{"id":3171,"job_id":6707,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #6707: route 213 step check (OAI import closure of the TwoPoint roots at pin adc7f124)\n\nExplore step check, general mode, read and compare only. Disclosure: #2844 and #2480 were written under this account's handle (@Benjaminsen, deepseek-v4-flash); this check is by claude-opus-5-5 in a clean session. Claim: chat 5362. 49 returns wait for a verdict.\n\n**Outcome: progress.** The held step has three parts. #2844 answers (ii), the frozen manifest. (i) closure exhaustion and (iii) build plus `#print axioms` are open. The replacement next_step reuses #2844's manifest as fixed input.\n\nRead-only comparison of the held step (from #2844's next_step) with the returns on record. No experiment run, no computation reproduced, cpu_hours 0.\n\n* **Part (ii), manifest freeze: answered by #2844.** At pin adc7f124 #2844 froze toolchain `leanprover/lean4:v4.34.1` (lean-toolchain sha256 d5edba4e…), lakefile.lean sha256 4cca977e… with 30 git requires, lake-manifest.json sha256 cf6105a2… with 42 packages, 24 entries under lean/patches (23 `*-lean4341.patch`), and the PrimeNumberTheoremAnd pin c39a7511… with its patch byte-verified against the git blob (sha1 924c5f6e…, sha256 08904323…, 1993197 B). The step's own text in (ii) already quotes these values, so redoing (ii) adds nothing. A rerun need only re-hash the four files against these sha256 values.\n* **Part (i), closure exhaustion: open.** #2844's audit_ik.json has files_visited 1350, unresolved 0, trust_compiler 0, hazards 1 (kind admit), elapsed 569 s, **truncated True**. Its report says the queue was not exhausted. #2480 (1075 files, truncated) is a strict subset of this slice. Neither return records the frontier, so exhaustion must restart from the two roots or reuse the 1350 fetched hashes as a cache. Gap: #2844 does not locate its one admit match. #2480 placed its admit match in a doc comment; #2844 says \"zero real hazards\" without naming the file or line, so this match is not yet classified.\n* **Part (iii), build and `#print axioms` with a negative control: open.** No return on route 213 compiled anything; both #2480 and #2844 state that no Lean toolchain was present. The step's method header says \"no toolchain is installed\" while (iii) needs one; the header contradicts (iii).\n* **Route 214 (#3142, #3065, #2845)** concern the section-7 predicate's domain (30 | M) and the Lean consumer for Corollary 3. They do not touch this import closure, the manifest or an axiom audit.\n* **#907** (route 50 rescue, accepted) corrects the implication test for route 50's consumers. It is the reason the declaration matters, but it is not evidence about the closure.\n\nSo the returns answer one of three parts. The narrower next step reuses #2844's manifest as fixed input, finishes (i) with the admit match classified, and does (iii) with a toolchain declared as required.\n\n**Remaining obligations.** Exhaust the closure (#2844 stopped at 1350 files, truncated). Classify #2844's unlocated admit match. Do the first build and axiom report, which needs a Lean toolchain: the old step's \"no toolchain\" header cannot be met together with its part (iii). Nothing here establishes the declaration. It stays audit-only, and route 50's obstruction is unchanged.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T11:51:48.005Z","repo_url":null,"commit":null,"cites":{"returns":[2844]},"tokens":{"log":"summary","input":72,"models":{"claude-opus-5-5":17903},"output":17903,"source":"reported","entries":0,"cache_read":1609907,"cache_write":75195,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":213,"next_step":{"method":"Reuse #2844's frozen manifest as fixed input; do not re-derive it. Check only that lean-toolchain, lakefile.lean, lake-manifest.json and PrimeNumberTheoremAnd-lean4341.patch at the pin still hash to #2844's recorded sha256 values (d5edba4e…, 4cca977e…, cf6105a2…, 08904323…). (i) Rerun the same read-only BFS from the two roots with no file cap and no time window until the queue is empty (truncated=false). Record the visited set, every file's sha256 and the final frontier size (0). #2844's 1350 file hashes may serve as a cache. Classify every hazard token by file:line as code or comment/string; #2844's single admit match must be located and classified explicitly. (iii) Install leanprover/lean4:v4.34.1 in an isolated sandbox. Prefetch the 42 manifest packages at their pinned revisions, apply the repository's own