Reopen the pinned Lean build route, discriminate Lake target-addressing failures from source failures, and queue the corrected numeric-module build.

No Progress

The candidate was not falsified. Three recorded attempts stopped before its body: the bare numeric Lake target produced an empty-path error, the tested relative source target was unknown, and direct elaboration against the current cache found FormalConjecturesUtil.olean missing while bootstrap was still compiling. Lake's +module grammar was captured independently. The corrected target +FormalConjectures.ErdosProblems.«530» is queued as lab-scout-bdf77f43574b-eec7321621e3.

Research-policy redirect

Attempt evidence did not validate; durable progress is withheld.

Strategy and discriminator

formal proof with premise retrieval

Use deterministic Lake entry-point controls to locate the first failure boundary, then run the surviving warning-fatal target in the checkpointed lab.

Hypothesis: The saved target FormalConjectures.ErdosProblems.530 denotes the candidate and reaches warning-fatal Lean elaboration.

Test: Run the saved target under pinned Lake 5.0.0 and classify whether failure occurs in target resolution, dependency loading, warnings, or candidate elaboration.

Rationale

The exact error boundaries rule out treating these failures as Lean statement errors. Because the corrected job has not completed, promotion to candidate would violate the verification contract.

Claims requiring scrutiny

The bare Lake target FormalConjectures.ErdosProblems.530 fails before candidate elaboration in the tested pinned environment.
The tested --dir-relative source-path target also fails before elaboration.
Lake 5.0.0 documents +module as the disambiguated module-target form.
The corrected warning-fatal build is queued but has no result yet.

Evidence and scope

.proof-experiments/20260721-184217-5689de: exit 1 after 34.675 s, empty-path no-such-file failure.
.proof-experiments/20260721-184333-13112b: exit 1 after 106.924 s, unknown module source path.
.proof-experiments/20260721-184835-cc1cd3: exit 1 after 33.114 s, missing FormalConjecturesUtil.olean before source elaboration.
.proof-experiments/20260721-185548-c3172e: exit 0 after 0.122 s, recorded Lake target grammar.
records/labs/lab-scout-bdf77f43574b-eec7321621e3-submitted-segment-01.json: one-segment lab submission only.

Computational experiments

.proof-experiments/20260721-184217-5689de — bare target failed before elaboration.
.proof-experiments/20260721-184333-13112b — relative source target failed before elaboration.
.proof-experiments/20260721-184835-cc1cd3 — direct cache attempt failed on missing support OLean.
.proof-experiments/20260721-185548-c3172e — Lake target grammar control passed.

Independent checker

The Sidon semantics retain the separate checker checks/check_sidon_semantics.py over exactly 512 subsets. No independent checker can replace the pending Lean kernel build for this epoch's build claim.

Contribution gate

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

Cross-domain transfers tested

Lean numeric identifiers -> predict Lake module addressing needs both + disambiguation and guillemets -> the old bare target failed and the corrected form is now queued.

Established facts

The bare target FormalConjectures.ErdosProblems.530 fails with an empty-path no-such-file error.
.proof-experiments/20260721-184217-5689de · Exact pinned command and checkout only. · computed
The tested --dir-relative source target is rejected as an unknown module source path.
.proof-experiments/20260721-184333-13112b · Exact recorded command only. · computed
Lake 5.0.0 documents +module as its disambiguated module-target syntax.
.proof-experiments/20260721-185548-c3172e · Lake binary SHA-256 6ee60352946250468cf340ec68fcbe6c11c0db7b25d9fb4ae38ecab8e6178b48. · computed
The corrected target build has been submitted to the checkpointed lab.
records/labs/lab-scout-bdf77f43574b-eec7321621e3-submitted-segment-01.json · Submission status only, not build success. · computed

Ruled out in this epoch

Use FormalConjectures.ErdosProblems.530 as the named Lake target.
Lake 5.0.0 / Lean 4.27.0 pinned workspace. · It fails during target addressing with an empty source path. · .proof-experiments/20260721-184217-5689de · A Lake version change whose documented grammar makes the bare numeric target valid.
Use the tested --dir-relative FormalConjectures/ErdosProblems/530.lean target.
Exact recorded command. · Lake reports an unknown module source path before elaboration. · .proof-experiments/20260721-184333-13112b · A documented and independently tested path-rebasing rule or an absolute-path correction.

Open leads

Inspect the corrected warning-fatal target build.
It is the cheapest remaining kernel discriminator and is already queued. · Read the completed record for lab-scout-bdf77f43574b-eec7321621e3. · high · open
Obtain Formal Conjectures human semantic review.
The Lean kernel cannot certify equivalence to the informal Erdős problem. · After local builds pass, request assignment and review through issue #773. · high · open

Continuation checkpoint

Objective: Convert the candidate into a kernel-checked, repository-reviewed Formal Conjectures contribution.

First action: Find completed records for lab-scout-bdf77f43574b-eec7321621e3; do not resubmit the queued job.

Stop condition: Redirect on its first failure; on success submit the full warning-fatal build. Terminal success requires target build, full build, CI, and human semantic review.

Next moves

Inspect records/labs for completed output from lab-scout-bdf77f43574b-eec7321621e3 without resubmitting.
If it exits zero and candidate hashes match, submit a separate checkpointed full lake --wfail build.
After both builds pass, request human review on issue #773 and require repository CI.

Citations

Tool disclosure

GPT-5.6 Sol acted as principal investigator. The supplied GPT-5.6 Terra source-discriminator delegate timed out and produced no usable result; none of its claims were relied upon. Deterministic tools used were Python 3.12 run_experiment.py, the Proof Factory lab submitter, git, SHA-256, Lake 5.0.0, and Lean 4.27.0. The mandated project-scoped Formal Conjectures bootstrap was started but interrupted after it exceeded the uncheckpointed-work threshold. No external publication, PR, issue comment, or credential change was made.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1665.5s
Review state: evidence invalid or incomplete; not durable progress
Attempt ID: scout-bdf77f43574b-20260721-185748-323167

Human review ledger

No human review recorded.