Audited the failed API-refactored Lean target, repaired the single adversarial-control argument-order mismatch, hash-locked the repaired source, and escalated its warning-fatal target build to the checkpointed lab.

isolated adversarial reconstruction

Compare the candidate with the repository's actual IsSidon API, use an independently compiled equivalence/control file to guard semantics, and let the pinned Lean kernel discriminate exact source hashes.

Hypothesis: Changing the project-IsSidon control invocation from legacy order (0,2,1,1) to project order (0,1,2,1) removes the only observed elaboration failure without changing the formal conjecture or its extremal API.

Test: Run the hash-locked exact Problem 530 target with lake --wfail and require exit 0 plus a nonempty newly hashed 530.olean.

The failure log and pinned definition identify a concrete positional mismatch, while the prior independent audit already exhibits the correct collision ordering. The one-line repair is therefore justified, but only a fresh OLean for the repaired hash can establish technical completion.

• Pinned project IsSidon takes membership arguments in order i₁,j₁,i₂,j₂ and tests i₁+i₂=j₁+j₂.
• Source hash e27b8c80… failed after 625.802 seconds with one reported unsolved goal at the {0,1,2} control.
• The repaired workspace and pinned-checkout sources are byte-identical at SHA-256 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466.
• The unchanged audit retry timed out after 120.135 seconds with empty stdout and stderr and does not validate the repair.
• The repaired target is queued under job lab-scout-bdf77f43574b-135f90912547; queueing is not evidence.
• GitHub issue #773 was open and unassigned on 2026-07-22.

• sha256sum FormalConjectures/ErdosProblems/530.lean checks/run_erdos530_lean_build.sh checks/Erdos530SemanticAudit.lean
• cmp --silent FormalConjectures/ErdosProblems/530.lean .upstream/formal-conjectures/FormalConjectures/ErdosProblems/530.lean
• bash -n checks/run_erdos530_lean_build.sh
• Prior semantic experiment 20260721-223233-e53846: return code 0, 10.082 seconds, empty diagnostics.
• Bounded retry 20260722-043421-7797b3: return code 124, timed_out true, 120.135 seconds, empty diagnostics.
• Failed refactor lab stdout: line 102 unsolved goal h : IsSidon {0,1,2} ⊢ False.

• .proof-experiments/20260721-223233-e53846: unchanged independent semantic audit passed Lean 4.27.0 in 10.082 seconds with empty diagnostics.
• lab-runs/lab-scout-bdf77f43574b-03d1a8ffc4cf/segment-000001/20260721-223701-49232e: API-refactored target failed after 625.802 seconds at the single reported control proof state.
• .proof-experiments/20260722-043421-7797b3: bounded audit retry timed out at 120.135 seconds with empty diagnostics; no semantic conclusion.

checks/Erdos530SemanticAudit.lean is separately written and proves LegacyFinsetIsSidon S ↔ IsSidon (S : Set ℝ) for every Finset ℝ, with repeated-summand and swap controls. Its prior kernel pass remains valid because the checker bytes are unchanged.

not_requested

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

Original model outcome

progress

Public classification

progress

• API migration auditing -> positional quantifier order may differ despite extensional equivalence -> inspect the defining equality and rerun a collision witness -> the project predicate required (0,1,2,1), explaining the failed legacy-order call.

• LegacyFinsetIsSidon S ↔ IsSidon (S : Set ℝ) for every S : Finset ℝ.
  Lean theorem legacyFinsetIsSidon_iff_projectIsSidon in experiment 20260721-223233-e53846. · All finite subsets of the real numbers under the pinned project API. · proved
• The API-refactored source hash e27b8c80… produced an unsolved goal at line 102 under the exact warning-fatal target.
  lab-scout-bdf77f43574b-03d1a8ffc4cf record and content-addressed stdout. · Pinned checkout 8f6e745…, Lean 4.27.0, exact Problem 530 target. · computed
• The repaired workspace and checkout candidate files have SHA-256 3ff7038c3c08f48408f48d53c4503182944cfd8c51b549cbab570a3b062e8466 and compare byte-identically.
  sha256sum and cmp checks recorded this epoch. · The two candidate paths in the current workspace. · computed
• The 2026-07-22 audit retry timed out after 120.135 seconds without diagnostics.
  .proof-experiments/20260722-043421-7797b3/experiment.json. · That bounded local execution only. · computed

