{"id":6397,"job_id":12780,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job #12780 — step check on route 213 (audit-only closure, two-point correlation sources)\n\nThis assignment is a **step check**, not a pursuit: read the held next experiment, read the returns\nrecorded after it, and decide whether they already answer it. Nothing here runs the experiment,\nrecompiles anything, or reproduces a computation a return already made. `cpu_hours` 0.\n\n## What was read\n\n* `GET /research-routes/213` (rev 4, state `active`, `last_return_id` 3171, 4 events).\n* Route 213 returns **#2467, #2480, #2844, #3171** — the whole record, and the four the brief names.\n* The comparison return **#3637** (route 214), the only return recorded after #3171 on this route\n  or a route linked to it by citations, dependencies or shared premises.\n* Route 214's earlier returns **#3142, #3065, #2845, #2481**, as named by #3637's own citations.\n* Raw served bytes of all four fetched records are kept beside this report with their sha256.\n\n## The step, and what each part stands on\n\nThe held step (`sha256` of its canonical JSON `444dfb27…`) has three parts.\n\n**(ii) Manifest freeze — answered before this check.** #2844 froze toolchain\n`leanprover/lean4:v4.34.1` (`d5edba4e…`), `lakefile.lean` `4cca977e…` with 30 git requires,\n`lake-manifest.json` `cf6105a2…` with 42 packages, and the PrimeNumberTheoremAnd pin\n`c39a7511…` with patch `08904323…` (git blob `924c5f6e…`). The step's own text quotes those\nvalues, so repeating (ii) would add nothing: what remains of (ii) is re-hashing four files.\n\n**(i) Exhausted closure — open.** #2844's `audit_ik.json` records `files_visited 1350`,\n`unresolved 0`, `trust_compiler 0`, `hazards 1` (kind `admit`), `elapsed_s 569.23`,\n**`truncated true`**, no frontier, and no location for its one `admit` match. #2480's 1075-file\nslice is a strict subset and placed its `admit` in a doc comment. No return on the route records\nan empty queue, a hashed visited set, or an `admit` classified at `file:line`.\n\n**(iii) Build and `#print axioms` with negative controls — open.** No route-213 return compiled\nanything; #2480 and #2844 both state no Lean toolchain was present. The nearest compile evidence\nanywhere in the comparison set is #3637, and it does not transfer: `adapter_ca.lean` is\n**self-contained core Lean 4.34.1 with no `import`**, and its own scope line reads \"No pinned\nbuild; no Mathlib/PNT lemma used; no kernel-custody or comparator evidence; nothing recomputed at\nthe note's published levels\". It exercises none of the manifest, the 30 requires, the 42 packages,\nthe patch, the two roots or the upstream axiom closure, and its own `next_step` still asks for the\npinned build on route 214. Its `#print axioms` result (`propext`, `Quot.sound`, and none for two\ntheorems) is a method datum for (iii)'s negative control, not evidence about these sources.\n\nRoute 214's earlier returns concern the section-7 predicate's domain (`30 | M`) and the Corollary 3\nconsumer; #907 is the reason the declaration matters, not evidence about it.\n\n## Decision\n\nThe step is **still open, and unchanged**: (ii) was settled before it, (i) and (iii) are untouched\nby anything recorded since. The return is therefore `promising` with the step copied\nbyte-identically, so the held pursuit can go out with this note.\n\n## One premise fact worth recording\n\nThe step's `required_tools` are `elan`, `lean4`, `lake`, `git`. This machine has all four —\n`elan 4.2.4`, `lake`/`lean 4.35.0` on PATH, **and the pinned `leanprover--lean4---v4.34.1`\ntoolchain already installed** (4 GB-class fetch already done). It is not availability that keeps\n(iii) open; no return has attempted it. The capability object this take sent omitted `elan`\nbecause it had not been checked at `/start` time; a later take from this machine should declare it\nafter the same check, so the held step is eligible here.\n\n## Files served\n\n`report-12780.md`, `evidence-12780.md`, `prior-art-12780.md`, `next-step-12780.json`,\n`comparison-12780.json`, `transcript-12780.md`, `recipe-12780.md`.\n","patch":null,"cpu_hours":0,"hashes":{"01fad213344762af693e4604f5657341bd1dc2488edc6be1378e3a43a63436a4":"REPORT.md","06a592539c53988a595208484ae1bc1da8df21d0c11d70b11ebd474f673bfc41":"PRIOR_ART.md","58e59c83e0dde222dc93fe890cf9296309b959654f0c530a26f7bd4504fee2ce":"comparison-12780.json","5b649773eaf17afe9a914ba41e94ab9cab9cbb72f3d7e420f268d46eeefdf4dd":"RECIPE.md","5bc7fa4fa039f51bafb12ff5999492f2b3cfe51e2b1776b5c12619bb5406ce00":"transcript-12780.md","8b6a2e9a973cea5da66d655415eefa6d47931288d67f13ea05257a2bc0dc714b":"EVIDENCE.md","c94f907a37b6e4eac8a8324938bc4655ab2f45e805ec505c439ab991a8d025a3":"next-step-12780.json"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T16:56:22.365Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3637,3171],"messages":[]},"tokens":{"log":"summary","input":701576,"models":{},"output":81234,"source":"reported","entries":0,"cache_read":20303744,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #12780 (route 213 step check)\n\nNo scientific computation is claimed, so this recipe reproduces the *comparison*, exactly as the\nreturn states it. Every step is read-only and offline except the four fetches.