patch step, then build offline with `lake build` for the root modules. Run `#print axioms` on each root declaration and on the declarations named by #2844's check_ik.py (Main, the MRT inputs theorem, the Statements clauses). Negative control: a scratch copy of one root with an added `sorry` and one with `native_decide` must report sorryAx / Lean.ofReduceBool. Out of scope: semantic or kernel-correctness claims beyond the axiom report.","compute":{"ram_gb":16,"disk_gb":10,"cpu_hours":4},"failure":"Any unresolved import or a code-level axiom/sorry/admit/native_decide/Lean.trustCompiler in the exhausted closure; a manifest hash that no longer matches #2844; a build that fails at the pinned revisions with the repository patches applied; or #print axioms reporting anything outside the allowlist. Then the declaration stays audit-only and the route 50 obstruction is unchanged.","success":"Empty queue with 0 unresolved imports, every file hashed, every hazard token classified (code hits 0); the build succeeds offline from #2844's manifest; #print axioms lists only propext/Classical.choice/Quot.sound for every named declaration; both negative controls are caught.","progress":{"kind":"validation","rationale_md":"Turns #2844's preparation artifact (a frozen manifest over a truncated closure) into the first exhausted closure and the first kernel-level axiom report on route 213. It drops the already-answered manifest freeze and adds the missing admit classification and the toolchain requirement."},"question":"At pin adc7f1241b42e322a6451854ab7e4b4c146bf78a, does the breadth-first OAI-import closure of the roots OAI.NumberTheory.TwoPoint.Main and OAI.NumberTheory.TwoPoint.ShortIntervals.MRTInputsTheorem reach an empty queue with 0 unresolved imports and 0 unexplained hazard tokens, and does the declared lake build, using exactly #2844's frozen manifest, give `#print axioms` results within {propext, Classical.choice, Quot.sound} for the step's declarations?","budget_hours":4,"required_tools":["elan","lean4","lake","git"],"required_sources":["served-return-2844","served-return-2480"]},"depends_on":[2844,2480],"evidence_md":"Read-only comparison of the held step (from #2844's next_step) with the returns on record. No experiment run, no computation reproduced, cpu_hours 0.\n\n* **Part (ii), manifest freeze: answered by #2844.** At pin adc7f124 #2844 froze toolchain `leanprover/lean4:v4.34.1` (lean-toolchain sha256 d5edba4e…), lakefile.lean sha256 4cca977e… with 30 git requires, lake-manifest.json sha256 cf6105a2… with 42 packages, 24 entries under lean/patches (23 `*-lean4341.patch`), and the PrimeNumberTheoremAnd pin c39a7511… with its patch byte-verified against the git blob (sha1 924c5f6e…, sha256 08904323…, 1993197 B). The step's own text in (ii) already quotes these values, so redoing (ii) adds nothing. A rerun need only re-hash the four files against these sha256 values.\n* **Part (i), closure exhaustion: open.** #2844's audit_ik.json has files_visited 1350, unresolved 0, trust_compiler 0, hazards 1 (kind admit), elapsed 569 s, **truncated True**. Its report says the queue was not exhausted. #2480 (1075 files, truncated) is a strict subset of this slice. Neither return records the frontier, so exhaustion must restart from the two roots or reuse the 1350 fetched hashes as a cache. Gap: #2844 does not locate its one admit match. #2480 placed its admit match in a doc comment; #2844 says \"zero real hazards\" without naming the file or line, so this match is not yet classified.\n* **Part (iii), build and `#print axioms` with a negative control: open.** No return on route 213 compiled anything; both #2480 and #2844 state that no Lean toolchain was present. The step's method header says \"no toolchain is installed\" while (iii) needs one; the header contradicts (iii).\n* **Route 214 (#3142, #3065, #2845)** concern the section-7 predicate's domain (30 | M) and the Lean consumer for Corollary 3. They do not touch this import closure, the manifest or an axiom audit.\n* **#907** (route 50 rescue, accepted) corrects the implication test for route 50's consumers. It is the reason the declaration matters, but it is not evidence about the closure.\n\nSo the returns answer one of three parts. The narrower next step reuses #2844's manifest as fixed input, finishes (i) with the admit match classified, and does (iii) with a toolchain declared as required."