Audited the Terra delegate's bounded live-status receipt, then executed a separately written deterministic checker that compared it byte-for-byte with run 6 and asserted every fail-closed ownership predicate.

Progress

Run 7 confirmed that PR 4044 remains open, unmerged, non-draft, at the same head and labelled awaiting-author. A separate deterministic checker validated the delegate-generated snapshot against run 6. No Lean source was changed, and no contribution or novelty claim is made.

Research-policy redirect

Automated lab review may recommend validate/promote, but only an operator may apply it with an independent validation receipt.

Strategy and discriminator

receipt-level adversarial validation

Exact hashing, byte comparison, and independent jq assertions validate the captured primary-source snapshot before permitting any source work.

Hypothesis: The run-7 normalized live-status receipt is byte-identical to run 6 and still satisfies every fail-closed ownership predicate, so no independent replacement is currently authorized.

Test: Run checks/check_erdos530_run7_receipt.sh through the deterministic experiment wrapper and require exact snapshot hash, byte equality, open/unmerged PR state, unchanged head, awaiting-author label, and unchanged review counts.

Rationale

The public evidence leaves no legitimate independent submission path. The fail-closed response is to preserve the kernel-checked local artifact, record the unchanged blocker, and await explicit coordination.

Claims requiring scrutiny

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, and labelled awaiting-author.
The run-7 normalized snapshot was byte-identical to run 6 with SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c.
The independent run-7 checker returned 0 in 0.045 seconds with empty stderr.

Evidence and scope

.proof-experiments/20260722-103042-a9ed1e returned 0 in 2.131 seconds; stdout SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c; stderr empty.
.proof-experiments/20260722-103248-ebea24 returned 0 in 0.045 seconds; checker stdout SHA-256 17d35c9f48a9fef0083a625e2a12251e735da884f3f3ab77b41143e0a96bc3db; stderr empty.
research/run7_live_status_result_20260722.json records the compared fields, scope limitation, provenance, and decision.
jq validation, Bash syntax checking, independent checker replay, and git diff --check passed.

Computational experiments

.proof-experiments/20260722-103042-a9ed1e: five-endpoint live audit returned 0 in 2.131 seconds and produced a snapshot byte-identical to run 6.
.proof-experiments/20260722-103248-ebea24: independent receipt checker returned 0 in 0.045 seconds and confirmed every fail-closed predicate.

Independent checker

checks/check_erdos530_run7_receipt.sh independently hashes and compares the run-6 and run-7 snapshots, then asserts the official, issue, pull-request, label, head, timestamp, comment-count, and review-count predicates.

Contribution gate

not_requested

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

Original model outcome: progress
Public classification: progress

Cross-domain transfers tested

None recorded.

Established facts

PR 4044 is an open, unmerged, same-target Formal Conjectures formalization at head e9caf02a19d55dff055d89d441b45272e1fa134b.
.proof-experiments/20260722-103042-a9ed1e/stdout.txt and independent experiment 20260722-103248-ebea24 · Public page and GitHub REST state captured on 2026-07-22. · computed
The run-7 normalized ownership snapshot is byte-identical to run 6.
checks/check_erdos530_run7_receipt.sh returned 0; snapshot SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c. · The exact normalized fields emitted by checks/audit_erdos530_live_status.sh. · computed
The 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 target only. · computed

Ruled out in this epoch

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/20260722-103042-a9ed1e/stdout.txt · Documented consent from the author or maintainers, or closure/abandonment followed by explicit maintainer approval for a replacement.
Treat awaiting-author status or inactivity as abandonment.
Interpretation of PR 4044's public state. · The pull request remains open, unmerged, and owned by an identified author. · .proof-experiments/20260722-103248-ebea24/stdout.txt · A public author or maintainer statement explicitly declaring abandonment or inviting replacement.

Open leads

Monitor PR 4044 for a public coordination, closure, merge, or replacement-authorization event.
This is the cheapest event capable of reopening legitimate implementation work. · Run checks/audit_erdos530_live_status.sh once and compare with the run-7 normalized result. · normal · open
Coordinate the kernel-validated IsSidon-reusing cleanup with the existing author or maintainers.
It addresses the maintainer's API comment without duplicating the scholarly target. · After documented authorization, port only the requested delta and run a fresh warning-fatal exact-target build. · high · open

Continuation checkpoint

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

First action: Run checks/audit_erdos530_live_status.sh once through scripts/run_experiment.py and compare its normalized output with research/run7_live_status_result_20260722.json.

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

Next moves

Do not edit the Lean source, rebuild it, or open a competing pull request.
In run 8, execute the fixed live-status audit once and compare it with research/run7_live_status_result_20260722.json.
If documented authorization appears, inspect its precise scope before porting only the requested delta and generating fresh target and CI receipts.

Citations

Tool disclosure

GPT-5.6 Sol acted as principal investigator. A pre-supplied GPT-5.6 Terra source-discriminator performed the bounded live retrieval; its memo was treated as advisory, while its main-workspace experiment receipt was hash-audited and checked independently by Sol. 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: 379.2s
Review state: not a result claim
Attempt ID: scout-bdf77f43574b-20260722-103623-04157b

Human review ledger

No human review recorded.