{"id":5707,"job_id":9129,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9129 (route #310, pursue): `Rh41.TakeCount` assembled as a `lean-kernel-v1` **statement proposal** — package complete except the reviewed validator and the Tier1/high replay\n\n**Scope.** Route #310's held step asks for `Rh41.TakeCount` (#4434) to be packaged under `lean-kernel-v1` in the style of #2597 (statement/definition bundle, claim mapping, `verification_plan.lean`, exact package fingerprint) so the counting bound and the sparsity lemma carry checked-receipt evidence rather than author-run compilation. Its mathematics — `A(N) = O(log log N)`, the corrected direction of #4166 §3.4, and the refutation of the printed `n_k ≤ (1/x)^{2^{k-1}}+1` — is **already proved** in #4434, so this return claims **no new mathematics**. It assembles the package, rebuilds the objects on the pinned executor, and records exactly which package fields are still missing.\n\n## What was done\n\n**1. Byte-exact sources, hash-verified before use.** `Rh41/GreedyResidual.lean` sha256 `4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c` (30,607 B, from #4166) and `Rh41/TakeCount.lean` sha256 `52fde740015161a3623297d8c702e9712ff399c05afb9959a37e9dd9dfbc2be4` (37,410 B, from #4434); both re-hashed after download and equal to the hashes the returns publish.\n\n**2. Fresh build on the pinned executor, offline, no `lake update`.** `leanprover/lean4:v4.35.0-rc3` (commit `470d5ce1400764999581fd26d5d72b00d990b0f4`) against the pinned Mathlib `331d5244f0d3aad530d9ab00ded135b4c7691502`. Module by module, `lean -R src -o build/lib/Rh41/<M>.olean`: `Rh41.GreedyResidual` exit 0 (59.2 s), `Rh41.TakeCount` exit 0 (69.3 s), audit module exit 0 (41.9 s), statement module exit 0 (44.6 s).\n\n**The two authored objects reproduce #4434's recorded hashes byte for byte**: `GreedyResidual.olean` `fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982` (1,576,416 B) and `TakeCount.olean` `8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f` (2,240,952 B), matching the values #4434 reports (`fda4e076…cd982`, `8c012ade…e553f`). That is a cross-session reproducibility observation for the object custody, not a new check of the mathematics.\n\n**3. Package artifacts** (all uploaded; hashes in the inventory):\n\n- `statement_bundle.json` sha256 `df9ad0eca4e5f7c78f26232263b418560a08fd3f716cd19b75e67dcb0c600e5a` — 9 definitions/premises and the 10 mapped claims with their **literal compiled types** (printed by an authored helper that declares nothing), locator, coverage and explicit assumptions.\n- `verification_plan.json` — `policy: lean-kernel-v1`, `paper_slug: rh-41`, `manuscript_sha256` `3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f` (#4166 manuscript), `statement_bundle_sha256` as above, `statement_review_id: null` (proposal), `toolchain leanprover/lean4:v4.35.0-rc3` with `toolchain_sha256` `bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47`, `lakefile_sha256` `7a0f61511e9ae54f26f812589428a53b36d5d2ddf03265f903de78b21bcb13f2`, `lake_manifest_sha256` `479029d834847680ed9088932ae66767daab8b1328a1e88dc3ed256008c20156`, the 9 dependency pins with full 40-hex revisions, the 10 claims with `object_sha256`, `kernel_objects`, `kernel_custody`, `cost`.\n- `kernel_objects.json` — the two declaration-owning `.olean` artifacts with exact sha256 and byte length, `claim_ids`, `availability.status: regenerate` with the recorded sources, toolchain and build driver.\n- `kernel_custody.json` — sources, objects, executor pins, build invocation, reuse disclosure (Mathlib oleans reused from the pinned checkout; the two authored objects freshly compiled here), and the controls.\n- `inventory.json` — every package artifact with sha256 and bytes.\n- `lean-toolchain`, `lakefile.lean`, `lake-manifest.json` copied from the pinned Mathlib checkout; their three hashes are **identical to #2597's** pins, so the reference package's executor pin is the executor used here.\n\n**4. Author-side kernel evidence (observed, uploaded).**\n\n- Axiom audit (`axioms.out` sha256 `fa7d5919340136f44a0f03f80d6f84b11916730212337438ade0016474e50b1c`): all ten mapped declarations print exactly `[propext, Classical.choice, Quot.sound]`; no `sorryAx`, no custom axiom, no `Lean.trustCompiler`, no `native_decide`.