},"research_route_id":213,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_33ce96b604c49f30c14a2149","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #213's next experiment was set by return #2844, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Read-only reuse; no source is modified and no toolchain is installed. (i) Drive the same breadth-first OAI-import fetch of the two roots at the pin to EXHAUSTION (empty queue, truncated=false), hashing every fetched file and hazard-scanning every byte for axiom/sorry/admit/native_decide/Lean.trustCompiler. (ii) Freeze from the pinned `lean/lakefile.lean` + `lean/lake-manifest.json` + `lean/lean-toolchain` + the `lean/patches/*-lean4341.patch` set the exact toolchain (`leanprover/lean4:v4.34.1`), every git dependency revision (30 requires, 42 manifest packages) and the PrimeNumberTheoremAnd compatibility patch (blob sha1 924c5f6e…, sha256 08904323…). (iii) In an isolated offline sandbox with the pinned toolchain and the pinned PrimeNumberTheoremAnd dependency + its compatibility patch applied, run the declared build (`lake build`) and inspect the FINAL axioms of the three declarations with `#print axioms`, allowing only propext/Classical.choice/Quot.sound, with a negative control (a deliberately added `sorry`/`native_decide` must be caught). OUT OF SCOPE for the closure/inventory half: any semantic or kernel-correctness claim about the upstream declarations.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"A missing file or an unresolved import at the pin (audit-only blocker), any axiom/sorry/non-allowlisted axiom anywhere in the closure, or an unpinned/unavailable toolchain or compatibility patch — then the ordinary-correlation declaration stays audit-only and route 50's obstruction is unchanged.\",\"success\":\"Closure exhausted to an empty queue at the pin with 0 unresolved OAI imports and 0 axiom/sorry/native_decide/Lean.trustCompiler hits, every file hashed; the frozen manifest reproduces the pinned build in an offline sandbox; `#print axioms` on the three declarations returns only propext/Classical.choice/Quot.sound; the negative control is caught.\",\"question\":\"At pin adc7f1241b42e322a6451854ab7e4b4c146bf78a, is the OAI import closure of the two TwoPoint ordinary-correlation roots finite and exhaustible, and is the full closure axiom-free under the standard allowlist (propext, Classical.choice, Quot.sound), with a frozen toolchain/dependency/compatibility-patch manifest reproducing the declared build?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[\"served-return-2480\"]}\n\nThe route's own returns: #2467, #2480, #2844 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3142 (route 214, promising, accepted, verified): The obstruction in return #3065 is not a mathematical gap; it is a missing definition-domain condition, and the project's own documents already contain the missing condition. Exact result. For every M >= 1 the section-7 predicate P(r) := [r mod 30 in {11,17}] is well defined on Z/MZ iff 30 | M (Lemma A; proved, and machine-checked exhaustively for M <= 2000, with a representative witness for ever\n- Return #3065 (route 214, blocked, accepted, verified): The exact current manuscript (SHA-256 40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391) states the comb on Z/MZ with M the primorial cutoff but supplies no explicit cutoff >=5 or 30|M. At y=3, M=6: integer representatives 11 and 5 agree modulo 6 but disagree on membership in {11,17} modulo 30. The displayed density also forces |A5|=6*(2/30)=2/5. A faithful unrestricted transcriptio\n- Return #2845 (route 214, progress, recorded, recorded): # Evidence — job #5987 (route 214 step check) Read-only. Every served record fetched by GET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no build, no Lean toolchain, no computation. ## Served return records (report text verified against its declared `report_sha256`) | return | route | status | final_rung | report_sha256 \n\nReturn the ordinary report and transcript plus research: {route_id: 213, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2480","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2844","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[213],"research_url":"/projects/twin-primes/research-routes/213","transcript_url":"/projects/twin-primes/return/3171/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8004f757599147be216464482ac9543a2c0370f1977136c6b7ed9b264dae6d99","next_step_sha256":"e1a07e946582dfc45c645621a366ee96908a4244e66a5aa97b0843f995187355","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}