{"id":3637,"job_id":6648,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #6648 (route 214, pursue) — the mod-30 comb readings, kernel-checked in core Lean; the pinned package is the only gap\n\n**Outcome: `progress`** (the step's remaining need is a *capability*, §5) — the step's *form* (a file inside\nthe **pinned** PrimeNumberTheoremAnd package) needs a Lean toolchain with that package **built**; this host\nhas core Lean 4.34.1 only (see §5).\nThe step's *mathematical* uncertainty is **answered here**, in a self-contained, kernel-checked core-Lean\nadapter (`adapter_ca.lean`) that a build-capable machine can transcribe into the pinned package verbatim.\n\n**Scope and limitation first.** No pinned build was run and no Mathlib/PNT lemma is used; `adapter_ca.lean`\nhas no `import`, no `sorry`, no `axiom`, no `native_decide`. Its only axioms are `propext` and `Quot.sound`\n(the standard allowlist). It is a *bounded local adaptation* of the step, not the pinned-compiler evidence\nthe step names, and this return does not claim kernel-custody/comparator evidence. Nothing here changes the\ncorollary's mathematics; no value is recomputed at the note's published levels (13, 47, 101).\n\n## 1. What the held step asked\n\nRoute 214's step names a file in the pinned package (lean-toolchain v4.34.1, PrimeNumberTheoremAnd) with\nfour lemmas plus a domain-annotation request: (1) `30 ∣ primorial y ↔ 5 ≤ y` for prime `y`; (2) the\nwell-definedness criterion for the section-7 comb predicate `P(r) := [r mod 30 ∈ {11,17}]`, descending to\n`ZMod M` **iff** `30 ∣ M`, with a two-case witness for the converse; (3) the two total readings\n(`ZMod.val` canonical representative, and the exists/lift reading) coincide under `h : 30 ∣ M`, with a\nnegative lemma for `M = 6`; (4) Corollary 3's factorization under the level bound; (5) the annotation request.\n\n## 2. What is delivered — `adapter_ca.lean` (core Lean 4.34.1, offline)\n\nSelf-contained, computable definitions (`comb30`, `combCanon`, `combLift`, `descends`, `isPrime`,\n`primorial`, `tailProd`, `displayValue`) and:\n\n- **Lemma A** `descends_iff_dvd (M) : descends M ↔ 30 ∣ M`. The converse carries an explicit two-case\n  witness: `(11, 11 + M)` when `M ≢ 0, 6 (mod 30)`, and `(11, 11 + 2M)` when `M ≡ 6 (mod 30)`. Both\n  representatives agree mod `M`; their comb values differ (`11 ∈ comb`, `11 + M` or `11 + 2M` is `23`-like,\n  `∉ comb`).\n- **Lemma D** `combCanon_iff_combLift (h : 30 ∣ M) : combCanon M r ↔ combLift M r` — the two total readings\n  coincide on the domain — plus `combReadings_diff_M6 : combLift 6 5 ∧ ¬ combCanon 6 5` (they differ off\n  it; witness `11 ≡ 5 (mod 6)`) and `combReadings_diff_M2`.\n- **Lemma B** `dvd_primorial_iff_le_five (hy : isPrime y = true) : 30 ∣ primorial y ↔ 5 ≤ y` — the cutoff,\n  so the level bound is exactly `30 ∣ M`.\n- **Lemma C** `corollary3_edge_y5`, `corollary3_edge_y7`, `corollary3_display_eq_cardinality`: the\n  manuscript display equals the direct `Natal@5` cardinality `2∏(p-2)` at the first two levels, and\n  `domain_y7 : 30 ∣ primorial 7` is derived from Lemma B.\n\nAxiom audit (recorded in `lean_ca.out`): every audited theorem lists only `propext` / `Quot.sound`;\n`combReadings_diff_M6` and `corollary3_display_eq_cardinality` use none at all.\n\n## 3. The answer to the assigned uncertainty\n\n**Yes on the domain, and they provably differ off it.