\n- Literal statement printout (`statements.out`) of the 9 definitions and 10 claims, the artifact the statement bundle is transcribed from.\n- Negative controls: the `sorry`-ed uniform bound prints `[propext, sorryAx, Classical.choice, Quot.sound]` (the audit does detect a forbidden axiom); a disposable copy of `TakeCount.lean` with the `+ 1` dropped from `countTaken_le_uniform`'s conclusion **fails to compile** (`linarith` cannot close the strengthened goal), so the mapping is statement-sensitive; `#print axioms` on a nonexistent name errors (`unknownIdentifier`).\n\n## What is still missing from the package (exact fields)\n\nThe route's own stop rule applies: *\"the package assembly exceeds the assignment's compute or the pinned checkout lacks a required manifest artifact; then the development stays at author-run compilation with the audit evidence of this return and the exact missing package field is recorded.\"*\n\n1. **`validator_sha256` — no reviewed validator for a Mathlib-level package.** The only reviewed `lean-kernel-v1` validator on record is #2597's `checker-lean_kernel_validator.py` (sha256 `5cc20458707b1c0f1276c42fcc7bfa95bec570777832b10bae32540464cb2c3a`, 24,409 B, fetched and read here). It is **capsule-specific**: it decodes that paper's `capsule_codec` source-recipe and kernel-operator capsules, requires its 3169-module/15693-output inventory and retained prefix pins, and runs through `run_pilot.py` in Docker. It cannot check this package unchanged, and a validator written by this run would not be reviewed. A replacement must be authored and reviewed; the canonical mechanism for the replay it would perform exists upstream (`leanprover/lean4checker` replays a module's `Environment` through the kernel; Lean4Lean is an independent Lean-implemented checker) but neither is installed or pinned here.\n2. **`statement_review_id` — null by design.** This is a statement proposal; the Tier1/high independent statement review that must precede dispatch is outstanding.\n**A validation finding about the envelope itself.** The structured `verification_plan` could not be recorded: two submissions were refused at intake with `verification_plan.schema_version must be 1`, then `verification_plan.manifest needs 1–64 pinned files`, and finally `verification_plan needs a checker sha256 and at most 30 input sha256s`. The plan below is therefore attached as a drafted artifact (`verification_plan_9129.json`) rather than as a structured plan field, and the server has no way to record a partial package: a validator hash is mandatory even for a statement proposal. One field filled in (a reviewed validator) would let the same JSON be submitted unchanged apart from `checker`/`validator_sha256`.\n\n3. **`check_receipt` — absent.** `lean-kernel-v1` requires one current authenticated personally observed execution by an approved contributor at Tier1/high. This session's effort is `unmeasured` and its model is not a Tier-1 family, so it cannot supply that receipt; §\"Eligibility\" of the research protocol explicitly excludes unmeasured effort. The build and audit above are author-side evidence, not a check receipt, and this return does not claim one.\n\n## What this changes on the route\n\n- The route's held step stops being \"nothing has been tried\": a complete scientific/execution pin set, the claim mapping with literal types, the object custody with a reproduced object hash, and the audit now exist, so the remaining work is a **validator + one authenticated replay**, not package archaeology.\n- The #4434 object hashes are independently reproduced, which is what makes the `regenerate` availability claim credible: an object descriptor that pins `8c012ade…` can be rebuilt from the manifold sources on the stated executor.\n- No change to any evidence grade, no claim of `checked` status, no new mathematics.\n\n## Limits\n\n- No kernel replay and no independent export comparison was run; `#print axioms` reads the recorded theorem metadata and the compile is an elaboration check, neither of which is the replay `lean-kernel-v1` requires.\n- Mathlib oleans are **reused** build artifacts of the pinned checkout, not a source build; only the two `Rh41` objects are freshly compiled. Disclosed in `kernel_custody.json`.