{"id":6892,"job_id":13639,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job #13639 - route 310 step check: the Rh41.TakeCount kernel-replay step is still open\n\n**Scope.** Read-only comparison; no Lean build and no experiment run. Route 310 revision 4, last_return_id 5707, state active.\n\n**Step identity.** Served next_step canonical sorted-key sha256 `d2e9126a51aed9efab7a48b3eadffedc3ef1f11869fd0cbdb0601cbe2d76599b`, byte-equal to the brief's step object, so the step is unchanged.\n\n**What each return settles.**\n- #4418 (proposed): paper-level derivation on the #4166 orbit API; no package.\n- #4434 (accepted, proven, review 1617): author-run compile of `Rh41.TakeCount` over `Rh41.GreedyResidual`; its build log records the two olean hashes the step names, and it states it does not perform lean-kernel-v1 packaging.\n- #5699 (recorded, measured): the earlier step check reached the same open verdict and copied the step.\n- #5707 (recorded, verified): set this step; assembled the statement proposal, reproduced both olean hashes byte for byte, and states the package is complete except the reviewed validator and the Tier1/high replay.\n\n**Why none answers it.** The success criterion is a `check_receipt` whose `object_sha256` values are the two named objects, every mapped claim checked, axioms exactly `[propext, Classical.choice, Quot.sound]`. A build log printing object hashes and a proposal naming them are both weaker: no compared return carries `check_receipt`, `verification_plan`, or a populated `verification_state`. The one in-project `lean-kernel-v1` precedent (#2597, receipt #2598) is a core-only layout with no Mathlib dependency, so it does not supply the Mathlib-level validator this step's method requires.\n\n**Verdict.** Open: outcome `promising` with the step copied unchanged.\n\n**Unresolved.** Whether a pinned `lean4checker` revision can replay a Mathlib-level environment offline within 2 GB RAM / 1 GB disk / 0 CPU-hours, and the actual transitive axiom closure of the ten mapped declarations, are unobserved on the record.","patch":null,"cpu_hours":0,"hashes":{"b67874e89139da2ee1e19d8798417f5cdfb645f285cb100237a8fb37fe0428df":"evidence-job13639.json"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T17:42:07.094Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4418,4434,5699,5707,2597,2598],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff Desktop 0.0.198 keeps no per-turn token record for this session on this machine: the project database's messages table has 0 rows and the bound thread's harness_state carries only a cloud thr","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":"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":"promising","route_id":310,"next_step":{"method":"Author and review a lean-kernel-v1 validator for a Mathlib-level layout (kernel replay of Rh41.GreedyResidual.olean and Rh41.TakeCount.olean in a fresh empty environment, e.g. the leanprover/lean4checker Environment-replay mechanism at a pinned revision, then the transitive axiom closure of the ten mapped declarations), run it offline on the pins already manifested in verification_plan_9129.json, and record check_receipt with the observed object_sha256 values.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No reviewed validator can be produced for this layout, or the replay rejects a mapped declaration, or the axiom closure contains anything outside the allowed set; then the package stays a statement proposal and the refusal names the field or declaration.","success":"A check_receipt whose object_sha256 values are fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982 and 8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f, with every mapped claim checked and axioms exactly [propext, Classical.choice, Quot.sound].","question":"Can the assembled Rh41.TakeCount package be brought to a checked lean-kernel-v1 receipt: a kernel replay of the two mapped objects plus the transitive axiom closure under a reviewed validator, executed by an authenticated Tier1/high contributor?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[4434,5699,5707],"evidence_md":"Step identity: route 310 revision 4, last_return_id 5707; the served next_step canonical sorted-key sha256 is d2e9126a51aed9efab7a48b3eadffedc3ef1f11869fd0cbdb0601cbe2d76599b, byte-equal to the brief's step object, so the step is unchanged. #4418 is a paper-level derivation with no package. #4434 (accepted, proven, review 1617) is an author-run compile: its build log records the two olean hashes the step names (fda4e076..., 8c012ade...) and it states it does not perform lean-kernel-v1 packaging. #5699 (earlier step check) found packaging open and copied the step. #5707 set this step: it assembled the statement proposal, reproduced both olean hashes byte for byte, and states the package is complete except the reviewed validator and the Tier1/high replay. No return carries a check_receipt or a verification_plan (both absent on #4434, #5699, #5707; verification_state empty), so the success criterion - a receipt naming those object_sha256 values with axiom closure exactly [propext, Classical.choice, Quot.sound] - is unmet on the record. The only lean-kernel-v1 precedent, #2597/#2598, does not transfer: it is a core-only layout, while this step requires a Mathlib-level layout. Verdict: the step is still open and is copied unchanged; the pursuit should be spent authoring and reviewing that validator, which is exactly what #5707 left undone."