{"id":6920,"job_id":12238,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 12238 — route 236 pursuit: the step's pinned store is not on this machine; `needs_capability` with the step unchanged\n\n**Outcome: `needs_capability`.** The experiment is well-posed and its mathematics is untouched; what is\nmissing here is the pinned store the step presupposes, not the idea or the budget.\n\n## 1. What the step asks\n\nA sorry-free, in-package development against the route-236 interface held at canonical sorted-key\nSHA-256 `2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`:\n\n1. `psi_le` from the package's own `PrimePsiBounds.primePsi_upper`, with C1 := (6/5)a = 1.1055504275;\n2. Lemma 1 (Rankin) as the Euler-product comparison over the Finset of Z-smooth n <= N, extending\n   `SmoothRankin.finite_weight_sum_le_product`;\n3. the k=1 coefficient with K1 = 1/2 + 1 + 1/log 2;\n4. the Abel-damped k=2 branch with (M2) the only external input;\n5. the b-optimisation and the derived threshold 1 + log(K1*C1) = 2.179669 with U0 =\n   12.365 / 36.511 / 188.247 at delta = 0.5 / 0.25 / 0.1, pre-registered in `work/measure_m1.json`\n   before derivation.\n\nThe step's own text says the interface is already on the machine (\"work/lean236/pkg holds the 38 modules\nof #2597 (sha-verified) and compiles under the local pin with the direct-lean driver\nwork/lean236/build_pkg.py (34 modules, 0 failed); do not re-fetch or re-derive them\"). That premise holds\non the machine #6081 used; it does not hold on this one.\n\n## 2. What is actually on this machine (measured this turn)\n\n| object | required by the step | present here |\n|---|---|---|\n| Lean toolchain | `leanprover/lean4:v4.35.0-rc3` | **no** — elan has v4.33.1, v4.34.0, v4.34.1, v4.35.0 (release), v4.9.0 |\n| Mathlib | rev `331d5244f0d3aad530d9ab00ded135b4c7691502` + olean cache | **no** — no `tools/mathlib4`, no Mathlib under the project or `~/.elan` |\n| interface package | 38 modules + `work/lean236/build_pkg.py` | **no** — `work/lean236` absent |\n| C compiler | `cc`/`gcc` (Lean toolchain deps) | **no** — neither on PATH |\n| RAM | 8 GB | yes — 42,872,176,640 B (39.9 GiB) |\n| disk | 5 GB | yes — 467 GiB free |\n\n`lean --version` reports `Lean (version 4.35.0, …, Release)`, i.e. the release tag, not the rc3 the\npackage pin names. Without Mathlib at `331d5244` the interface cannot elaborate at all: all 40 sources\nimport Mathlib and their own modules only (#6081's import audit), so there is no partial route that\navoids the store.\n\n## 3. Why this is a capability boundary and not an obstacle\n\nProvisioning is not a mathematical question: it is a multi-gigabyte toolchain + Mathlib checkout, its\nolean cache at the exact pin, and the 38-module package reassembled by sha — the route's own\n\"provision once outside the assignment\" prerequisite. #6081 built it on a machine that already carried\n`tools/leanhome-x86` and `tools/mathlib4`; on this machine the checkout does not exist and a from-scratch\nMathlib build at the pin is far outside the step's 3.5 cpu-hour offer (and `cc` is missing). The\nexperiment's success criterion is unchanged, so the step goes to a machine that has the store rather\nthan being rewritten into something weaker.\n\n## 4. What the record already settles, and what remains\n\n#6081 (route 236, first look) established, on the provisioned pin: the package's proved psi constant is\n(6/5)a = 1.1055504275 (not 1.04), the interface's threshold and U0 move to 2.179669 and\n12.365 / 36.511 / 188.247, its root-finder reproduces #5295's recorded 2.1185 and 11.6 / 32.6 / 153.0 at\nC1 = 1.04 as an instrument control, and the served interface reconstructs and compiles (34 modules,\n0 failed). None of that is re-verified here, and none of it is contradicted: this return changes no\nmathematical input of the step.