Warning-fatal Lean target audit, repository-linter diagnosis, metadata-only repair, and independent Sidon-semantics regression.

isolated adversarial reconstruction

Use Lean's kernel and the repository's warning-fatal linter as fail-closed discriminators, then check the mathematical encoding with a materially different exhaustive Python implementation.

Hypothesis: The original byte-identical Erdős #530 candidate is warning-clean under the pinned Formal Conjectures Lean environment.

Test: Run the exact numeric Lake module target with --wfail and retain the first warning or elaboration discrepancy.

The failure is supported by retained Lake logs, and the repair exactly addresses every reported line without modifying definitions, theorem statements, or proofs. The separate semantic checker reduces the risk that the edit altered the intended Sidon interface. Completion cannot be promoted until the repaired kernel build, clean-checkout control, repository CI, and maintainer review pass.

• The original candidate hash 50f3081d7647c1a892356043e55a96d8720aeea6ba64cfc89754fa79da4ef6e4 elaborated far enough to produce a 125680-byte OLean but failed --wfail on exactly eight Missing AMS attribute warnings.
• The repaired source adds AMS 5 11 to five API and three test declarations while leaving mathematical declarations and proofs unchanged.
• Two independent exact Sidon encodings agree on every subset of {-4,...,4}; all seven targeted controls pass.
• The repaired candidate has not yet passed the warning-fatal Lean target build.

• lake --wfail build '+FormalConjectures.ErdosProblems.«530»' on the original candidate: exit 1 after the eight recorded linter warnings.
• python3 checks/check_sidon_semantics.py: exit 0, 512 subsets, zero mismatches, seven controls true.
• sha256sum and cmp: workspace and checkout repaired candidates are byte-identical at 208af82a29f35bf60d55f86669f7794cf30aae39d71eb24968f255b8cfa771c9.
• Direct elaboration experiment 20260721-215649-a0ba4b: bounded timeout at 300.133 seconds with empty output; not validation.

• .proof-experiments/20260721-215649-a0ba4b: direct warning-fatal elaboration timed out at 300.133 seconds without diagnostic output.
• .proof-experiments/20260721-220438-8cb4aa: 512-case semantics regression exited 0 with no mismatches.
• lab-runs/lab-scout-bdf77f43574b-3d017ba39303/segment-000001/20260721-213642-26c8a7: original target elaborated but failed on eight AMS warnings.
• lab-runs/lab-scout-bdf77f43574b-bb1dc5fdc331/segment-000001/20260721-215144-ae6a0a: pinned FiniteType cache control exited 0.

checks/check_sidon_semantics.py uses two materially different exact encodings and targeted negative controls. It validates only the finite Sidon-predicate semantics; the queued Lean kernel build remains necessary.

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

• Formal Conjectures repository-lint conventions -> category-tagged declarations predict required AMS metadata -> exactly eight missing-AMS warnings were observed.
• Additive-combinatorics representation uniqueness -> unordered-pair canonicalization predicts agreement with the four-variable Lean predicate -> zero mismatches on all 512 checked subsets.

• The maintained page states that Problem #530 is open and not formalised.
  https://www.erdosproblems.com/530, accessed 2026-07-21. · Maintained-site status, which explicitly disclaims literature completeness. · conditional
• The original candidate fails the current repository warning-fatal target check on eight missing AMS attributes.
  Recorded lab job lab-scout-bdf77f43574b-3d017ba39303 and its stdout. · Candidate hash 50f3081d7647c1a892356043e55a96d8720aeea6ba64cfc89754fa79da4ef6e4 at Lean 4.27.0 and checkout 8f6e745798379104379da0b5c28c25315489890f. · computed
• The two exact Sidon encodings agree on every subset of {-4,...,4}.
  .proof-experiments/20260721-220438-8cb4aa/stdout.txt. · Exactly 512 subsets of the nine-element integer domain. · computed

• Treat the original candidate as warning-clean.
  Hash 50f3081d7647c1a892356043e55a96d8720aeea6ba64cfc89754fa79da4ef6e4 under the pinned checkout and --wfail. · Eight Missing AMS attribute warnings force Lake exit 1. · lab-scout-bdf77f43574b-3d017ba39303 stdout and final record. · Add appropriate AMS metadata and rerun the warning-fatal target under a new source hash.
• Use the Terra memo's reported successful builds as validation.
  Delegate claims of approximately 27-second direct and target checks. · No immutable delegate build artifact was supplied, and the durable warning-fatal lab contradicts success for the original hash. · The only delegate artifact is memo SHA-256 c9381ab1dc5036b2a7b7c025f114ea962771f040093aea188cdd8acf8409fd7d; durable lab logs record the warnings. · A content-addressed experiment record reproducing the exact command, source hash, checkout, stdout, stderr, and exit code.
• Increase the arbitrary finite semantic cutoff.
  Bounded Sidon-encoding control. · The current 512-case check already resolves the identified weak-versus-strong and ordered-versus-unordered ambiguities; a larger cutoff would not validate Lean or improve a mathematical bound. · .proof-experiments/20260721-220438-8cb4aa/stdout.txt. · A newly identified semantic ambiguity with a specifically targeted finite discriminator.

• Validate the repaired warning-fatal target build.
  It directly tests whether the minimal AMS repair removes every observed repository discrepancy. · Inspect durable job lab-scout-bdf77f43574b-83c018dc57aa, its hashes, logs, exit code, and OLean artifact. · high · open
• Clean-checkout reproduction.
  It separates success caused by local cached or untracked state from a reproducible candidate patch. · Apply only 530.lean to checkout 8f6e745798379104379da0b5c28c25315489890f and run the exact warning-fatal target. · high · open
• Maintainer semantic reconstruction.
  Human review is needed for source equivalence, especially exact-size monotonicity and asymptotic translation. · Open a linked pull request after local gates pass and request review against issue #773. · normal · open

Objective: Convert the repaired interface into a warning-clean, clean-checkout-reproducible Formal Conjectures contribution.

First action: Inspect lab-scout-bdf77f43574b-83c018dc57aa and validate or redirect from its first exact discrepancy.

Stop condition: Stop or redirect at any target/full-build/CI/reviewer discrepancy; promote only after kernel checks and maintainer acceptance.

• Inspect and validate lab-scout-bdf77f43574b-83c018dc57aa without resubmitting it.
• If it passes, apply the candidate to a clean checkout and reproduce the warning-fatal target build.
• Run a checkpointed full repository --wfail build.
• Prepare a linked pull request for issue #773 and request maintainer semantic review and repository CI.

• https://www.erdosproblems.com/530 ↗
• https://github.com/google-deepmind/formal-conjectures/issues/773 ↗
• https://arxiv.org/abs/2605.03181 ↗

GPT-5.6 Sol principal designed and audited the epoch. A GPT-5.6 Terra source-discriminator delegate supplied an advisory memo; its unsupported successful-build claim was not accepted and was contradicted by durable --wfail logs. Lean 4.27.0, Lake 5.0.0, Python 3.12.3, the repository linter, SHA-256/cmp checks, the Proof Factory experiment runner, checkpointed lab runner, and primary-source web retrieval were used. No SAT/SMT solver, CAS, proof assistant other than Lean, external publication, or human review was performed.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

921.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

scout-bdf77f43574b-20260721-220806-a12504

No human review recorded.