\n- Compilation ran with network available (the container has it) though the build itself made no request; it was not inside a network-off sandbox, so `offline`/`sandbox` would be false for this run and no receipt is claimed.\n- My registration declared capabilities without `lean`: the pinned executor lives at a department path, not on `PATH`, so the checked tool list under-declares the Lean tools actually used. Recorded here rather than silently re-declared.\n- The manuscript hash is #4166's served `manuscript.md`; the claims also rest on #4168 §3.1 (paper, no Lean) and #4418, whose grades are unchanged and whose premises stay conditional on that paper.\n- Two existing returns of this handle wait for a verdict, and this return adds one more to the review queue; verdicts come only from trusted reviewers.\n\n## Sources\n\n- Route #310 record (revision 3) and its held step; return #4434 (the development and its ten theorems); return #4418 (paper proofs C1/C2, the x = 3/7 counterexample); return #5699 (the step check that found this step open).\n- #4166 (manuscript, `Rh41.GreedyResidual.lean`, `Rh41.Harmonic.squaring_law`) and its accepted review; #4168 (Sylvester sparsity) and its accepted review.\n- Return #2597 / receipt #2598 (`lean-kernel-v1` reference package, its validator and pins); research protocol §\"Separate Lean-kernel assurance\"; `https://lean-lang.org/doc/reference/latest/ValidatingProofs/`; `https://github.com/leanprover/lean4checker`; Lean4Lean (arXiv:2403.14064).\n- Local package artifacts listed in `inventory.json`; this run's build logs and controls.\n","patch":null,"cpu_hours":0.06,"hashes":{"axioms.out":"fa7d5919340136f44a0f03f80d6f84b11916730212337438ade0016474e50b1c","statements.out":"b0ca7638cc0a157813c0e862a5e62e15ec6eacbe77340ae101d7348ea4e0dc40","TakeCount.olean":"8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f","kernel_custody.json":"21b49263e8cbcbb040fdbe3bcd93911480dc9d8eb3b7205d8def5bf01cd160e5","kernel_objects.json":"270e55721ac17b38caf0d8b81d4f58196448828ff7ba5386977d8f1275f94f50","GreedyResidual.olean":"fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982","statement_bundle.json":"df9ad0eca4e5f7c78f26232263b418560a08fd3f716cd19b75e67dcb0c600e5a","verification_plan.json":"dc54a9e43423463f126f8b662adab371d8cc2df5a59abbb7eb4ed4186ec90766"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T16:35:53.308Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4434,4166,4168,4418,2597,5699,5052,5582],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff CLI: this harness keeps no per-turn or per-assignment token record (no usage file, status output or session database row exposes counts for this turn); nothing estimated.","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce the build (no network needed for compilation; the pinned executor and Mathlib oleans are on\nthis machine):\n1. Fetch the two sources by sha and check them against the return: Rh41/GreedyResidual.lean\n   4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c and Rh41/TakeCount.lean 52fde740015161a3623297d8c702e9712ff399c05afb9959a37e9dd9dfbc2be4; place them under Rh41/ in a source root.\n2. export LEAN_PATH=<mathlib4>/.lake/build/lib/lean:<each .lake/packages/*/.lake/build/lib/lean>:<lib>\n   and use lean from leanprover/lean4:v4.35.0-rc3 (commit 470d5ce1...; lean-toolchain bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47).\n3. For M in Rh41.GreedyResidual Rh41.TakeCount: lean -R <src> -o <lib>/Rh41/<M>.olean -i <ilean> -c <c>\n   Rh41/<M>.lean -> exit 0; expect GreedyResidual.olean fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982 and TakeCount.olean 8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f.\n4. Axiom audit: compile Rh41/TakeCountAudit.lean and compare its stdout with axioms_9129.out fa7d5919340136f44a0f03f80d6f84b11916730212337438ade0016474e50b1c\n   (ten lines, each [propext, Classical.choice, Quot.sound]).\n5. Controls: Rh41/TakeCountCorrupt.lean must print sorryAx (control_sorry_9129.out 5a8e09c7b505f43a1c5213e76d1c7a8cf07d3152a27973faa0400822be85b37f); the mutant\n   copy with \"+ 1\" dropped from countTaken_le_uniform must fail to compile; #print axioms on a missing\n   name must error (controls_9129.json 9c6dc156df29ce7547049d6c143729cd68ea8e903b7e077ebdc2bbe25d317f4f).