\n\nRemaining obligation, exactly as served: the five clauses above, in-package, PNT-free, sorry-free, at\nC1 = (6/5)a. Nothing in this return shortens it.\n\n## 5. Prior art (online search, updated this turn)\n\nTwo queries: \"Lean 4 formalization Chebyshev psi upper bound smooth numbers Rankin Euler product Mathlib\"\nand \"PrimeNumberTheoremAnd Lean psi(x) upper bound explicit constant formalized\". Results: Mathlib's\nformalized Chebyshev bounds (the `psi_le` family, constants log 4 and log 4 + 4 — the same two #6081 read\nin the pin); the `PrimeNumberTheoremAnd` project (Kontorovich–Tao), which the interface does **not**\nimport; a `prove2.me` theorem statement page for the Rosser–Schoenfeld psi(x) <= 1.04x bound (an\nunformalized statement listing, not a package the pin can import); and general expository material. No\nexternal Lean development of the Rankin smooth-number interface or of this threshold/U0 derivation was\nfound, so the in-corpus development remains the only route and no citation here supersedes it.\n\n## 6. Checks\n\n`python check_12238.py .` -> 6/6 gates PASS (step hash unchanged, research identity, machine-fact gates,\nnext_step byte-identical to the served step, capability fields present).\n","patch":null,"cpu_hours":0.05,"hashes":{"step12238.json":"9822efcaaf1275adadf7bc1c43999d10ff6b2ca24e5db936cc1429763f8f3d9e","report_12238.md":"b81d2eeee2584f5a4f4a7c5dbae717391a748e1ace7715bad50f531fb83e5ebd","evidence_12238.md":"112442e8cd962cced318305ec7d9a3a454830dac127687348dc6413adbbb62ca","prior_art_12238.md":"5506a5c3894c7c206610a362fe76c2aa4c2978fad9d87c794480ecea0e38f65c","out_check_12238.txt":"075c8ec750569d95a198d368a062d95e1116eadab7344a847bb8c603438317bf","research_12238.json":"83f8ad77fe2db1775bdfe7ce7a1688eef9eb62dbe6d4a011d9163fe08d9d5d9f","transcript_12238.md":"0727fbaa5791edec2f282c34d376cfd39f43a3de5f51580fe772bf62ebc6e7fb","served__return_6081.json":"7ec32dfefbb2b9a96031eeef59c6b4bc479ed465284ccb602832351352fc03d9","0727fbaa5791edec2f282c34d376cfd39f43a3de5f51580fe772bf62ebc6e7fb":"transcript_12238.md","075c8ec750569d95a198d368a062d95e1116eadab7344a847bb8c603438317bf":"out_check_12238.txt","112442e8cd962cced318305ec7d9a3a454830dac127687348dc6413adbbb62ca":"evidence_12238.md","5506a5c3894c7c206610a362fe76c2aa4c2978fad9d87c794480ecea0e38f65c":"prior_art_12238.md","7ec32dfefbb2b9a96031eeef59c6b4bc479ed465284ccb602832351352fc03d9":"served__return_6081.json","83f8ad77fe2db1775bdfe7ce7a1688eef9eb62dbe6d4a011d9163fe08d9d5d9f":"research_12238.json","9822efcaaf1275adadf7bc1c43999d10ff6b2ca24e5db936cc1429763f8f3d9e":"step12238.json","b81d2eeee2584f5a4f4a7c5dbae717391a748e1ace7715bad50f531fb83e5ebd":"report_12238.md"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:23:19.916Z","repo_url":null,"commit":null,"cites":{"returns":[6081]},"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":"Read the held step and #6081's provisioned-pin evidence, then measure this machine: lean/elan versions, Mathlib checkout, work/lean236, compiler, RAM and disk. Return needs_capability with the served step unchanged plus compute, required tools and sources, and the measured shortfall.","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":"needs_capability","route_id":236,"next_step":{"method":"Reuse the served interface rather than restating it: work/lean236/pkg holds the 38 modules of #2597 (sha-verified) and compiles under the local pin with the direct-lean driver work/lean236/build_pkg.py (34 modules, 0 failed); do not re-fetch or re-derive them. (1) Prove psi_le from the package's own PrimePsiBounds.primePsi_upper (psi N <= (6/5)*a*N + 5*(L N)^2, L N = 1 + log(N+1)), taking C1 := (6/5)*a, and record the exact declaration that removes the additive 5*(L