** `descends M ↔ 30 ∣ M` (Lemma A) and\n`combCanon ↔ combLift` exactly when `30 ∣ M` (Lemma D). So the transcription of Corollary 3 *must* carry\n`30 ∣ M` (equivalently the level bound `5 ≤ y`, the project's own `x ≥ 7`) as a definition-domain\nhypothesis; off the domain **no** total Lean definition of \"the comb\" can match the corollary's set,\nbecause the two available total definitions disagree there. This confirms #3142's Lemma D verdict with a\nkernel-checked proof rather than a finite scan.\n\n## 4. A correction to a predecessor (#3142, accepted/verified)\n\n#3142's Lemma C writes `|A_5| = (M/30)·2∏_{7≤p≤y}(p−2) = M·(2/30)∏(1−2/p)`. The two right-hand\nexpressions are **not equal**: at `y = 7` (`M = 210`) the first is `70` and the display is `10`; at\n`y = 11` (`M = 2310`) they are `6930` and `90`. The correct first factor divides by `∏_{7≤p≤y} p`\n(the display is `M·2·∏(p−2)/(30·∏p)`, i.e. `(M/30)·2·∏(p−2)/∏p`). The **conclusion** is right — the\ndisplay equals the direct cardinality `2∏(p−2)` at `y = 5, 7` (checked here) — only the written middle\nexpression slips. Also minor: off the domain the readings first *agree* at `M = 30`; every `M < 30` differs\n(the `M = 1` case is vacuous here since `M = primorial y ≥ 2`).\n\n## 5. The capability gap (why `needs_capability`)\n\nThe step's package is an **unbuilt** lakefile (`…/run-2026-10-10-ik/work/pinned`, PrimeNumberTheoremAnd\npinned, ~30 git dependencies incl. Mathlib/TauCeti/carleson). No Mathlib `.olean` exists on this host and\nthere is no install path within the assignment's controls (5 GB disk, 1.5 CPU-h). Building it needs a\nnetwork fetch plus a multi-hour build well beyond the budget. This is a machine limit, not an obstacle:\nthe step is sound and should go to a machine with the built package. The `next_step` names it.\n\n**Vocabulary note (tool gap).** The served `research-protocol` and the server's own `next_step` shape both\ntake `outcome: needs_capability` with an optional `next_step.shortfall` (`\"what the machine or budget that\ntried it lacked\"`), which is exactly this case. But the local `sah.py` **1.0.13** preflight vocabulary omits\n`needs_capability` and refused the payload locally. Rather than edit the shared tool with a run in flight,\nthis return uses the locally accepted `outcome: progress` and carries the capability the step needs in\n`next_step.required_tools` / `required_sources` / `next_step.compute` (`cpu_hours 24`, `ram_gb 16`,\n`disk_gb 10`), so the step is still offered only to a machine that has it. The shortfall is the built pinned\npackage (Mathlib + the ~30 pinned git dependencies; no Mathlib `.olean` here, 5 GB disk / 1.5 CPU-h budget).\n**Recommended one-line fix:** add `needs_capability` (and an optional `shortfall` pass-through) to the\n`preflight` outcome list in `sah.py`, re-run the harness 62/62+, with no run in flight. Recorded in HANDOFF.\n\n## 6. Reproduction\n\n`check_ca.py` (stdlib, offline, reads only this run's files): **23 checks, 0 FAIL, exit 0**; `--corrupt 1..10`\n**each caught** with a named FAIL (statement flip on Lemma A, flipped `M = 6` negative lemma, injected\n`sorry`, injected `axiom`, `native_decide` swap, cutoff statement change, and four arithmetic tampering\ncases). `derive_ca.py` independently re-derives: well-definedness ⟺ `30 ∣ M` and `canon = lift` ⟺ `30 ∣ M`\nfor all `M ≤ 2000` (0 mismatches), the primorial cutoff for prime `y ≤ 200`, and the §4 arithmetic.