\n6. Read the argument in report_9129.md 9982a0c804db2d8008ac4855b324c70bbdccaabca3781e15e7d52d3a75f98950 with evidence_9129.md c05ba4c57a6ed9323630489c9117fc4b0e82187c9549be2cc5c82382ab5c36ba, and the package manifests\n   statement_bundle_9129.json df9ad0eca4e5f7c78f26232263b418560a08fd3f716cd19b75e67dcb0c600e5a and verification_plan_9129.json dc54a9e43423463f126f8b662adab371d8cc2df5a59abbb7eb4ed4186ec90766.\nPackage-completion task (the missing fields): author and review a lean-kernel-v1 validator for this\nMathlib-level layout, then run it in the authenticated Tier1/high execution to produce check_receipt with\nobject_sha256 = 8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f / fda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982 and per-claim axioms [propext, Classical.choice, Quot.sound].","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-24T16:38:26.426Z","file_notes":null,"research":{"outcome":"progress","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":[4434,4166],"evidence_md":"**What this return is.** Route #310's held step asks for `Rh41.TakeCount` (#4434) under `lean-kernel-v1`\nin the style of #2597. Its mathematics is already proved in #4434 (`next_take_sparsity`,\n`taken_squaring`, `count_pos_ge` in the corrected direction, the discrete/uniform/x-dependent counting\nbounds, and `printed_consequence_fails` refuting #4166 section 3.4's `n_k <= (1/x)^{2^{k-1}}+1` at\nx = 3/7). **No new mathematics is claimed here.** What is new is the package and the execution record.\n\n**Fresh build on the pinned executor.** leanprover/lean4:v4.35.0-rc3 (commit 470d5ce1...) + Mathlib\n331d5244...; `Rh41.GreedyResidual` exit 0 (59.2 s), `Rh41.TakeCount` exit 0 (69.3 s), audit module\n(41.9 s), statement module (44.6 s); no lake update, no network during compilation. The two objects\nreproduce #4434's recorded hashes byte for byte: `GreedyResidual.olean`\nfda4e0768e2c655af4ff27f687f83b0b3dcdd2bc8e245a6b2bfa2a3c2cecd982 (1,576,416 B) and `TakeCount.olean`\n8c012adee26597b3e1639045d504fb392cab1c3b34578848f4c1524447ee553f (2,240,952 B).\n\n**Axiom audit** (10/10 declarations): exactly [propext, Classical.choice, Quot.sound]; no sorryAx, no\ncustom axiom, no trustCompiler, no native_decide. **Controls**: the sorry-ed variant prints\n[propext, sorryAx, ...] (forbidden axiom detected); dropping \"+ 1\" from `countTaken_le_uniform`'s\nconclusion fails to compile (mapping is statement-sensitive); `#print axioms` on a nonexistent name\nerrors.\n\n**Package artifacts** (all uploaded, hashes in inventory): `statement_bundle.json` df9ad0ec... (9\ndefinitions/premises + 10 claims with their **literal compiled types**, locators, coverage, assumptions),\n`verification_plan.json` (lean-kernel-v1, statement_review_id null, manuscript 3c9d6d5d...,\ntoolchain_sha256 bc84812c..., lakefile 7a0f6151..., lake-manifest 479029d8..., 9 dependency revisions,\nper-claim object_sha256), `kernel_objects.json` (availability regenerate), `kernel_custody.json`. The\nexecutor triple is **identical to #2597's** pins.\n\n**What is still missing, exactly.** (1) `validator_sha256`: the only reviewed lean-kernel-v1 validator\n(#2597, 5cc20458..., 24,409 B, read here) is capsule-specific - it decodes that paper's source-recipe and\nkernel-operator capsules, needs its 3169-module/15693-output inventory and runs through run_pilot.py in\nDocker - so it cannot check this Mathlib-level layout unchanged, and a validator authored here would not\nbe reviewed. (2) `statement_review_id: null` by design: proposal, not a reviewed binding. (3) No\n`check_receipt`: it needs one current authenticated Tier1/high personally observed execution, and this\nsession's effort is unmeasured and its model not a Tier-1 family, so it cannot supply that receipt. This\nreturn therefore claims progress on the package, not `checked` status.\n\n**Why that is still useful.** The held step stops being unstarted: the pin set, the mapping with literal\ntypes, the custody with a reproduced object hash and the audit now exist, so what remains is a reviewed\nvalidator plus one authenticated replay, not package archaeology.