• Use the call ordering (0,2,1,1) to witness 0+2=1+1 under project IsSidon.
  The line-102 control under the pinned project definition. · Those positions encode 0+1=2+1, not the intended collision. · Pinned Basic.lean definition and failed lab diagnostic. · Only a project API signature change.
• Treat the timed-out 20260722 audit retry as a successful semantic check.
  Experiment 20260722-043421-7797b3. · It returned code 124 and produced no kernel acceptance receipt. · .proof-experiments/20260722-043421-7797b3/experiment.json. · A completed hash-bound kernel run.
• Claim that the exact target eliminated 8037 unrelated jobs.
  Search-efficiency accounting for the pinned checkout. · The target log itself reports an 8038-job dependency closure. · Validated and failed exact-target stdout artifacts. · A measured dependency-graph comparison against the full build.

• Review the repaired exact-target lab.
  It is the cheapest decisive check of the current source hash. · Inspect records and content-addressed outputs for lab-scout-bdf77f43574b-135f90912547. · high · open
• Relocate and index extremal helpers.
  The repository contribution guide explicitly requires conjecture-supporting definitions and results in FormalConjecturesForMathlib. · After the current hash passes, create one helper module, update FormalConjecturesForMathlib.lean, import it from 530.lean, and rebuild the named target. · high · open
• Clean-checkout and full-CI reproduction.
  These remain explicit verification-contract gates after interface placement stabilizes. · Apply only the stabilized patch to a clean pinned checkout, run the exact target, then submit the full warning-fatal build to the lab. · normal · open

Objective: Convert the repaired API-reusing declaration into a kernel-checked and repository-layout-compliant contribution.

First action: Inspect records/labs and lab-runs for lab-scout-bdf77f43574b-135f90912547; do not resubmit it.

Stop condition: Redirect on the first build diagnostic; if it passes, stop editing the current file until the helper-module relocation is designed and hash-bound.

• Inspect immutable completion artifacts for lab-scout-bdf77f43574b-135f90912547 without resubmitting it.
• On exit 0, verify source and driver hashes, empty diagnostics, and a nonempty newly hashed 530.olean.
• Then move GuaranteedSidonSize, ell, and reusable proved API lemmas into an indexed FormalConjecturesForMathlib file and rebuild.
• After placement stabilizes, reproduce from a clean checkout and submit a checkpointed full lake --wfail build.

• https://www.erdosproblems.com/530 ↗
• https://github.com/google-deepmind/formal-conjectures/issues/773 ↗
• https://github.com/google-deepmind/formal-conjectures/blob/main/CONTRIBUTING.md ↗
• https://github.com/google-deepmind/formal-conjectures/blob/8f6e745798379104379da0b5c28c25315489890f/FormalConjecturesForMathlib/Combinatorics/Basic.lean ↗

Sol principal: this GPT-5-based Codex agent performed source inspection, experiment design, editing, and synthesis. One supplied GPT-5.6-Terra delegate memo provided advisory reconnaissance; every relied-on claim was checked against pinned source or deterministic artifacts, and model agreement was not treated as validation. Lean 4.27.0 and Lake 5.0.0 performed or are queued to perform kernel checks; Bash utilities supplied hashing, byte comparison, and syntax checks; the computational-researcher run_experiment and checkpointed-lab scripts recorded bounded executions. GitHub API/raw-source checks and web access were used for current repository metadata. No CAS, SAT/SMT solver, or additional sub-agent was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

717.0s

Review state

not a result claim

Attempt ID

scout-bdf77f43574b-20260722-044204-213e81

No human review recorded.