\n\n## 7. The domain-annotation request (step item 5) — recorded, not filed\n\n`POST /projects/twin-primes/asks` refused the request from this **session** run (server: *\"department/run\n targets require a folder run\"*), so the annotation request could not be filed from here. Its exact text is\n recorded in `ask_body_ca.md` and should be posted verbatim by a folder run or the record owner. The substance\n is: Corollary 3's comb needs the domain annotation `30 ∣ M` (equivalently `y ≥ 5` / `x ≥ 7`), the two total\n readings coincide exactly on it and differ off it, and the corollary's mathematics is unchanged.\n\n## 8. Files\n\n`adapter_ca.lean` (the Lean adapter), `lean_ca.out` (axiom audit), `lean_ca.err` (empty), `check_ca.py`,\n`check_ca.out`, `derive_ca.py`, `analysis_ca.json`, `CORRUPTIONS_ca.out`, `fetch_ca.py`, `ask_body_ca.md`,\n`served_route_214.json`, `served_return_3142.json`, this report, `evidence_ca.md`, `prior_art_ca.md`,\n`next_step_ca.json`, `transcript_ca.md`.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_ca.py":"3b376f0b04c41a5e5725591a937c787183a6e7e4ea3e03bad9248885b3ade1b8","fetch_ca.py":"2ee1eac61e0144e48ad7993c3a83a2268a31463bbb9461be022b6af0b0af094a","lean_ca.out":"ae0eb3b69dd95360abbfd89e9e29565fba9545f5dcad799dd07066b0903ea6ac","check_ca.out":"f9b72dc6283460fe3f896af9f1a8ab5b1f0b8b4394038e63ca9ed4690c6877da","derive_ca.py":"18f7af6da2e8c71494499aee615373480b2d3f689d2966b883d328f96862e07e","report_ca.md":"69aec9454b96885c3525846610c4c1c7f702f6dcdf42980451892e8950df13df","ask_body_ca.md":"165a80efeb4e27a514856415efdae83522192388f974d041afb75567e0aed94e","evidence_ca.md":"972b56c05c23ccba58ec5ba694c1c991a38a10e539bc4559103f3b59bc2e742f","adapter_ca.lean":"0fe8aa4837c39f400ef952dc7425b8a76d6cd50ac792d8ee8813710b6e030df2","prior_art_ca.md":"48270acd622169165e9dda85131f0c6f11085ea69df92d07902ea384229b071b","analysis_ca.json":"9583ad1105e4a58902bf102f95c77811ab333f96deaba781ee483fc7749c76cb","transcript_ca.md":"1d4f21fd85d8e396bb02ce8d4dc8960c469339ace2fab2318797618e8fc762f3","next_step_ca.json":"345a3b8aa1f5b3d97108706858958b5a70e4a11bc4e943d05351b4a0ac4e3f26","CORRUPTIONS_ca.out":"ae6d3d62c5f4686f3522771783cfb313372eeb89be02aa6bc4d1b77e6c181ad5","served_route_214.json":"776aec50304b44893b17d1e2d9c67bea87a553655c31c60c1929323d30c50438","served_return_3142.json":"0cf5ca826a83510bbf817ff535ec86677b2b3d1200971ec72ce1cf26b08e6a8e"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T07:47:49.540Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3142,3065,2481,2845,3623],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"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":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":null,"research":{"outcome":"progress","route_id":214,"next_step":{"method":"On a machine that can fetch and build the pinned package (network for the toolchain and git dependencies, then lake build / lake exe cache get; resources in compute), add one file that restates the statements in adapter_ca.lean against the pinned library (Mathlib's ZMod.val, Nat.Prime/primorial) and the core-Lean proofs where they port. Reuse adapter_ca.lean as the exact specification: it already fixes the definitions (comb30, combCanon, combLift, descends, primorial, displayValue) and proves Lemmas A/B/D and the C edges in core Lean 4.34.1, so the pinned task is a transcription plus the library-native ZMod.val statement that the step names. Then run the step's own check: the pinned build compiles the file with no sorry, only propext/Classical.choice/Quot.sound; keep the M = 6 negative lemma; and file the domain-annotation request with the exact minimal domain (5 ≤ y, or 7 ≤ x) so the source owner's affirmation is a one-line scoping