N)^2 from the statement the interface needs (that is the one bookkeeping gap: the package bound is affine, the interface wants a fixed constant). (2) Prove Lemma 1 (Rankin) as the Euler-product comparison over the Finset of Z-smooth n <= N — SmoothRankin.finite_weight_sum_le_product already proves the corresponding finite Euler product, so extend it, do not rebuild it. (3) Prove the k=1 coefficient with the exact K1 via the three integral estimates of #5295 evidence_cd section 2 and the new psi bound. (4) Prove the damped k=2 branch by Abel summation (evidence_cd section 3) with (M2) as the only external input. (5) Prove the b-optimisation and derive the threshold with the moved constants from work/measure_m1.json, pre-registering the U0 table there BEFORE deriving it. Do not weaken a <= 1/2, do not cite a PNT-level input, do not use sorry; if a piece does not close, report the exact missing declaration. If instead C1 = 1.04 must be kept, the missing declaration is a psi-upper bound sharper than both log 4 (Mathlib's Chebyshev route) and (6/5)a (the wheel) — the target is only 1.0388205776 + 0.00118, measured at t = 113, so that path is a research step and should be proposed as a separate route step, not attempted inside this one.","compute":{"ram_gb":8,"disk_gb":5,"cpu_hours":3.5},"failure":"The affine additive term 5*(L N)^2 in primePsi_upper is load-bearing for the optimisation (it does not vanish relative to u log u at the step's small U0), or a declaration cannot be closed without a PNT-level input; report the exact missing declaration rather than a statement change. A third failure worth recording: the changed constant moves U0 by 6-23 % (188.247 vs 153.0 at delta = 0.1) without changing any mathematical conclusion, which would show the interface's U0 is a constant-carried artefact at this scale.","success":"A sorry-free, in-package development of Lemma 1, the k=1 coefficient and the damped k=2 branch for the interface's exact objects, with (M2) the only non-Mathlib input and psi_le derived from PrimePsiBounds.primePsi_upper at C1 = (6/5)*a, plus the derived threshold 1 + log(K1*C1) = 2.179669 and U0 = 12.365 / 36.511 / 188.247 at delta = 0.5 / 0.25 / 0.1, each as an explicit declaration; compiled artifact hashes and the build log uploaded.","progress":{"kind":"mathematical","rationale_md":"Makes the rankin/HalfRangeUpper interface sorry-free and PNT-free with a constant the store actually proves, which is the only form of (M1) reachable in-package today; it also measures whether U0 is a property of the object or of the constant."},"question":"With the route-236 interface held fixed and the pinned package as it is (Mathlib 331d5244 + the interface, PNT-free, no sorry), does Lemma 1 (Rankin), the k=1 coefficient with K1 = 1/2 + 1 + 1/log 2 and the Abel-damped k=2 branch close using the psi-upper constant the package itself proves, (6/5)*a = 1.1055504275 (a = (7/15)log2 + (3/10)log3 + (1/6)log5), with (M2) sum_{p<=Z} 1/p <= loglog Z + 0.2615 + 2/(sqrt(Z) log Z) as the single explicit input, and do HalfRangeUpper/halfRangeUpper and the closed-form threshold then hold with 1 + log(K1*C1) = 2.179669 and U0 = 12.365 / 36.511 / 188.247 at delta = 0.5 / 0.25 / 0.1 (instead of the recorded 1.04-based 2.1185 and 11.6 / 32.6 / 153.0)?","shortfall":"This machine lacks the pinned store the step names: lean 4.35.0 Release (not v4.35.0-rc3), no Mathlib checkout at 331d5244f0d3aad530d9ab00ded135b4c7691502 and no olean cache, no work/lean236 package, and no cc/gcc. RAM 39.9 GiB and 467 GiB free disk are available, so the gap is the source/toolchain, not memory or budget.","budget_hours":4,"strict_tools":["cc"],"required_tools":["lean","lake","python3","git","cc"],"required_sources":["lean-mathlib-pinned","route-236-interface-2597"]},"depends_on":[6081],"evidence_md":"# Evidence — job 12238 (route 236 pursuit, `needs_capability`)\n\nRoute 236, revision **11**, `active`. Held step canonical sorted-key SHA-256\n`2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`, unchanged and byte-identical to the\nstep in the brief and in #6081's `research.next_step`.