{"id":2480,"job_id":5229,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 213 first look: audit-only closure of ordinary two-point correlation source declarations\n\nJob #5229 (explore/first_look), this run's issued attempt, general mode, no lane.\nRoute #213, revision 1; basis return #2467 (proposed, gpt-6.1-sol, @Benjaminsen).\n\n## What was asked\n\nDecide whether one bounded next experiment is justified for route 213: a separate **source\naudit** of the \"extraordinary ordinary two-point correlation declarations\" of the pinned OpenAI\n`math` repository, excluded from established results until every trust gate passes. The route's\nproposed next step is to freeze the statements and definitions, inventory the full dependency\ngraph / toolchain / patch, and prepare a reproducible bounded build+axiom+kernel audit.\n\n## What this first look did (bounded, reproducible)\n\n1. Read the served route record (`GET /research-routes/213`) and the basis return #2467, and\n   re-fetched its canonical artifact `source-map-2026-10-07.md` (`GET /files/9269972845…`, sha256\n   matched the published value, 14834 B).\n2. Independently fetched the exact pinned declarations this route concerns at pin\n   `adc7f1241b42e322a6451854ab7e4b4c146bf78a` (read-only raw HTTP):\n   `OAI/NumberTheory/TwoPoint/Main.lean`, `.../Statements.lean`, `.../ShortIntervals/MRTInputsTheorem.lean`,\n   `.../MainWithMRTInputs.lean`. Hashes recorded and re-checked offline.\n3. Ran a breadth-first fetch of the OAI import closure of the two declaration roots under an\n   enforced wall-clock limit (`sah.py bounded`), recording per-file status/bytes/sha256 and scanning\n   every fetched file for Lean trust hazards (`axiom`, `sorry`, `admit`, `native_decide`,\n   `Lean.trustCompiler`).\n\n## Findings\n\n- **The three named results are theorems, not axioms.** `Main.lean` declares `liouvilleLogSaving`,\n  `binaryCorrectedElliott`, `affineCorrectedElliott` as `theorem … :=` from MRT inputs, and\n  `MRTInputsTheorem.lean` declares `mrtShortExponentialInput` / `mrtLiouvilleShortInput` as theorems\n  too. So the declarations are not assumptions at the roots; the audit question is whether the\n  closure is axiom-free, not whether it is axiomatic by construction.\n- **`Statements.lean` matches the route's description.** It defines three `Prop`s: an ordinary\n  **unweighted** affine Liouville correlation with a single exponent `c>0` independent of the four\n  affine coefficients and a coefficient-dependent constant (`LiouvilleLogSaving`); the corrected\n  Elliott theorem for ordinary multiplicative, one-bounded factors with a nonpretentious\n  disjunction and `h₁ ≠ h₂` (`BinaryCorrectedElliott`); and the nonproportional affine corollary\n  including coefficients sharing prime factors (`AffineCorrectedElliott`).\n- **The closure is larger than the supplied scan claims and resolves.** In 420 s the BFS visited\n  **1075** OAI files, all fetched (status 200), with **0 unresolved OAI imports** and **0 real\n  `axiom`/`sorry`/`native_decide`/`Lean.trustCompiler` hits** (the single `admit` match is in a\n  doc comment). The queue was not exhausted, so the fixpoint is >1075 files.\n- **The source map's stated obstacle is not reproduced.** The map reports \"a textual scan of 276\n  OAI files and 74 unresolved direct OAI imports\"; over 1075 files at the pin we find **zero**\n  unresolved OAI imports and a closure already **>1075** files. The \"74 unresolved imports\" is\n  therefore most consistent with an **incomplete offline checkout**, not a defect of the pinned\n  repository. This changes the audit plan: the binding constraints are closure *size* and the\n  build/toolchain/axiom work, not missing files.\n\n## Assessment\n\nThe route is a legitimate, previously un-executed audit; the basis return #2467 is a *direction*\nproposal, not the audit itself. This first look finds the declaration chain theorem-backed and\naxiom-free over a large inspected slice, with no missing-import blocker. One bounded next experiment\nis justified (finish the closure to fixpoint, then a bounded build/axiom/kernel audit plan), but the\nwork should be re-priced: the closure alone is ≥1075 files, far above the 276 assumed.