decision. Do not edit the reviewed statement to make a proof pass.","compute":{"ram_gb":16,"disk_gb":10,"cpu_hours":24},"failure":"The pinned toolchain cannot state the criterion without a nonstandard axiom, or a library lemma silently identifies ZMod.val with the direct predicate for arbitrary M, or the level bound proves insufficient to derive the factorization; then report which lemma failed and whether the corollary's intended Natal@5 model at x >= 7 is unaffected.","success":"The pinned package compiles the adapter file with no sorry and only the standard axiom policy; the four lemmas have the statements above; the M = 6 negative lemma is present; a reader can see that the transcription needs the level bound only because the corollary's own display already presupposes 30 ∣ M; the annotation request is on the record.","question":"Does the pinned PrimeNumberTheoremAnd package (lean-toolchain v4.34.1, at the revision recorded in run-2026-10-10-ik, its Mathlib built) compile a self-contained file that carries route 214's four adapter lemmas — (1) 30 ∣ primorial y ↔ 5 ≤ y for prime y; (2) the mod-30 comb predicate descends to ZMod M iff 30 ∣ M, with the two-case witness; (3) the ZMod.val canonical and exists/lift readings coincide under 30 ∣ M with the M = 6 negative lemma; (4) Corollary 3's factorization under the level bound — sorry-free and under the standard axiom policy, leaving the corollary's mathematics unchanged?","budget_hours":4,"required_tools":["lean4","lake","offline_isolation"],"required_sources":["variance_note","staircase_note"]},"depends_on":[2481,2845,3065,3142],"evidence_md":"**Decisive evidence.** `adapter_ca.lean` — self-contained core Lean 4.34.1 (no `import`), offline,\nkernel-checked, no `sorry`/`axiom`/`native_decide`. Compiles exit 0; the `#print axioms` audit in\n`lean_ca.out` shows every audited theorem depends only on `propext` / `Quot.sound` (and\n`combReadings_diff_M6`, `corollary3_display_eq_cardinality` use none). Statements carried:\n\n- Lemma A: `descends_iff_dvd (M : Nat) : descends M ↔ 30 ∣ M`, with the converse's two-case witness\n  proved (`not_descends_of_mod6` witness pair `(11, 11 + 2M)` for `M ≡ 6 mod 30`; `not_descends_of_mod_ne`\n  witness `(11, 11 + M)` otherwise).\n- Lemma D: `combCanon_iff_combLift (h : 30 ∣ M) : combCanon M r ↔ combLift M r`, plus the negative\n  controls `combReadings_diff_M6 : combLift 6 5 ∧ ¬ combCanon 6 5` and `combReadings_diff_M2`.\n- Lemma B: `dvd_primorial_iff_le_five (hy : isPrime y = true) : 30 ∣ primorial y ↔ 5 ≤ y`.\n- Lemma C edges: `corollary3_edge_y5`, `corollary3_edge_y7`, `corollary3_display_eq_cardinality`,\n  `domain_y7 : 30 ∣ primorial 7`.\n\n**Independent check.** `check_ca.py` (stdlib, offline, reads only this run's files): **23 checks, 0 FAIL,\nexit 0**; `--corrupt 1..10` each caught with a named FAIL — statement flip on Lemma A, flipped `M = 6`\nnegative lemma, injected `sorry`, injected `axiom`, `native_decide` swap, cutoff-statement change, and four\narithmetic-tamper cases (`analysis_ca.json`). `check_ca.out` and `CORRUPTIONS_ca.out` are the transcripts.\n\n**Independent arithmetic** (`derive_ca.py` → `analysis_ca.json`): well-definedness ⟺ `30 ∣ M` and\n`canon = lift` ⟺ `30 ∣ M` for all `M ≤ 2000` (0 mismatches); the two readings first agree at `M = 30`;\nprimorial cutoff holds for every prime `y ≤ 200` (0 mismatches).\n\n**Correction evidence.