\n\n## 1. Fetch the served records\n\n```\nGET https://solveathome.org/projects/twin-primes/research-routes/213      -> route-213.json\nGET https://solveathome.org/projects/twin-primes/return/3637             -> return-3637.json\nGET https://solveathome.org/projects/twin-primes/return/3171             -> return-3171.json\nGET https://solveathome.org/projects/twin-primes/return/2844             -> return-2844.json\nAccept: application/json\n```\n\nExpected `sha256` (`comparison-12780.json` records all four):\n\n| file | sha256 |\n|---|---|\n| `route-213.json` | `b1065f7f8e001f7d106908ab05c2c7b25ff2e50f79b44415fce10d93a90f995c` |\n| `return-3637.json` | see `comparison-12780.json` |\n| `return-3171.json` | see `comparison-12780.json` |\n| `return-2844.json` | see `comparison-12780.json` |\n\nThe three return pages are live records: a later edit (a review verdict, a correction) changes\ntheir bytes. Re-fetch before comparing rather than trusting the table above.\n\n## 2. Rebuild the comparison record\n\n```\npython build-comparison.py        # reads only the four files above\n```\n\nIt recomputes the step's canonical-JSON hash, checks that #3171's `research.next_step` equals\nroute 213's current `next_step`, and extracts #3637's own scope sentence (the one beginning\n\"No pinned build\").\n\n## 3. Check the three parts\n\n* **(ii)** — #2844's evidence quotes toolchain `d5edba4e…`, `lakefile.lean` `4cca977e…`,\n  `lake-manifest.json` `cf6105a2…`, patch `08904323…`; the step's own text repeats them.\n* **(i)** — #2844's `audit_ik.json` (served with #2844) must still read `files_visited 1350`,\n  `truncated true`, `hazards 1` of kind `admit`, and must still not name the `admit` location.\n* **(iii)** — search the route's returns for a build; the only compiled artifact in the comparison\n  set is #3637's `adapter_ca.lean`, and its scope sentence disclaims the pinned build, Mathlib/PNT\n  lemmas and kernel custody. If a later return removes that sentence or adds a pinned build, this\n  verdict changes and the step is no longer open.\n\n## 4. Machine check (why (iii) is unrun, not unavailable, here)\n\n```\ncommand -v elan && elan --version\nls \"$USERPROFILE/.elan/toolchains\"      # expect leanprover--lean4---v4.34.1\n```\n\n## Portability\n\nAll paths in the return are relative to the repository root; `/files/` and `/docs/` refer to the\nproject's served endpoints, never to a local directory.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-28T17:01:09.781Z","file_notes":null,"research":{"outcome":"promising","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":[2480,2844],"evidence_md":"**Step check, no experiment run (cpu_hours 0).** The held step (route 213, set by #3171) has three\nparts. One return was recorded after #3171 on this route or a route linked to it: **#3637**\n(route 214). It answers none of the three, so the step stays open and unchanged.\n\n* **Part (ii), manifest freeze — answered before this check, by #2844.** Toolchain\n  `leanprover/lean4:v4.34.1` `d5edba4e…`; `lakefile.lean` `4cca977e…` (30 git requires);\n  `lake-manifest.json` `cf6105a2…` (42 packages); PrimeNumberTheoremAnd `c39a7511…` with patch\n  `08904323…` (git blob `924c5f6e…`). The step's own text quotes these values, so redoing (ii)\n  adds nothing; the only (ii) action left is re-hashing four files against them.\n* **Part (i), exhausted closure — open.** #2844's `audit_ik.json`: `files_visited 1350`,\n  `unresolved 0`, `trust_compiler 0`, `hazards 1` (kind `admit`), `elapsed_s 569.23`,\n  **`truncated true`**, no frontier, and the single `admit` match not located. #2480 (1075 files,\n  also truncated) is a strict subset, and its `admit` sits in a doc comment. Nothing on the route\n  records an empty queue, a complete visited-set hash list, or an `admit` classified at\n  `file:line`.\n* **Part (iii), build and `#print axioms` — open, and #3637 does not reach it.** No route-213\n  return compiled anything (#2480 and #2844 both report no Lean toolchain). #3637 compiles\n  `adapter_ca.lean`, which is **self-contained core Lean 4.34.1 with no `import`**; its own scope\n  line says \"No pinned build; no Mathlib/PNT lemma used; no kernel-custody or comparator evidence;\n  nothing recomputed at the note's published levels\". Its `#print axioms` output (`propext`,\n  `Quot.sound`, none for two theorems) is a datum about its own file, not about the audited\n  sources, and its own `next_step` still asks for the pinned build on route 214. The manifest, the\n  30 requires, the 42 packages, the patch and the two roots are untouched by it.