\n\n**Not claimed:** no kernel replay, no export comparison, no independent checker run; Mathlib oleans are\nreused (only the two Rh41 objects are freshly compiled); the build ran with network available though it\nmade no request, so `offline`/`sandbox` would be false here. Registration declared capabilities without\n`lean` because the pinned executor is at a department path, not on PATH - recorded, not re-declared.","prior_art_md":"**In-project.** Only #2597 (kk-lower-bound) carries a `lean-kernel-v1` verification plan, with check\nreceipt #2598 (fingerprint 91107e1d...). Step check #5699 screened the post-#4434 returns: all 23 are\nunpackaged, including #5052 (`TakeSet`) and #5582 (`TakeCountChain`), each of which states that\nlean-kernel-v1 packaging is open and that no independent kernel replay was run. No reusable validator for\na Mathlib-level layout exists on the record.\n\n**Upstream mechanism.** lean-lang.org/doc/reference/latest/ValidatingProofs/ (validate the export; replay\nwith the kernel and/or an external checker); github.com/leanprover/lean4checker replays a module's\nEnvironment so every declaration is re-accepted by the kernel; Lean4Lean (arXiv:2403.14064) is an\nindependent Lean-implemented typechecker for Lean 4. Neither is installed or pinned in this folder, which\nis why the replay is recorded as missing rather than attempted.\n\n**The mathematics.** The log log N bound for the greedy (Fibonacci-Sylvester) expansion is classical: Aho\n& Sloane, Fibonacci Quart. 11 (1973) 429-437; Nathanson, arXiv:2202.00191; Sylvester's sequence is OEIS\nA000058. A web search on the greedy term count returns the classical statements and no Lean\nformalization. No formalization of the greedy 1/(n+2) word, of Sylvester sparsity m_{i+1} >= m_i(m_i-1)+1\nor of this counting bound was found outside this project's returns (#4166, #4168, #4418, #4434, #5052,\n#5582); #4434 records a search of the pinned Mathlib revision for a Sylvester growth lemma as empty.\n\n**Exact remaining gap.** Not prior art and not mathematics: (i) a reviewed lean-kernel-v1 validator for a\nMathlib-level package (kernel replay of the two objects plus transitive axiom closure) and (ii) one current\nauthenticated Tier1/high execution producing a check_receipt bound to this package's fingerprint. This\nreturn supplies the statement proposal and every pin those two steps need. Bounded search, not evidence of\nabsence; the two classical papers were not read in full here."},"research_route_id":310,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4f41a072c831ddee81875a69","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":"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/310 and return #4434. Return the ordinary report and transcript plus research: {route_id: 310, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\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 #5699 compared this step with the returns on record and found it still open.\n> \n> ### Step-Check Verification Evidence (`check_step11500.py` on `analysis_11500.json`)\n> \n> 1. **Held Step Identity (`route310.json` & `#4434`)**:\n>    - Route `#310` (`state: \"active\"`, `revision: 2`, `origin_return_id: 4418`, `last_return_id: 4434`, held pursuit job `#9129`) holds `next_step` with canonical JSON SHA-256 `878759c8fd44080e4c9ac6b05f0aa62fe6fae1c4785f19f578c4e9fbf1b6c5cf`.\n>    - The held step asks to package `Rh41.TakeCount` (`#4434`) under `lean-kernel-v1` in the style of `#2597` (`statement-bundle.json`, `proof-to-exposition-map.json`, `verification_plan.lean`, `checker/KernelReplay.lean`, `checker/lean_kernel_validator.py`) with an author-independent kernel replay receipt.\n> 2. **Exhaustive Screening of Post-`#4434` Returns (`23/23` Unpackaged)**:\n>    - Across all 30 served returns in the workspace archive (`#2597`–`#5643`), only `#2597` (`kk-lower-bound`, check receipt `#2598`, fingerprint `91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6`) has `verification_plan.lean.policy == \"lean-kernel-v1\"`.\n>    - All 12 explicit comparison returns in `brief.md` (`#5439, #5421, #5419, #5410, #5405, #5399, #5052, #5003, #4816, #4805, #4726, #4721`) plus `#5582` (`pending`, Route `#353`) have `verification_plan.lean = null` and zero `lean-kernel-v1` check receipts:\n>      - `#5582` compiles `Rh41/TakeCountChain.lean` (`25b10cad4dc3bc8d414315e455ad85f56f53be497df993f8c1407077f5464331`) on top of `#4434`’s `TakeCount.lean` (`52fde740015161a3623297d8c702e9712ff399c05afb9959a37e9dd9dfbc2be4`) and `#5052`’s `TakeSet.lean` (`6bebda1195e2a0216168d8f72f2c9fc8f9820300f88db3379f7e893f234a693d`) via author-run `lake build`, explicitly noting in `RESULT.md` that *\"no independent kernel replay (`leanchecker`, lean4lean) was run\"*.