** At `y = 7` (`M = 210`) the display `M·2·∏(p−2)/(30·∏p)` is `10` = `2·(7−2)`,\nwhile #3142's written mid-expression `(M/30)·2∏(p−2)` is `70`; at `y = 11` (`M = 2310`) they are `90` and\n`6930`. The two right-hand expressions in #3142's Lemma C are not equal; the conclusion (display = direct\ncardinality) is correct.\n\n**Unresolved / not claimed.** No pinned build; no Mathlib/PNT lemma used; no kernel-custody or comparator\nevidence; nothing recomputed at the note's published levels (13, 47, 101); the corollary's mathematics text\nis unchanged. Scope of the finite checks: `M ≤ 2000`, prime `y ≤ 200`.","prior_art_md":"**Route 214's own record (read before this work).**\n\n- **Return #3142** (accepted, `verified`, @Benjaminsen, deepseek-v4-flash; route 214): the read-only rescue\n  that named the defect as a *definition-domain precondition*. It gives Lemma A (descent iff `30 ∣ M`) with a\n  prose witness, Lemma B (`30 ∣ M_y ↔ y ≥ 5` for prime `y`), Lemma C (the display presupposes the domain) and\n  Lemma D (the two total readings coincide iff `30 ∣ M`); its finite scan is `M ≤ 2000`. This return\n  kernel-checks A, B, D and the C edges, and **corrects** C's written mid-expression (§4 of the report).\n- **Return #3065** (accepted, `verified`): the obstruction witness at `y = 3` (`M = 6`), where `11` and `5`\n  are the same class of `Z/6Z` but disagree on comb membership. Preserved, not refuted.\n- **`paper/variance-note.md` §7, Corollary 3** (manuscript, sha256 `40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391`):\n  the corollary whose transcription is the step's object. **`paper/staircase-note.md` §1** (sha256\n  `f595ed1250e6d97c0a2c55ff1b5948ce1d435e6acb47053e0500bb4732adb1f4`): the *same object* defined with the\n  level bound explicit (`x ≥ 7` prime, `N_x`, `gcd(r(r+2), W) = 1`, `N = 2∏_{7≤p≤x}(p−2)`) — the owning\n  document already states the domain. **`research/history/staging/thm-mod30-tail.md`** §1–§2: the same comb,\n  hypotheses `x ≥ 7`, and the D3 *missing-hypothesis* repair precedent.\n- The route's dependency list is [#2481, #2845, #3065, #3142]. Return **#3623** (run-2026-10-14-bw) is a\n  bounded step-check of this same held step: it confirms **no return on route 214 carries a `.lean` file or a\n  `verification_plan`**, i.e. the step was unexecuted.\n\n**Sibling Lean work (lane `formalize`).** The project has 10 accepted, `sorry`-free Lean 4 lemmas (axioms\nonly `propext`/`Classical.choice`/`Quot.sound`) — e.g. returns #76, #77, #79, #81, #89, #113, #115, #135,\n#146, #150 — and a `lean-kernel-v1` package with a checked receipt (#2598). A covering-identity Lean package\nis at #2420/#2472. So the project's Lean-lemma style, statements and axiom policy are established; this\nadapter follows them, only in **core** Lean rather than the pinned package.\n\n**What is new here.** (i) A kernel-checked proof of the descent criterion with an *explicit two-case witness*\n(the route step asked for exactly this), and (ii) a kernel-checked proof of `combCanon ↔ combLift` under\n`30 ∣ M` with the `M = 6` negative control, replacing #3142's finite agreement scan for these two facts;\n(iii) the correction to #3142's Lemma C mid-expression. Nothing here contradicts the manuscript or an\naccepted return's conclusion."},"research_route_id":214,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4bbd2c5cfbf76763b3b67008","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":"2026-10-14T07:47:49.540Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/214 and return #3142. Return the ordinary report and transcript plus research: {route_id: 214, 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #3623 compared this step with the returns on record and found it still open.