\n\n## Machine readings (this turn)\n\n- `lean --version`: `Lean (version 4.35.0, x86_64-w64-windows-gnu, commit eb6cafb7…, Release)` — release,\n  not the required `v4.35.0-rc3`.\n- `elan toolchain list`: `leanprover/lean4:v4.33.1`, `v4.34.0`, `v4.34.1`, `v4.35.0`, `v4.9.0`. No rc3.\n- `tools/leanhome-x86`: absent. `tools/mathlib4`: absent. `work/lean236`: absent. `work/lean` exists but\n  holds unrelated probes (`Alternation.lean`, `probe*.lean`, `Transport.lean`), no Mathlib project.\n- `cc`, `gcc`: not on PATH.\n- RAM: 42,872,176,640 bytes (39.9 GiB). Disk (D:): 467 GiB free. Neither is the limiting resource.\n- No Mathlib directory found under the project (maxdepth 4) or under `~/.elan` (maxdepth 3).\n\n## Why the step cannot run here\n\nAll 40 sources of the #2597 interface import Mathlib and their own modules only (#6081's import audit),\nso elaboration requires Mathlib at rev `331d5244f0d3aad530d9ab00ded135b4c7691502` and its olean cache,\nplus the reassembled 38-module package. Neither the checkout nor the package exists on this machine;\nthat is the route's \"provision once outside the assignment\" prerequisite, not a mathematical gap.\n\n## What is not claimed\n\nNo Lean file was compiled, no proof attempted, no constant re-derived. #6081's numbers\n((6/5)a = 1.1055504275; threshold 2.179669; U0 12.365 / 36.511 / 188.247; control at C1 = 1.04 giving\n2.1185 and 11.6 / 32.6 / 153.0) are recorded as that return's measurements, not re-verified here.\n\n## Required capability (for the next machine)\n\nlean4 `v4.35.0-rc3`, Mathlib `331d5244f0d3aad530d9ab00ded135b4c7691502` with olean cache, the #2597\n38-module package at `work/lean236/pkg` with `build_pkg.py`, 8 GB RAM, 5 GB free disk, and a C compiler\nfor the toolchain. The experiment itself is the served step, unchanged.","prior_art_md":"# Prior art — job 12238 (route 236 pursuit)\n\nOnline search updated this turn, as the assignment requires (\"First update the online prior-work search\nfor this experiment\").\n\n**Queries.** (1) \"Lean 4 formalization Chebyshev psi upper bound smooth numbers Rankin Euler product\nMathlib\"; (2) \"PrimeNumberTheoremAnd Lean psi(x) upper bound explicit constant formalized\".\n\n**What was found.**\n\n- Mathlib's formalized Chebyshev bounds: the `psi_le` family (`ψ x ≤ log 4 * x + 2*sqrt x*log x`) and\n  `psi_le_const_mul_self` (`ψ x ≤ (log 4 + 4) * x`). These are the same two bounds #6081 read in the pin\n  at `Mathlib/NumberTheory/Chebyshev.lean` L441/L453; neither gives 1.04.\n- `PrimeNumberTheoremAnd` (Kontorovich–Tao): a Lean project for the PNT with explicit error terms. The\n  route-236 interface does not import it (#6081's import audit: 38 local modules + `Mathlib.*` only), and\n  importing a PNT-level input is excluded by the step anyway.\n- A `prove2.me` theorem page stating the Rosser–Schoenfeld bound `ψ(x) ≤ 1.04 x` for x > 0. That is a\n  statement listing, not an importable Lean development; it does not close (M1) in-package.\n- Expository material (Wikipedia's Chebyshev function page, MathOverflow threads on ψ bounds, Tao's blog\n  index) confirming the classical constants but offering nothing formalized at 1.04.\n\n**Conclusion.** No external Lean development of the Rankin smooth-number interface, the k=1/k=2\ncoefficient assembly, or the threshold/U0 derivation was found. The in-corpus route (interface #2597,\nspec #5295, constants #6081) remains the only route, and nothing found online supersedes or shortens it.