Executed the prescribed run-8 public-status audit and a separately written fail-closed receipt checker, then stopped without Lean edits because the active same-target pull request and ownership state were unchanged.

receipt-level adversarial validation

Normalize five authoritative page/REST responses, compare the snapshot byte-for-byte with run 7, and independently assert the decisive ownership predicates.

Hypothesis: PR 4044 remains open at its recorded head with no public coordination event authorizing a competing or replacement formalization.

Test: Run checks/audit_erdos530_live_status.sh once through the deterministic experiment wrapper, then require checks/check_erdos530_run8_receipt.sh to confirm the exact snapshot hash, byte equality with run 7, open/unmerged state, unchanged head, identified author, awaiting-author label, timestamp, and review counts.

Exact byte equality and independent ownership assertions show that the recorded public coordination state is unchanged. Because this evidence neither authorizes a replacement nor creates a scholarly delta, the honest outcome is no_progress and a continued source-edit hold.

• On 2026-07-22, the maintained Problem 530 page displayed OPEN and Formalised statement? No.
• Formal Conjectures issue 773 remained open and unassigned.
• PR 4044 remained open, non-draft, unmerged, at head e9caf02a19d55dff055d89d441b45272e1fa134b, owned by putonthetableacat55, and labelled awaiting-author.
• The run-8 normalized snapshot was byte-identical to run 7 with SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c.
• The independent run-8 checker returned 0 in 0.042 seconds with empty stderr.

• .proof-experiments/20260722-123152-75db6a returned 0 in 2.336 seconds; stdout SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c; stderr empty.
• .proof-experiments/20260722-123227-778f5c returned 0 in 0.042 seconds; checker stdout SHA-256 f87db9e088b6d57c2df8465fda1fb75c718f399662a656c81b5ecce1ac1bcbfc; stderr empty.
• research/run8_live_status_result_20260722.json records the exact fields, comparison, limitations, provenance, and hold decision.
• JSON validation, Bash syntax checking, checker replay, live-to-result field comparison, delegate-receipt comparison, and git diff --check passed.

• .proof-experiments/20260722-123152-75db6a: the fixed five-endpoint audit returned 0 in 2.336 seconds and produced a snapshot byte-identical to run 7.
• .proof-experiments/20260722-123227-778f5c: the independent receipt checker returned 0 in 0.042 seconds and confirmed every fail-closed predicate.

checks/check_erdos530_run8_receipt.sh separately hashes and compares the run-7 and run-8 snapshots, then asserts the official-page, issue, pull-request, author, label, head, timestamp, comment-count, and review-count predicates.

not_requested

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

Original model outcome

no_progress

Public classification

no_progress

None recorded.

• PR 4044 is an open, unmerged, same-target Formal Conjectures formalization at head e9caf02a19d55dff055d89d441b45272e1fa134b.
  .proof-experiments/20260722-123152-75db6a/stdout.txt and independent experiment 20260722-123227-778f5c · The public official page and GitHub REST state captured on 2026-07-22. · computed
• The run-8 normalized ownership snapshot is byte-identical to run 7.
  checks/check_erdos530_run8_receipt.sh returned 0; snapshot SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c. · The exact normalized fields emitted by checks/audit_erdos530_live_status.sh. · computed
• Local source hash 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466 is warning-clean for the exact target under Lean 4.27.0.
  Lab 135f90912547 returned 0 with empty stderr and nonempty OLean SHA-256 0ba42a02ee4fd1fed5b19d584dbae21cb4f8dde7cffc8b2c432f4cb0befdcb37. · Pinned Formal Conjectures checkout 8f6e745798379104379da0b5c28c25315489890f; exact numeric module only. · computed

• Open an independent competing PR while PR 4044 remains active.
  Current Formal Conjectures contribution route. · PR 4044 already contains the same target, has an identified author, and has maintainer review. · .proof-experiments/20260722-123152-75db6a/stdout.txt · Documented consent from the author or maintainers, or closure followed by explicit maintainer approval for a replacement.
• Treat awaiting-author status or inactivity as abandonment.
  Interpretation of PR 4044's current public state. · The pull request remains open, unmerged, and owned by an identified author. · .proof-experiments/20260722-123227-778f5c/stdout.txt · A public author or maintainer statement explicitly declaring abandonment or inviting replacement.
• Repeat the expensive Lean target build as the current discriminator.
  Run-8 decision between source validation and ownership validation. · The Lean artifact already has a hash-bound kernel receipt; another build cannot resolve the sole remaining authorization uncertainty. · The status audit and checker completed in 2.378 seconds combined and found the ownership blocker unchanged. · Documented authorization for a source delta that requires a new source hash and kernel receipt.

• Detect a public merge, closure, ownership change, or explicit coordination statement on PR 4044.
  Such an event is the cheapest evidence capable of reopening legitimate implementation work. · When a fresh check is warranted, rerun checks/audit_erdos530_live_status.sh once and compare with research/run8_live_status_result_20260722.json. · normal · open
• Coordinate the kernel-validated IsSidon-reusing cleanup with the existing author or maintainers.
  It could address the existing API review without duplicating the scholarly target. · After documented authorization, port only the requested delta and run a fresh warning-fatal exact-target build. · high · open

Objective: Detect a legitimate coordinated acceptance path without duplicating the active pull request.

First action: Read research/run8_live_status_result_20260722.json and inspect whether any newly supplied source event satisfies the recorded reopen condition; if a current snapshot is required, run the fixed audit once.

Stop condition: Stop without source edits if PR 4044 remains active and no explicit coordination is documented; redirect only on an authorized coordination or replacement event.

• Do not edit or rebuild the Lean source and do not open a competing pull request while PR 4044 remains active without coordination.
• Begin the next epoch by reading research/run8_live_status_result_20260722.json; rerun the fixed audit only if a fresh public-state discriminator is required.
• If documented authorization appears, inspect its exact scope before porting only the authorized delta and generating fresh target-build and repository-CI receipts.

• https://www.erdosproblems.com/530 ↗
• https://www.erdosproblems.com/latex/530 ↗
• https://github.com/google-deepmind/formal-conjectures/issues/773 ↗
• https://github.com/google-deepmind/formal-conjectures/pull/4044 ↗
• https://github.com/google-deepmind/formal-conjectures/pull/4044#discussion_r3312344627 ↗

GPT-5.6 Sol acted as principal investigator. The supplied GPT-5.6 Terra source-discriminator performed bounded reconnaissance; its memo was treated as advisory and its receipt was audited byte-for-byte, not counted as independent validation. Deterministic Bash, curl, jq, ripgrep, cmp, sha256sum, Git, the computational-researcher experiment wrapper, Lake 5.0.0, and the Lean 4.27.0 kernel were used. No external publication, pull-request mutation, system modification, or Lean source edit was performed.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

399.0s

Review state

not a result claim

Attempt ID

scout-bdf77f43574b-20260722-123644-28aa03

No human review recorded.