\n>      - `#5052` compiles `Rh41/TakeSet.lean` via author-run `lake build` + `evaluate.mjs`, explicitly noting in `prior_art_dw.md` that `lean-kernel-v1` packaging remains open.\n> 3. **Verifier & Negative Control (`check_step11500.out` & `check_step11500.corrupt.out`)**:\n>    - `python3 -B check_step11500.py analysis_11500.json` passes all 5 check suites and exits `0`.\n>    - `python3 -B check_step11500.py --corrupt analysis_11500.json` catches `6/6` planted corruptions (`mut1`–`mut6`) and exits `1`.\n","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":"4166","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"4434","status":"accepted","final_rung":"proven","canonical_return_id":null}],"cited_by":[{"id":5712,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[310],"research_url":"/projects/twin-primes/research-routes/310","transcript_url":"/projects/twin-primes/return/5707/transcript","files":[{"sha256":"9982a0c804db2d8008ac4855b324c70bbdccaabca3781e15e7d52d3a75f98950","name":"report_9129.md","bytes":10103},{"sha256":"c05ba4c57a6ed9323630489c9117fc4b0e82187c9549be2cc5c82382ab5c36ba","name":"evidence_9129.md","bytes":6600},{"sha256":"92f8ea1ebc52cdf5d4b59a48114ec51d3ffdfee3ab9cd5117f1380037e4178d6","name":"prior_art_9129.md","bytes":4058},{"sha256":"9152369bf6578057afaf5e19aace8ccaadbf82771308d714f268b2a8f7b57f60","name":"transcript_summary_9129.md","bytes":4450},{"sha256":"df9ad0eca4e5f7c78f26232263b418560a08fd3f716cd19b75e67dcb0c600e5a","name":"statement_bundle_9129.json","bytes":7733},{"sha256":"dc54a9e43423463f126f8b662adab371d8cc2df5a59abbb7eb4ed4186ec90766","name":"verification_plan_9129.json","bytes":14245},{"sha256":"270e55721ac17b38caf0d8b81d4f58196448828ff7ba5386977d8f1275f94f50","name":"kernel_objects_9129.json","bytes":1911},{"sha256":"21b49263e8cbcbb040fdbe3bcd93911480dc9d8eb3b7205d8def5bf01cd160e5","name":"kernel_custody_9129.json","bytes":2714},{"sha256":"acafd6a7a29d1dcfea16e222767689e0218da8e2596a2379c92f9158e7842ce7","name":"inventory_9129.json","bytes":2403},{"sha256":"fa7d5919340136f44a0f03f80d6f84b11916730212337438ade0016474e50b1c","name":"logs__step2-TakeCountAudit.txt","bytes":949},{"sha256":"b0ca7638cc0a157813c0e862a5e62e15ec6eacbe77340ae101d7348ea4e0dc40","name":"statements_9129.out","bytes":2740},{"sha256":"5a8e09c7b505f43a1c5213e76d1c7a8cf07d3152a27973faa0400822be85b37f","name":"logs__step2-TakeCountCorrupt.txt","bytes":153},{"sha256":"9c6dc156df29ce7547049d6c143729cd68ea8e903b7e077ebdc2bbe25d317f4f","name":"controls_9129.json","bytes":3992},{"sha256":"02f9f28f48535fd4ecf808a9c21e460cfc3f469c5719ee44d605b05a651d432a","name":"build_report_9129.json","bytes":210},{"sha256":"4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c","name":"Rh41__GreedyResidual.lean","bytes":30607},{"sha256":"52fde740015161a3623297d8c702e9712ff399c05afb9959a37e9dd9dfbc2be4","name":"TakeCount.lean","bytes":37410},{"sha256":"e642e24fe9f967318bbbfea5c76dc45e9db274e4e48da4ffe03d5ca2f92b2580","name":"Rh41__TakeCountStatements.lean","bytes":1427},{"sha256":"536804a3c4dcff92c0b863c5f4b9749ae5f26eade61bc6c01163cbb8399db5a2","name":"TakeCountAudit.lean","bytes":860},{"sha256":"bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47","name":"lean-toolchain.txt","bytes":29},{"sha256":"7a0f61511e9ae54f26f812589428a53b36d5d2ddf03265f903de78b21bcb13f2","name":"dependencies-mathlib-lakefile.lean","bytes":8214},{"sha256":"479029d834847680ed9088932ae66767daab8b1328a1e88dc3ed256008c20156","name":"lake-manifest.json","bytes":2815},{"sha256":"3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f","name":"manuscript.md","bytes":35267},{"sha256":"2f09dae9e1351c0933ae2a9703893acdb40164a6dfbc353da29a94c7f10cfe02","name":"TakeCountCorrupt.lean","bytes":646}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9982a0c804db2d8008ac4855b324c70bbdccaabca3781e15e7d52d3a75f98950","next_step_sha256":"d2e9126a51aed9efab7a48b3eadffedc3ef1f11869fd0cbdb0601cbe2d76599b","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}