\n\nNothing here proves, disproves, or promotes the upstream declaration; it remains **audit-only**.\nNo Lean toolchain is present in this container; no compilation, dependency install, kernel replay or\nindependent proof check was performed. Twin-prime infinitude and the signed arithmetic margin remain\nopen, and route 50's obstruction is unchanged.\n\n## Controls\n\n`check_dd.py` (stdlib, no producer import) re-verifies the four pinned hashes, the theorem-vs-axiom\nstatus of the roots, the structural clauses of the three Props, and the internal consistency of the\nBFS record: **35 checks, 0 FAIL, exit 0**. A planted counterfactual (inject the unreproduced\n276/74 claim and a stray axiom) drives the same checker to **5 FAIL**, exit 0 in control mode.\n","patch":null,"cpu_hours":0.1,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","audit_dd.py":"fb04b631085d16174fb461772883ce818c515f0f9fa40e52547894b8d065eb86","check_dd.py":"8a75e6cc5b45595ca49ac32f4162ac403b2bc4b48f4bc0cb3e740f795206cbec","check_dd.out":"141d8f53e3d71ff9c7f1021c7903d412a8cad997e54c5cbc13851d18a8d43f13","report_dd.md":"8a6d70b075756f0defa84630e57bc5f47761816dc5bfbb2c2b382f7c47b1f8d6","audit_dd.json":"e18abda12f4d94ddcbc00aefbbfeaaecd7f5b6a74d733110e3996cc46c831e70","evidence_dd.md":"f029c24c81f5ec1d4fec0fb7c71dac5901abf7a60ac358e75816b95e8d4a9a94","next_step.json":"4f96c493b2ea5e624884c73190a84853697b9a56342e46e54477bbf36fcf7b21","prior_art_dd.md":"e1abfae7d8a8dec7d68de9c80457445cc23c8172045f28b1a68904b2b1192e25","check_dd.control.out":"3b234f879f8cde083ec26f7931de40fa052c6d2b02ad1bbd15ce775f96edb5a5"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T17:16:33.335Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2467],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"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":null,"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":[{"sha":"fb04b631085d16174fb461772883ce818c515f0f9fa40e52547894b8d065eb86","name":"audit_dd.py","notes":["prints what looks like progress or timing to stdout on line 127 (\"\"elapsed_s\": out[\"elapsed_s\"], \"hazard_kinds\": sorted({h[\"kind\"] for h in hazard\"), inside the statement that starts on line 124: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"4c4253804f34101fc3126f3f10b35d9d94340fd198b83f29aafa347a53ac3408"}],"research":{"outcome":"promising","route_id":213,"next_step":{"method":"Continue the bounded BFS in audit_dd.py from the two recorded roots to fixpoint (currently stopped at 1075 files, truncated) and hazard-scan every file for axiom/sorry/native_decide/Lean.trustCompiler, recording per-file sha256; then freeze the pinned lean-toolchain/lakefile/lake-manifest and dependency revisions, identify the PrimeNumberTheoremAnd compatibility patch and its license, and prepare a reproducible bounded build plus axiom/kernel-audit plan (isolated, no network during check). Execute the build/fragment only if a Lean toolchain is actually available in the container; otherwise record the exact capability blocker and stop.","compute":{"ram_gb":2,"disk_gb":2,"cpu_hours":0.5},"failure":"A missing-file or unresolved-import blocker, an axiom/sorry/non-allowlisted axiom anywhere in the closure, or an unpinned/unavailable toolchain or compatibility patch: the ordinary-correlation declaration then stays audit-only and route 50's obstruction is unchanged.","success":"A complete closure inventory (fixpoint, every file hashed, zero unresolved imports) with an explicit hazard list, plus a frozen manifest of toolchain/dependency/patch revisions and the exact axiom-allowlist obligation (propext, Classical.choice, Quot.sound only). Only an independently reproduced full build with kernel + external checker could later establish the declaration; the inventory and manifest alone are a preparation artifact.","question":"Is the OAI import closure of the TwoPoint ordinary-correlation declaration roots axiom-free at pin adc7f1241b42e322a6451854ab7e4b4c146bf78a, and what are the exact pinned toolchain, dependency patch and final-axiom obligations for a reproducible build audit?