v0.1 candidate — unrefereed certificate-backed all-N result

Status

Unrefereed candidate computer-assisted result offered for scrutiny.

This release presents a candidate certificate-backed proof that
(f(N)=\lfloor(N+18)/25\rfloor) for every positive integer (N), with the
diagonal case (a=b) included. It is not independent external reproduction,
external human peer review, or end-to-end formal verification. The official
Erdős Problems record still said “resolved up to a finite check” when checked
on 28 July 2026; this candidate release does not alter that external status.

Exact release replay

Commit 56b27ae765f04195dc867db5e1c52750d5f721ae was exported as the attached
candidate ZIP, extracted into a new directory, and replayed with the complete
19-stage profile.

• Result: PASS complete_fresh_extraction_release_replay
• Stage time: 2,028.717 seconds
• Wall time: 2,028.99 seconds
• Peak resident set size: 1,263,566,848 bytes
• Root manifest: 99 payload files
• Manifest SHA-256:
  8aca7604f94c6f282c772b074fe57bd840d4dad9cd2b63db5f518b2ef6597673
• Candidate ZIP SHA-256:
  55e56cfee5833bf50658a74d053e9dc23861e14eb9aa311a784376b89d50468d
• Replay log SHA-256:
  2554e38b03fef9e140e1e30d594500ea6927d8037f7e0a4df6ab152b40a3d79d

The public wrapper verified the same manifest before and after the complete
replay. The attached JSON receipt and checksum list bind the sidecars.

Prepublication audit changes

• Replaced optimization-sensitive Python assert controls with explicit
  fail-closed exceptions.
• Added a negative control proving that corrupted hashed input is rejected
  under python -O; aggregate release runners reject optimized mode.
• Clarified that the lower (p=17) census enumerates an ambient
  (17^2)-root-class superset and is used only as a conservative upper bound.
• Added scoped CC0-1.0 terms, provenance and assurance records, TeX/PDF paper,
  human- and machine-readable AI evidence maps, CI, replay receipts, and a
  complete public-tree manifest.

Licensing

Except where otherwise indicated, and only to the extent Ian Pitchford holds
the relevant copyright and related rights, the original repository contents
are offered under CC0 1.0 Universal. The third-party explicit-threshold PDF is
not bundled or relicensed.

Zenodo archival record

• Concept DOI (all versions): 10.5281/zenodo.21647628
• Exact version DOI: 10.5281/zenodo.21647629
• Zenodo record: https://zenodo.org/records/21647629
• Deposited archive: erdos-848-all-n.zip
• Deposited archive SHA-256: fcd83b8986bf55784cf97513513d628af1fa5fe3bb0a2bdb869e1307dbbb8060
• Published: 2026-07-28T14:05:20.241538+00:00

This post-deposition metadata identifies the fixed archived bytes. It does
not change the release tag, release assets, mathematical claim, or assurance
status, and it is not a new independent reproduction or verification.