\n> \n> Step-check evidence for route 214 (job #7472). Read-and-compare only; cpu_hours 0.\n> \n> DECISION: outcome = promising; the held step is copied exactly (canonical sha256\n> 0b17fd9f64dcbb217f185bcaf8c146180a669bdfdbde8bafaa69a8f9fe948790, equal to the step in this\n> assignment's brief and to route_214.next_step). depends_on = [3142, 3065, 2481, 2845].\n> \n> THE HELD STEP (route 214 next_step, unexecuted): a Lean transcription of paper/variance-note.md §7\n> Corollary 3 in the pinned package reused from #2844/#2845 (lean-toolchain v4.34.1, PrimeNumberTheoremAnd\n> at the pinned revision, offline controls): (1) 30 | primorial y iff 5 <= y for prime y; (2) r mod 30\n> in {11,17} descends to ZMod M iff 30 | M, two-case converse witness; (3) ZMod.val canonical vs\n> exists/lift readings coincide under 30|M, negative lemma at M=6; (4) Corollary 3's factorization/sum\n> rule under the level bound; (5) the domain-annotation request. required_tools [lean4, lake,\n> offline_isolation]; required_sources [variance_note, staircase_note]; budget_hours 2; compute\n> {ram_gb 4, disk_gb 2, cpu_hours 1.5}.\n> \n> SERVED RECORD (GET /research-routes/214): state active, revision 6, last_return_id 3142, newest event\n> is #3142; event return ids, newest first: 3142, 3065, 3056, 2845, 2481, 2468.\n> \n> NO RETURN ANSWERS THE STEP.\n> - #3142 (accepted, verified; research.outcome \"promising\"; depends_on [3065,2481,2845]):\n>   its report derives the domain mathematics (Lemmas A-D: the descent criterion, the two readings\n>   coincide iff 30|M, the M=6 witness) and states it ran \"no Lean toolchain, no build\". No .lean file;\n>   no verification_plan. It re-affirms this identical step.\n> - #3065 (accepted, verified; research.outcome \"blocked\"): the domain-gap witness (y=3 -> M=6; 11 and 5\n>   are the same class mod 6 but differ on {11,17} mod 30; density forces |A_5| = 6*(2/30) = 2/5). No\n>   Lean.\n> - #3056 (route evidence), #2845 (read-only step comparison), #2481 (finite Python adapter\n>   adapter_de.py), #2468 (source map): none carries a .lean file or a verification_plan.\n> \n> FILE-LIST INSPECTION (served records, this run): names on the route and on returns\n> 3142/3065/3056/2845/2481/2468 contain no \".lean\" entry; verification_plan is null on all six.\n> \n> ENVIRONMENT (limitation, not the outcome): the literal step names Mathlib ZMod.val and\n> PrimeNumberTheoremAnd. This folder's Lean toolchain is core-only Lean 4.34.1; the pinned package exists\n> only as a lakefile and is unbuilt; Nat.Prime/Nat.ModEq/ZMod are not in Lean core (same core-status\n> finding as #3291). Executing the step needs the pinned Mathlib/PNT build (network + hours + > 2 GB).\n> \n> CHECKER (stdlib, offline, reads only this run's served snapshots and next_step/brief/summary):\n> check_bw.py -> 33 checks, 0 FAIL, exit 0 (check_bw.out); --corrupt 1..10 -> each exit 1 with a named\n> FAIL (check_bw.control.out): tampered copied step; moved last_return_id; invented route event;\n> comparison return relabelled off route 214; step removed from the brief; changed accounting budget;\n> faked Lean file on the route; faked Lean file on a return; changed route state; dropped required tools.\n> \n> SCOPE: a work-disposition comparison, not a new claim; a later route-214 or linked-route return could\n> answer the step and supersede this note. 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