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2467],"evidence_md":"What the evidence changes for route 213.\n\nBefore this run the route had one basis return (#2467, a direction/proposal) and a supplied source\nmap claiming a 276-file OAI scan with 74 unresolved direct imports. It carried no independent\nclosure measurement and no root-level statement/axiom check.\n\nNew observed evidence (all re-checkable offline via check_dd.py, 35 checks, 0 FAIL):\n\n1. Root declarations are theorems, not axioms. `Main.lean` proves\n   `liouvilleLogSaving`/`binaryCorrectedElliott`/`affineCorrectedElliott` from\n   `mrtLiouvilleShortInput`/`mrtShortExponentialInput`; `MRTInputsTheorem.lean` proves those two as\n   theorems from Halasz/Riesz/weak-VK short-interval lemmas. Pinned hashes:\n   Main.lean sha256 6a87385e9b5f7855…, Statements.lean 54331158f566b84c…, MRTInputsTheorem.lean\n   8b85cae51196dda5…, MainWithMRTInputs.lean 54950cea16042c54….\n\n2. Exact statement shape (Statements.lean). `LiouvilleLogSaving` is an ordinary unweighted affine\n   correlation of `liouville liouville` with one exponent `c>0` independent of the four affine\n   coefficients and a coefficient-dependent constant: ‖affineSum …⌊X⌋₊‖ ≤ C·X/(log X)^c for all\n   X≥3 and all nonproportional positive affine slopes. `BinaryCorrectedElliott` is the corrected\n   Elliott claim for ordinary multiplicative, one-bounded factors under a\n   `UniformlyNonpretentious` disjunction with h₁≠h₂. `AffineCorrectedElliott` is the nonproportional\n   affine corollary. So the route's central-uncertainty text (\"conventional ordinary unweighted\n   meanings and quantifiers\") is confirmed at the source, not merely asserted.\n\n3. Closure measurement (audit_dd.json). A bounded BFS of the OAI import closure of the two roots\n   visited 1075 files in 420 s under an enforced wall-clock limit; every file fetched (HTTP 200);\n   0 unresolved OAI imports; 0 `axiom`/`sorry`/`native_decide`/`Lean.trustCompiler`; the only\n   `admit` match is a doc comment. The queue was not exhausted (truncated=true).\n\n4. The supplied \"276 files / 74 unresolved imports\" is NOT reproduced. Zero unresolved imports over\n   1075 resolvable files and a closure already exceeding 1075 files. The unresolved-import figure is\n   most consistent with an incomplete offline checkout at map-writing time, not with the pinned\n   repository. This removes \"missing files\" as the likely blocker and makes closure size and the\n   build/axiom/toolchain work the real cost.\n\nScope and limits. This is a finite textual + import-graph audit at one pin. It does not compile\nanything, install dependencies, verify PrimeNumberTheoremAnd compatibility, replay a comparator or\nkernel, or inspect the transitive axiom closure of a built artifact — no Lean toolchain exists in\nthis container. It does not promote the upstream declaration: that remains audit-only and route 50's\nobstruction is unchanged. It is not a novelty certificate. Consumer interfaces (Lambda conditioning,\nnonmultiplicative weights, coefficients/cutoffs growing with x) are untouched.\n\nWhat this changes for the next step. A bounded continuation is justified, but re-priced from the\nmap's 276-file assumption to a ≥1075-file closure: finish the BFS to fixpoint and hazard-scan it,\nthen prepare and, if a toolchain is available, execute the pinned build + axiom/kernel audit. The\nsmallest falsifier for the continuation: an `axiom`/`sorry`/`Lean.trustCompiler`/non-allowlisted\naxiom anywhere in the closure, or an unresolved import at the pin.","prior_art_md":"Prior-art and prior-work search record for route 213 (audit-only closure of ordinary two-point\ncorrelation source declarations).\n\nProject-internal (re-read on 2026-10-07, this run).\n- Route #213 record and its basis return #2467 (handle @Benjaminsen, model gpt-6.1-sol, type\n  `direction`, author_rung heuristic, status recorded, cites return907). #2467 is a proposal, not the\n  audit: it maps six source contracts and asks for the closure/axiom audit. It is the direct input to\n  this first look and is not re-executed here.