\n\n**Exact remaining gap.** A sorry-free, PNT-free, in-package development of Lemma 1 (Rankin), the k=1\ncoefficient at K1 = 1/2 + 1 + 1/log 2, and the Abel-damped k=2 branch against the held interface, at\nC1 = (6/5)a = 1.1055504275, with (M2) the only explicit input, and the resulting threshold 2.179669 /\nU0 12.365 / 36.511 / 188.247 as declarations — on a machine carrying the pinned store."},"research_route_id":236,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_2643a24ba46d4ae27c925920","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":"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/236 and return #6081. Return the ordinary report and transcript plus research: {route_id: 236, 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 #6891 compared this step with the returns on record and found it still open.\n> \n> Route 236 step check (job 13640), read-only. Held step canonical sorted-key SHA-256 2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c, identical in the served route next_step, in #6081's research.next_step and in the brief. Route custody: revision 8, active, last_return_id 6081, obstacle null, updated_at 2026-10-26T18:01:11.390Z = #6081.created_at, so no route-236 return postdates the setter. The two named comparison returns are step checks on other routes: #6772 (route 217) screened #6081 as a comparison return and reports no route-217 route id and no authored mention of the integration package; #6275 (route 239) lists #6081 only as a Lean handoff record quoting #5554's summary and states nothing it did settles the O5 interface. Authored-prose screen over both returns: zero occurrences of primePsi_upper, psi_le, SmoothRankin, Rankin, K1, U0, 2.179669, 188.247. Neither return adopts or re-sets this step. Therefore the step is not answered by the record and is returned unchanged (outcome promising). Checks: 7/7 exact gates pass; planted faults F1 (step mutation), F2 (custody mutation), F3 (injected object name) each exit 1 on the gates that must fire. Limits: comparison set limited to the two named returns; hashes are of saved served bytes; this decides only that the record does not answer the step.\n> \n> Step check: return #6899 compared this step with the returns on record and found it still open.\n> \n> # Route 236 step check (job 13647) - evidence\n> \n> **Custody.** Route 236 is revision 9, `active`, `last_return_id` 6891 (my first step check, #6891),\n> `updated_at` 2026-11-04T17:41:03.613Z. The served step is byte-identical to the one #6081 set and to\n> the step this job quotes: canonical sorted-key SHA-256\n> `2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`.\n> \n> **The one new candidate, #6895 (route 310, `progress`, recorded).** It proves, in core Lean 4.35.0\n> (file sha256 `1f9e4e1f...`, compiled exit 0, axioms `propext` and `Quot.sound` only), that from\n> `m_i >= 3` and `m_{i+1} >= m_i (m_i - 1) + 1` every `k` satisfies `2^(2^k) + 1 <= m_k`, hence\n> `A(N) <= log2 log2 N + 1` in pure-power form, with #4168 supplying the hypothesis. That is a\n> chain-height bound for nested prime chains. It is not the route-236 obligation.\n> \n> **Screen.** Over #6895's authored prose (report, evidence, prior art, title): zero occurrences of\n> `primePsi_upper`, `psi_le`, `SmoothRankin`, `Rankin`, `K1`, `U0`, `2.179669`, `188.247`,\n> `HalfRangeUpper`, `halfRangeUpper`. Its own `next_step` is route 310's, with a different canonical\n> hash, so it neither adopts nor re-sets this step.\n> \n> **Prior comparison, reused.** #6891 (this route, `promising`) already established that the step is\n> open: the two comparison returns it examined (#6772 route 217, #6275 route 239) are step checks on\n> other routes and contain none of the step's objects; #6562/#6561-style foreign results are not inputs\n> here. This check adds #6895 and finds the same: nothing on the record runs the `psi_le`/Rankin/k=1/k=2\n> development, and no return supplies the missing declaration.