not rerun during publication. RESTORED therefore records availability, not completion of a new independent audit of every computation.
See the recovery record and per-file checksums.
The later 207,224,098-byte v1.34 cumulative ZIP remains unavailable. The v1.26 release cannot contain the later evidence in the two OPEN rows. Manuscript statements, research-log descriptions and newer proof files do not substitute for those original witnesses and diagnostics.
Keep each row OPEN until its original evidence and dependencies have been recovered, checked against its stated provenance and made accessible in the repository or an immutable release asset. Recovering these files would close an availability gap; any new verification must be recorded separately. This ledger does not certify completeness of every historical archive. G2 and RH remain open.
Both later evidence groups remain OPEN. A fresh search checked all four available local ZIPs, matching script paths across repository refs, and the saved project records. No original missing script or witness was recovered. GitHub exposes only the already restored v1.26 evidence release. The earlier v1.34 library download failure remains recorded; no library-download connector is available in this session to retry it. Archive hashes and exact search scope are in the availability record. An accessible original archive or extracted evidence with provenance is still required. The v1.31 report remains a partial recovery only.
Classification: open input; availability search, not a certificate. NS-1 remains blocked and both evidence groups remain OPEN. No missing original script, witness or saved output was recovered in this follow-up.
The search refreshed all remote refs and checked matching paths in their history, then checked current GitHub release assets. Only the original v1.26 ZIP and its checksum are released. Local filename searches covered Downloads, Desktop, Documents (including the ChatGPT research directory and Codex workspaces), CloudStorage, Codex attachments, repository worktrees and temporary files. Saved research/recovery transcripts supplied references, not the absent originals. The four previously inspected ZIPs remain the available local bundles; this follow-up did not repeat their byte-level validation.
The recorded source in the v1.31 provenance
is fixed_space_prime_action_v1_34_bundle.zip, library file
libfile_386d5bdf90848191b485e716d0205c09, version 37, recorded size
207224098 bytes. These identifiers are historical metadata, not a fresh
verification that the remote binary is retrievable. No ChatGPT-library
connector is available in the current session; its accessible web session
is signed out. The historical HTTP 502 was not replayed. An accessible
original archive, or the six named original directories with their shared
dependencies and provenance, is required to continue recovery.
The public repository already contained v1.43 at the time of this search. This follow-up changes only the recovery ledger and task status. It does not close MAJOR M1, change the manuscript, regenerate historical evidence, or claim a new verification. G2 and RH remain open.
Classification: evidence-availability disclosure, not recovery or a new certificate. For each of the two original groups, the chosen action is explicit disclosure. No original witness, verifier or output was recovered or regenerated. Earlier OPEN entries above describe the search history; they are not a claim of archive availability.
The same sweep records additional companion gaps: the v1.29
g2_capacity_candidate register/review/recomputation artifacts and v1.30
g2_continuum_cancellation report, test_continuum_symbol.py and output
are NOT ARCHIVED. The underlying v1.24 λ=3 source certificate and complete
v1.29/v1.30 manuscript identities are present; they do not stand in for the missing
companion artifacts. V1.50 uses the printed identities, not those absent files.
V1.35 is not an absent scientific evidence set. All five original scientific
files under evidence/v135/ match hashes in the legacy v1.35 manifest. The same is
true of the five scientific files in each of v1.36 and v1.37; obsolete directory
names in the manuscript now point to these actual paths. The legacy v1.35 manifest checker also reports two publication paths missing and
a mutable research log mismatch in the current tree. Their exact original bytes
are already archived in tag v1.35: fixed_space_prime_action_v1.tex,
v1_revision_notes.md and RH_G1_G2_research_log.md each match the corresponding
legacy manifest hash. See the tag provenance.
These are path/relocation findings, not unavailable historical content. V1/v2 of
the NS-38 report incorrectly called the two snapshots unavailable; v3 corrects
that statement after checking the tag. Historical manifests are not rewritten.
The claim-by-claim changes, present-file hash comparison and versioned report record this disposition. Recovery remains an open input. The archival overclaim is corrected; availability has not been restored. No manuscript version bump is made for NS-38 alone, and no original numerical gate was replayed.
New exact dyadic witnesses and fresh 320/448-bit verifiers now establish failure
of the stipulated lambda=5 10^-8 D tail comparison and the N=25 tested dyadic
block-norm comparison in both parities. See NS-44 and
NS-45, indexed by v1.52. These are replacement
certificates, not recovered v1.27/v1.28 artifacts; the historical displayed
ratios, four-block tables, and original protocols remain unarchived. The first
evidence group therefore remains recovery OPEN, while these two precisely
scoped mathematical comparison closures now have current replayable evidence.
The concentration-era group is unchanged and remains recovery OPEN.
The six-agent audit
now supplies REPLACEMENT evidence for the numerical premise of
prop:v132-global-index: beta_(log4)(1)<-3/5. Direct Arb at 192/320 bits
and an independent digamma-series enclosure at 128/256 bits confirm the
historically reported interval; the third review records 37 passing
replay/integrity checks. Only the direct method certifies the narrower
45-place interval. This is a new implementation of the same fixed claim.
The beta certificate does NOT transfer to the physical lambda=4 form: its tests are not compactly supported in that physical window. It supplies evidence for the existing full-line even-sector negative-index implication, including fixed finite homogeneous constraints.
The original certify_beta4_negative.py and its output remain NOT ARCHIVED.
This note does not close either original-recovery row, recover the other
concentration-era scripts, or change RH/G2 or the cofinal signed floor.
The manuscript is preserved; this forward note qualifies its historical
statement that the numerical premise could not then be replayed.
The preserved audit notes refer to earlier local coefficient working files that are not included in this publication. Those provenance references are not an assertion that the files are archived in this public repository. The forward dependency note states the full inherited coefficient corollary from public NS78 needed by the present audit; the certificate replay does not depend on those local files.
v4 / monograph_v4) vs. historical recovery (OPEN)Per user direction on 2026-10-18, the scoped standalone extraction (manuscript/standalone_weil_certificates_and_obstructions_v4.tex and manuscript/standalone_weil_certificates_and_obstructions_monograph_v4.tex, with v1–v3 preserved) omits all unrecovered historical v1.27–v1.34 diagnostic tables and relies exclusively on archived replacement certificates and self-contained analytical proofs (verified by audits/standalone-paper-v4-verification-2026-10-18-v1/verify_standalone_v4.py, 61/61 checks passing):
320/448-bit flint.arb certificates in NS-44 (prop:v152-tail-comparison) and NS-45 (prop:v152-block-comparison), indexed in v1.52. The historical v1.27 ($N=16$) and v1.28 four-block diagnostic tables are omitted.manuscript/fixed_space_prime_action_v1.tex (prop:v131-concentration, prop:v132-schatten, prop:v132-flat-top, prop:v133-leakage, prop:v133-noncommute degree-two proof, prop:v134-disjoint, prop:v134-primitive), the 192/320-bit Arb and 128/256-bit digamma-series replacement certificates for prop:v132-global-index ($\beta_{\log 4}(1) < -3/5$) in bounds-six-agent-2026-09-30-v1, and the archived cofinal drawdown divergence (cor:v137-scalar-no-go) in v1.37.OPEN): Choosing replacement evidence for a scoped standalone paper does not constitute historical recovery. The 207,224,098-byte bundle fixed_space_prime_action_v1_34_bundle.zip remains unrecovered, so both historical original-recovery rows in this ledger remain OPEN. G2 and RH remain open.