Recovered on 2026-09-21 from the previously downloaded original
fixed_space_prime_action_v1_26_bundle.zip. This restores the missing
evidence for the complete fixed-window λ=4 result, without changing the
current manuscript or generating new mathematical results.
The original ZIP has 181,710,377 bytes and SHA-256:
ccdb8eaa882358ca5cef1668344180a325fc00799c97ed724d05a99ca0982d8f
All 468 extracted files match the archive byte-for-byte. All 58 files in
g2_simultaneous also match the separate original v1.25 bundle. The full
original directory layout is preserved so imports and witness references
remain valid. Historical manuscript copies, PDFs, unsuccessful trials and
old status statements are preserved as historical evidence, not current
claims. No PDF was generated by this recovery.
The ZIP integrity check and all extracted-file comparisons passed. Using python-flint 0.9.0, the following original proof gates were replayed with certificate writes disabled:
complete_margin.py at 768 and 896 bits: both passed the complete even
rational relative-margin gate 62629/100000 from the saved ingredients.direction_complement_certificate.py at 768 and 896 bits: both passed
the 1/1000 complement bound. The latter reuses the original 768-bit
ingredient enclosures, as documented by the original verifier.certify_odd_full_window.py: passed witness/report hash binding, head
invertibility, exact rational equality of the physical head, and the
directional inequalities reconstructed from the saved 1024/1280-bit
reports. The combination gives the stated odd relative bound 107/250.These checks consume the original saved complete residual ingredients. They are not a fresh replay of every residual row through J=65536 or an independent derivation of the analytic kernel. No trial was generated and no saved certificate was overwritten.
Use a disposable copy of the snapshot because the original verifiers write reports. Keep the sibling directories together.
The original instructions are:
Run only their verification commands to preserve the frozen witnesses. The even README’s statement that odd positivity remains open describes the v1.25 checkpoint; the v1.26 odd directory records the subsequent result. Finite window-scaling diagnostics are distinct from the complete λ=4 certificate and do not establish other complete windows.
The 207,224,098-byte v1.34 cumulative ZIP has not been recovered. The v1.26 release restores the two missing positivity-evidence directories, but does not claim to contain every later v1.27–v1.34 artifact or to be a complete reproduction release for the current manuscript. G2 and RH remain open.
The evidence availability ledger therefore keeps two groups OPEN: the λ=5 disproof evidence through v1.28 and the v1.31–v1.34 concentration evidence and diagnostics. Only the two λ=4 evidence groups are marked RESTORED.