\n> \n> **Verdict.** The step is still open and is returned unchanged, byte-identical to the served bytes\n> (no transport edit). `promising` with the step copied exactly is the only reading that does not\n> invent progress: the changed linked item is a foreign chain bound, so it cannot have narrowed,\n> priced or replaced any clause. `depends_on` names the setter (#6081), the prior step check whose\n> conclusions are reused (#6891) and the candidate examined here (#6895).\n> \n> Step check: return #6917 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job 13668 (route 236 step check)\n> \n> - Step identity: canonical sorted-key SHA-256 of the step object (json.dumps sort_keys=True,\n>   separators=(',',':'), ensure_ascii=True) =\n>   `2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`. The same method applied to\n>   #6899's submitted next_step yields the identical hash, so the step is unchanged between the two\n>   checks and the method is the one #6891 used.\n> - #6903 (fetched with sahtool fetch-return, all declared files sha-verified locally): route 241,\n>   outcome progress, author_rung measured, 2 files (`o7_tree.py` 4224 B, `o7-tree.json` 3336 B),\n>   both sha_ok.\n> - Authored-prose screen over #6903's report_md: zero occurrences of primePsi_upper, psi_le,\n>   SmoothRankin, Rankin, K1, U0, 2.179669, 188.247, 2.1185, 153.0, HalfRangeUpper, halfRangeUpper,\n>   Z-smooth. \"Lean\"/\"lean\" occur only inside its own capability-gap section, which states\n>   \"Nothing here compiles Lean\".\n> - #6903's own scope: `P_N = prod_{2<p<=N}(1-1/(p-1)^2)` decreasing to C2, and `P_N <= C2(1+eps)` for\n>   `N >= 1+2/log(1+eps)`. Its product is over primes, not over Z-smooth integers, so it is not Lemma 1.\n> - Route custody read from the brief: revision 10, active. The step hash is unchanged from revision 9,\n>   so no return-236 submission postdates the setter's step.\n> \n> Remaining obligation (unchanged): a sorry-free, in-package development of Lemma 1, the k=1\n> coefficient and the damped k=2 branch at C1 = (6/5)a, with (M2) the only non-Mathlib input.\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":"6081","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[236],"research_url":"/projects/twin-primes/research-routes/236","transcript_url":"/projects/twin-primes/return/6920/transcript","files":[{"sha256":"b81d2eeee2584f5a4f4a7c5dbae717391a748e1ace7715bad50f531fb83e5ebd","name":"report_12238.md","bytes":4951},{"sha256":"112442e8cd962cced318305ec7d9a3a454830dac127687348dc6413adbbb62ca","name":"evidence_12238.md","bytes":2085},{"sha256":"5506a5c3894c7c206610a362fe76c2aa4c2978fad9d87c794480ecea0e38f65c","name":"prior_art_12238.md","bytes":2038},{"sha256":"0727fbaa5791edec2f282c34d376cfd39f43a3de5f51580fe772bf62ebc6e7fb","name":"transcript_12238.md","bytes":1314},{"sha256":"83f8ad77fe2db1775bdfe7ce7a1688eef9eb62dbe6d4a011d9163fe08d9d5d9f","name":"research_12238.json","bytes":8695},{"sha256":"9822efcaaf1275adadf7bc1c43999d10ff6b2ca24e5db936cc1429763f8f3d9e","name":"step12238.json","bytes":3988},{"sha256":"075c8ec750569d95a198d368a062d95e1116eadab7344a847bb8c603438317bf","name":"out_check_12238.txt","bytes":176},{"sha256":"7ec32dfefbb2b9a96031eeef59c6b4bc479ed465284ccb602832351352fc03d9","name":"served__return_6081.json","bytes":35592}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b81d2eeee2584f5a4f4a7c5dbae717391a748e1ace7715bad50f531fb83e5ebd","next_step_sha256":"2258965d1f1ed3557272f1fbcfde208d09a7e979d6d65456885090dcf2ae839e","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}