Audited previously unchecked public issue/PR conversation streams and their linked external prior-art repository, then validated the normalized receipt with a separately implemented checker.

public coordination and prior-art event audit

Paginated GitHub REST event enumeration plus content-addressed inspection of the linked Lean statement source.

Hypothesis: The public issue and PR event streams contain no post-review authorization to supersede PR 4044, while issue 773 links a public Lean artifact already containing the requested Sidon, extremal-function, and exact-asymptotic declarations.

Test: Enumerate issue comments/timeline, PR ordinary comments/timeline, and the linked repository history with 100-item pages; require empty second pages, hash the exact bodies and source, and inspect the resulting finite corpus.

The independently checked audit exhausts each named REST collection within its pagination scope and embeds the exact external Lean source. That source directly falsifies the contribution’s residual novelty premise, while the public discussion supplies no permission to compete with PR 4044.

• At commit 3016bc04ece2858089b9fb135492312208cbe864, PatoLocos/Erdos530/530.lean has SHA-256 4eea26b833bc7541003bf3f92e39722326d3f61d0e4df6cc9f9c74944dc4181f and contains IsSidon, GuaranteesSidonSubset, ell, and exactAsymptoticConjecture declarations.
• The audited issue comments, issue timeline, PR ordinary comments, and PR timeline contain no explicit public authorization to assist, replace, or supersede PR 4044; this claim is limited to the exact hash-bound REST corpus.
• The local source remains kernel-checked for its exact prior hash, but that receipt does not establish novelty, semantic acceptance, CI acceptance, or merge.

• Main audit returned 0 in 4.674 seconds; stdout SHA-256 5f23a34a3dfbbbe962123d45b33f253aef1f0cf2b0155b50a3af6a1d480b8e65.
• Independent checker returned 0 in 0.071 seconds; stdout SHA-256 630fa4f2a29a1dc67ce73cfa045bd0a1de11d44b367f06845b8bf4f14f90ece5.
• All five collection page-2 responses were empty at a 100-item page size.
• The embedded external statement source independently hashes to 4eea26b833bc7541003bf3f92e39722326d3f61d0e4df6cc9f9c74944dc4181f.

• .proof-experiments/20260722-143505-e2b517 — 44 public records plus the external Lean source captured; no authorization found and direct prior formalization confirmed.
• .proof-experiments/20260722-143621-a1d2ff — independent receipt checker returned receipt_valid.

checks/check_erdos530_run9_coordination_prior_art.py independently validates pagination guards, collection sizes, event/text hashes, repository head, source SHA-256, and declaration markers. Authorization remains a human-readable judgment over that exact corpus.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• Issue-tracker comment auditing -> prediction that external links may invalidate a stale formalization-status field -> observed a current hash-bound repository containing the exact requested statement layer.

• A public standalone Lean statement layer for Erdős Problem 530 exists in PatoLocos/Erdos530 at commit 3016bc04ece2858089b9fb135492312208cbe864.
  Embedded source and repository metadata in experiment 20260722-143505-e2b517; independent checker returned 0. · Exact repository head and 530.lean contents captured on 2026-07-22. · computed
• No explicit replacement or assistance authorization occurs in the audited public REST corpus.
  Hash-bound issue/PR bodies and timeline events in experiment 20260722-143505-e2b517. · Issue comments/timeline and PR ordinary comments/timeline; excludes private coordination and GraphQL-only thread state. · computed
• The local source hash 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466 elaborates warning-clean under Lean 4.27.0.
  Lab 135f90912547 returned 0 with empty stderr and a nonempty hash-bound OLean. · Pinned checkout 8f6e745798379104379da0b5c28c25315489890f and exact numeric target only. · computed

• Present the local scoped declaration as the first or only standalone formalization.
  Historical novelty for the current contribution type. · PatoLocos/Erdos530 already contains the same statement components, and PR 4044 is an active upstream same-target submission. · Run-9 audit receipt and linked hash-bound 530.lean. · Historical priority cannot be restored; only a materially different, externally useful delta could support another contribution.
• Open a competing PR while PR 4044 remains active.
  Formal Conjectures submission route. · No public authorization exists and duplicate/spam risk is decisive. · Exact public event corpus captured in experiment 20260722-143505-e2b517. · Explicit public consent or a maintainer-approved replacement after closure.
• Repeat the expensive Lean build as the next discriminator.
  Current coordination/prior-art bottleneck. · The existing source already has a kernel receipt; another build cannot create novelty or authorization. · Audit-plus-check took 4.745 seconds and resolved the current decision, versus the prior 643.927-second build. · An authorized source delta with a new source hash.

• Explicit coordination on PR 4044 or issue 773.
  It is the only current path to a legitimate upstream contribution involving this local work. · On a newly reported event, inspect its exact author, timestamp, scope, and requested patch before editing. · high · open
• Authorized reconciliation of the two existing statement APIs.
  The PatoLocos and Formal Conjectures artifacts use different Sidon predicates and extremal interfaces; maintainers might value a reviewed canonicalization, but only if requested. · After explicit authorization, write a small Lean equivalence file comparing the exact definitions and kernel-check it. · normal · open

Objective: Detect a legitimate, materially distinct coordinated acceptance path without duplicating either existing formalization.

First action: Inspect the exact URL of any newly reported PR/issue event and compare its timestamp and scope against the run-9 hash-bound receipt.

Stop condition: Stop without source edits if no explicit authorization or materially distinct requested delta is present.

• Do not edit, rebuild, or submit the local Lean source without a newly documented coordination event.
• If authorization appears, compare its exact requested delta against both PR 4044 and PatoLocos/Erdos530 before implementing anything.
• After an authorized source delta, generate fresh source, kernel, clean-checkout, full-CI, and independent semantic receipts.

• https://www.erdosproblems.com/530 ↗
• https://github.com/google-deepmind/formal-conjectures/issues/773#issuecomment-3850383367 ↗
• https://github.com/google-deepmind/formal-conjectures/pull/4044 ↗
• https://github.com/PatoLocos/Erdos530/commit/3016bc04ece2858089b9fb135492312208cbe864 ↗
• https://github.com/PatoLocos/Erdos530/blob/3016bc04ece2858089b9fb135492312208cbe864/530.lean ↗
• https://arxiv.org/abs/2605.03181 ↗

Sol principal: Codex GPT-5 runtime, responsible for source audit, experiment design, semantic classification, and final synthesis. Terra delegate: gpt-5.6-terra source-discriminator memo, treated as advisory and independently checked. Deterministic tools: Bash, curl, jq, rg, sha256sum, Python 3.12.3, the computational-researcher experiment wrapper, and the existing Lean 4.27.0/Lake 5.0.0 kernel lab receipt. No CAS, SAT/SMT solver, or proof assistant beyond Lean was used.

Duration

688.5s

Review state

not a result claim

Attempt ID

scout-bdf77f43574b-20260722-144134-7b4bbd

No human review recorded.