\n- Canonical artifact re-fetched: source-map-2026-10-07.md (sha256 9269972845…, 14834 B), which names\n  eleven pinned contracts (SieveCRT, SieveModel, ResidueIntervalCount, PeriodicResidueCount,\n  OptimizedSelbergError, SelbergErrorBound, FundamentalBlockEstimate, SmoothCofactorTail,\n  SmoothTailDensity, TwoPoint/Main, TwoPoint/Statements) and reports a \"276 OAI file / 74 unresolved\n  direct OAI import\" textual scan.\n- Nearby prior work: route93 (residue-cap) is the nearest route in the map's own bounded registry\n  search; the map states no exact adapter match existed among the 208 routes it inspected. Route50\n  (parent) is blocked and its obstruction is preserved. Recent project returns on the sibling source\n  ports exist: #2477 (two-root Selberg remainder envelope, route 211), #2476 (endpoint residue counts,\n  route 210), #2475 (collision-preserving CRT fourth moment, route 209), #5228/return#2479 (smooth\n  cofactor tail adapter, route 212). All are finite source-adapter looks; none audits the TwoPoint\n  ordinary-correlation declarations, so none covers this route's contribution.\n\nExternal (bounded online check, this run).\n- The pinned upstream is the OpenAI `math` repository at commit adc7f1241b42e322a6451854ab7e4b4c146bf78a,\n  Apache-2.0. The declaration files (TwoPoint/Main.lean, TwoPoint/Statements.lean) were read directly\n  at the pin and their closure traced. No public independent audit, verification package, comparator\n  receipt or axiom-closure report for these specific declarations was located in this bounded search;\n  the repository itself carries no `verification_plan`-style receipt for them.\n\nExact remaining gap.\n- No independent closure-to-fixpoint inventory exists (the map's 276-file scan is smaller than the\n  ≥1075-file closure measured here, and its 74-unresolved-import figure is not reproduced).\n- No build, toolchain pin, PrimeNumberTheoremAnd compatibility patch audit, comparator/kernel replay\n  or transitive axiom-closure inspection has been done for these declarations.\n- Consumer interfaces (Lambda conditioning, nonmultiplicative prime-band weights, coefficients/cutoffs\n  growing with x) are not addressed by any located source.\n\nThis is a bounded search, not an exhaustive literature search or novelty certificate."},"research_route_id":213,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3d4f31c573a00cff61d4ca40","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/213 and return #2467. Return the ordinary report and transcript plus research: {route_id: 213, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2467","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/2480/transcript","files":[{"sha256":"8a6d70b075756f0defa84630e57bc5f47761816dc5bfbb2c2b382f7c47b1f8d6","name":"report_dd.md","bytes":4848},{"sha256":"f029c24c81f5ec1d4fec0fb7c71dac5901abf7a60ac358e75816b95e8d4a9a94","name":"evidence_dd.md","bytes":3480},{"sha256":"e1abfae7d8a8dec7d68de9c80457445cc23c8172045f28b1a68904b2b1192e25","name":"prior_art_dd.md","bytes":2804},{"sha256":"4f96c493b2ea5e624884c73190a84853697b9a56342e46e54477bbf36fcf7b21","name":"next_step.json","bytes":1757},{"sha256":"8a75e6cc5b45595ca49ac32f4162ac403b2bc4b48f4bc0cb3e740f795206cbec","name":"check_dd.py","bytes":6994},{"sha256":"141d8f53e3d71ff9c7f1021c7903d412a8cad997e54c5cbc13851d18a8d43f13","name":"check_dd.out","bytes":2038},{"sha256":"3b234f879f8cde083ec26f7931de40fa052c6d2b02ad1bbd15ce775f96edb5a5","name":"check_dd.control.out","bytes":2046},{"sha256":"fb04b631085d16174fb461772883ce818c515f0f9fa40e52547894b8d065eb86","name":"audit_dd.py","bytes":5067},{"sha256":"e18abda12f4d94ddcbc00aefbbfeaaecd7f5b6a74d733110e3996cc46c831e70","name":"audit_dd.json","bytes":328964},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"4c4253804f34101fc3126f3f10b35d9d94340fd198b83f29aafa347a53ac3408","name":"audit_dd.py","bytes":5241},{"sha256":"6de4856ffa7df136b622bf20f62afd497f377bff441574e2f75fb7f6c796ce7d","name":"report_dd.md","bytes":5105}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}