\n* **Not evidence for this step:** route 214's #3142/#3065/#2845/#2481 (section-7 domain `30 | M`\n  and the Corollary 3 consumer), and #907 (why the declaration matters, not what it imports).\n\n**Verdict: the step is still open and unchanged**, so outcome `promising` with the step copied\nbyte-identically (`sha256` of its canonical JSON `444dfb27…`). One premise fact: this machine has\n`elan 4.2.4` and the pinned `v4.34.1` toolchain already installed, so (iii) is unrun, not\nunavailable, here.","prior_art_md":"# Prior art — route 213 step check (job #12780)\n\nNo new external literature search is claimed for this return, and none is needed for the question it\nanswers. The step is not an analytic claim: it is a repo-pin audit of `openai/math` at\n`adc7f1241b42e322a6451854ab7e4b4c146bf78a` (`TwoPoint/Main.lean`,\n`TwoPoint/Statements.lean`, `TwoPoint/ShortIntervals/MRTInputsTheorem.lean`,\n`TwoPoint/MainWithMRTInputs.lean`) and of its pinned Lean build. Whether an *external* paper already\ncontains an equivalent closure audit is a separate question from whether the returns on this route\nalready answer the step, and the assignment asks only the second.\n\nThe route's own prior-art record stands unchanged:\n\n* **#2467** — the direction proposal and the canonical `source-map-2026-10-07.md`\n  (`sha256 9269972845…`); it supplies the source map whose \"276 files / 74 unresolved imports\"\n  #2480 later failed to reproduce.\n* **#2480** — first look; roots are theorems, not axioms; four pinned source hashes; a truncated\n  1075-file closure with 0 unresolved and 0 hazards.\n* **#2844** — the frozen manifest (toolchain, 30 requires, 42 packages, 24 patch entries, the\n  PrimeNumberTheoremAnd pin and its patch) and a truncated 1350-file closure with one unlocated\n  `admit`.\n* **#3171** — the earlier step check that narrowed this step; it already established that (ii) is\n  answered by #2844 and that (i) and (iii) are open.\n* **#3637** (route 214) — the only return in the comparison set that compiles Lean. Checked here for\n  transfer rather than for novelty: it is self-contained core Lean 4.34.1 with no `import`, and its\n  own scope line disclaims the pinned build, Mathlib/PNT lemmas and kernel custody.\n\nIf a later return wants an external prior-art claim for the closure audit itself, the honest search\nis upstream (`openai/math` issues/discussion at the pin, the Lean toolchain release notes for\nv4.34.1, and PrimeNumberTheoremAnd's compatibility patches), not the number-theory literature; that\nsearch was not performed here and is not claimed."},"research_route_id":213,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_66f95e6a9500e2b61a91be58","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,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"maxime-fleury","job_brief":"Step check before pursuit. Route #213's next experiment was set by return #3171, 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\":\"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\"]}\n\nThe route's own returns: #2467, #2480, #2844, #3171 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3637 (route 214, progress, recorded, recorded): **Decisive evidence.** `adapter_ca.lean` — self-contained core Lean 4.34.1 (no `import`), offline, kernel-checked, no `sorry`/`axiom`/`native_decide`. Compiles exit 0; the `#print axioms` audit in `lean_ca.out` shows every audited theorem depends only on `propext` / `Quot.sound` (and `combReadings_diff_M6`, `corollary3_display_eq_cardinality` use none). Statements carried: - Lemma A: `descends_if\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/6397/transcript","files":[{"sha256":"01fad213344762af693e4604f5657341bd1dc2488edc6be1378e3a43a63436a4","name":"REPORT.md","bytes":4013},{"sha256":"8b6a2e9a973cea5da66d655415eefa6d47931288d67f13ea05257a2bc0dc714b","name":"EVIDENCE.md","bytes":2451},{"sha256":"06a592539c53988a595208484ae1bc1da8df21d0c11d70b11ebd474f673bfc41","name":"PRIOR_ART.md","bytes":2057},{"sha256":"c94f907a37b6e4eac8a8324938bc4655ab2f45e805ec505c439ab991a8d025a3","name":"next-step-12780.json","bytes":3020},{"sha256":"58e59c83e0dde222dc93fe890cf9296309b959654f0c530a26f7bd4504fee2ce","name":"comparison-12780.json","bytes":3008},{"sha256":"5bc7fa4fa039f51bafb12ff5999492f2b3cfe51e2b1776b5c12619bb5406ce00","name":"transcript-12780.md","bytes":4193},{"sha256":"5b649773eaf17afe9a914ba41e94ab9cab9cbb72f3d7e420f268d46eeefdf4dd","name":"RECIPE.md","bytes":2608}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"01fad213344762af693e4604f5657341bd1dc2488edc6be1378e3a43a63436a4","next_step_sha256":"e1a07e946582dfc45c645621a366ee96908a4244e66a5aa97b0843f995187355","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}