Independently reran the bounded live-status audit for the existing same-target Formal Conjectures pull request and reviewed the completed hash-bound Lean build receipt.

Progress

The bounded audit confirmed that PR 4044 remains an active same-target formalization with no coordination signal. No Lean source was changed. The existing local target-build receipt was reviewed and validated for its exact kernel-checking claim, but the formalization is not an independently novel or accepted contribution.

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

coordinated upstream patch repair

Compare fixed primary-source and repository API fields against the prior snapshot, permitting source work only after an explicit coordination event.

Hypothesis: As of 2026-07-22, PR 4044 remains open at head e9caf02a19d55dff055d89d441b45272e1fa134b with awaiting-author and no API-visible event authorizing an independent replacement.

Test: Run checks/audit_erdos530_live_status.sh through the deterministic experiment wrapper and compare problem status, issue state, PR state, merge state, head SHA, labels, update time, comments, and reviews.

Rationale

The live primary-source state rules out a legitimate competing submission. Preserving the verified cleanup while awaiting explicit coordination maximizes reuse without creating duplicate upstream work.

Claims requiring scrutiny

On 2026-07-22, the maintained Problem 530 page remained OPEN and displayed Formalised statement? No.
On 2026-07-22, Formal Conjectures issue 773 remained open and unassigned.
PR 4044 remained open, non-draft, unmerged, at head e9caf02a19d55dff055d89d441b45272e1fa134b, and labelled awaiting-author.
Run 6 produced normalized audit stdout SHA-256 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c with empty stderr.
The local source hash 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466 passed its warning-fatal Lean 4.27.0 target build and emitted OLean hash 0ba42a02ee4fd1fed5b19d584dbae21cb4f8dde7cffc8b2c432f4cb0befdcb37.

Evidence and scope

.proof-experiments/20260722-083137-5a94c5 returned 0 in 2.135 seconds; stdout hash 22e9ad93abcc1954b15b35d4024853e1c71b9d46073653a135e24188b7003a8c; stderr empty.
research/run6_live_status_result_20260722.json records the compared fields, scope limitation, decision, and hashes.
Lab 135f90912547 returned 0; stdout reports 8038/8038 jobs and the exact OLean hash.
jq validation, bash syntax checking, and git diff --check passed after recording the checkpoint.

Computational experiments

.proof-experiments/20260722-083137-5a94c5: five-endpoint live-status audit returned 0 in 2.135 seconds and confirmed unchanged PR ownership state.
lab-runs/lab-scout-bdf77f43574b-135f90912547/segment-000001/20260722-044206-6702a3: exact warning-fatal Lean target returned 0 and emitted the recorded OLean hash.

Independent checker

The live audit was executed independently by the Sol principal and reproduced the Terra delegate's reported stdout hash. The formal target was checked by Lean's kernel; a separately written semantic audit exists, but upstream semantic review and CI remain outstanding.

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.
.proof-experiments/20260722-083137-5a94c5/stdout.txt · Public repository state observed on 2026-07-22. · computed
The repaired local exact target is warning-clean for source hash 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466.
Lab 135f90912547 returned 0 with empty stderr and a hashed nonempty OLean. · Pinned Formal Conjectures checkout 8f6e745798379104379da0b5c28c25315489890f with Lean 4.27.0. · computed

Ruled out in this epoch

Open an independent competing PR while PR 4044 remains active.
Current Formal Conjectures contribution route. · PR 4044 already formalizes the same extremal function and asymptotic target and has maintainer review. · .proof-experiments/20260722-083137-5a94c5/stdout.txt · Documented consent from the existing author or maintainers, or closure/abandonment followed by explicit maintainer approval for a replacement.
Treat awaiting-author 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/20260722-083137-5a94c5/stdout.txt · A public author or maintainer statement explicitly declaring abandonment or inviting replacement.

Open leads

Coordinate the kernel-validated IsSidon-reusing cleanup with PR 4044.
It addresses the principal maintainer API comment without duplicating the scholarly target. · After documented authorization, port only the requested delta to the designated branch and run the exact warning-fatal target. · high · open
Monitor the ownership state of PR 4044.
A coordination or closure event is the cheapest signal that can reopen implementation. · Run checks/audit_erdos530_live_status.sh once and compare against run6_live_status_result_20260722.json. · normal · 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 fields with research/run6_live_status_result_20260722.json.

Stop condition: Stop the epoch 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 or open a competing pull request.
In the next epoch, run the fixed audit once and compare PR state, merge state, head SHA, labels, update time, and public comments.
If explicit coordination appears, inspect its exact scope and port only the authorized delta before generating fresh hash-bound target and CI receipts.

Citations

Tool disclosure

GPT-5.6 Sol acted as principal investigator. A pre-supplied GPT-5.6 Terra source-discriminator memo was treated as advisory and independently audited. Deterministic Bash, curl, jq, ripgrep, SHA-256 utilities, the computational-researcher experiment wrapper, GitHub/official-site web retrieval, Lake 5.0.0, and the Lean 4.27.0 kernel were used. No external publication, pull-request mutation, or source modification was performed.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 389.5s
Review state: not a result claim
Attempt ID: scout-bdf77f43574b-20260722-083636-48022a

Human review ledger

No human review recorded.