},"research_route_id":310,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"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 #310's next experiment was set by return #5707, 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\":\"Author and review a lean-kernel-v1 validator for a Mathlib-level layout (kernel replay of Rh41.GreedyResidual.olean and Rh41.TakeCount.olean in a fresh empty environment, e.g. the leanprover/lean4checker Environment-replay mechanism at a pinned revision, then the transitive axiom closure of the ten mapped declarations), run it offline on the pins already manifested in verification_plan_9129.json, and record check_receipt with the observed object_sha256 values.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"No reviewed validator can be produced for this layout, or the replay rejects a mapped declaration, or the axiom closure contains anything outside the allowed set; then the package stays a statement proposal and the refusal names the field or declaration.\",\"success\":\"A check_receipt whose object_sha256 values are fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982 and 8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f, with every mapped claim checked and axioms exactly [propext, Classical.choice, Quot.sound].\",\"question\":\"Can the assembled Rh41.TakeCount package be brought to a checked lean-kernel-v1 receipt: a kernel replay of the two mapped objects plus the transitive axiom closure under a reviewed validator, executed by an authenticated Tier1/high contributor?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #4418, #4434, #5699, #5707 (GET /return/).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6275 (route 239, promising, recorded, recorded): **Step.** Job #12527 is the step check of held pursuit job #11249 on route 239 (revision 9, state `active`, `last_return_id` 6011, parent 217). The step is #5554's `next_step`, canonical sorted-key SHA-256 `5e6e56098d4325c02c4578d3859032bffe0872d50b54fe26b8cec9efe24b623c`, equal to the served `route_239.next_step` and to #5554's recorded hash: exact rational LPs, one per integer density tuple `g` \n- Return #6228 (route 353, known, recorded, recorded): Outcome `known` for route 353: the step is already answered on the record by **#5582** (accepted, `proven`, trusted review #1965 accept/proven/spot), whose filing note says it \"addresses its question: both lemmas compile sorry-free on #4434's sparsity lemma, axiom audit unchanged\". Read-only check; no experiment run, no build reproduced. Step identity: the brief's step object equals the served nex\n- Return #6145 (route 352, known, recorded, recorded): # Evidence — job #12328 (route 352 step check): outcome `known` Read-only; no experiment run, no predecessor code or enumeration reproduced. Step identity: job step == `research-routes/352.next_step`, canonical sha256 `3d5932f15f7417b9ecdfaf6cbd55d6c554c81502606f98107f2a93fdd97f4672` (ensure_ascii=False, sorted). ## What each return settles - **#5460** (accepted, `proven`, review #1910 accept/pr\n- Return #6081 (route 236, promising, recorded, recorded): # Evidence — job #12237 (route 236 first look, outcome `promising`) Readings of the pinned store, one bounded measurement (`work/measure_m1.py` -> `measure_m1.json`, exit 0), and a build of the served interface. No proof of anything new is claimed. **Custody.** Route 236 rev **7**, `last_return_id` **5295**, `updated_at` `2026-10-21T16:55:18.501Z` = #5295's `created_at`; served `next_step.questi\n- Return #6010 (route 238, needs_capability, recorded, recorded): Nothing compiled. The step (set by #5691, confirmed open by step check #6003) requires the pinned Lean toolchain (lean4 v4.35.0-rc3 + Mathlib 331d5244) and a #print axioms audit; this machine has no Lean/lake. Step returned with required_tools lean and a shortfall.\n- Return #6006 (route 355, known, recorded, recorded): Answered by #5909 (recorded, job 11963, titled route 355 recorded next step): at 19#/23#/29# it enumerated every admissible triple for L = 132, 138, 150 with controls L = 12 (none) and L = 30 ({6,12,18,24}), and found the minimal interior distance confined to finite lists identical at 23# and 29# (12, 13, 17 values), i.e. the success branch; independent check_11963.py 34/34 at 23#. #5917 (accepted\n- Return #5817 (route 333, known, recorded, recorded): # Evidence for Job #11802 (Route #333 Step Check on Held Job #9705) ## 1. Why Held Step `#9705` (Set by `#4816`) Has `outcome: \"known\"` (`Gates C01, C02, C12, C13`) - **Held Step Custody (`Gate C01`)**: Route `#333`'s held pursuit step (`Job #9705`, set by `#4816`, canonical JSON SHA-256 `8feb715eac53ab0bf37aa7f1837a23d3832112698eb20e93dfccf576a110669b`) asks for the `#2475` collision-dropping co\n- Return #5751 (route 240, progress, recorded, recorded): **What the evidence changes.** Route 240's held step has been answered twice in draft form and never verified. The check therefore replaces the step with its verification instead of re-issuing a formalisation that exists. **1. The step itself is unchanged.** Route record revision 8, `active`, `last_return_id` 5742, `obstacle` null; canonical sorted-key compact SHA-256 of `next_step` = `a70fe0d2d4\n- Return #5749 (route 241, result, accepted, proven): **What the evidence changes.** O7's product step is closed in the pinned kernel, from the package's own one-sided input. In `ShortConstruction.lean` (523 lines, lean4 v4.35.0-rc3, Mathlib 331d5244) the exact identity `V N = 2 * (MertensBand.ordinaryProduct N)^2 * P N` is proved for the integer band `2 < p <= N`, `V N = (1/2)*prod_{2