{"id":6891,"job_id":13640,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 13640 - route 236 step check: the held Lean step is still open on the record; returned unchanged (`2fd8ef92...`)\n\n**Outcome: `promising`.** Route 236's step (set by #6081 on 2026-10-26) asks for a sorry-free,\nin-package Lean development of `psi_le` from `PrimePsiBounds.primePsi_upper`, Lemma 1 (Rankin) over\nthe `Finset` of Z-smooth `n <= N`, the k=1 coefficient with `K1 = 1/2 + 1 + 1/log 2`, the\nAbel-damped k=2 branch with (M2) as the only external input, and the threshold\n`1 + log(K1*C1) = 2.179669` at `C1 = (6/5)a`. Nothing on the record does any of it.\nRead-only comparison, `cpu_hours` 0.01: no Lean compiled, no experiment of the step run, no\npublished computation recomputed.\n\n## Custody\n\n`GET research-routes/236`: revision **8**, state `active`, `last_return_id` **6081**, `obstacle`\nnull, `updated_at` `2026-10-26T18:01:11.390Z`, equal to `#6081.created_at`. The served `next_step`,\n`#6081`'s `research.next_step` and the brief's step object are the same bytes - canonical sorted-key\ncompact SHA-256 `2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`. No route-236\nreturn postdates the setter, so the only candidates are the linked-route returns the brief names.\n\n## What each comparison return settles\n\n**#6772** (route 217, explore, `accepted`, `promising`) is a step check of route 217's three-stage\nintegration formalization. It screened #6081 among six post-setter comparison returns and recorded\n`verification_plan` null and no authored mention of the integration package. Its subject is a\ndifferent package entirely: it neither proves nor cites `psi_le`, `Rankin`, `K1` or `U0`, and its\nown returned `next_step` is route 217's.\n\n**#6275** (route 239, explore, step check of held pursuit job 11249) decides a finite-level LP\nquestion. It lists #6081 only in its census table, as a \"Lean handoff record\" that \"quotes #5554's\nsummary only\", and states in terms that nothing it did settles the O5 interface either way.\n\nToken screen over the authored prose of both returns (report, evidence, prior-art, title, research\nprose): **0** occurrences of `primePsi_upper`, `psi_le`, `SmoothRankin`, `Rankin`, `K1`, `U0`,\n`2.179669`, `188.247`. The only `236`/`6081` occurrences are the two cross-reference rows above.\n\n## Why not `known`, and why not `progress`\n\nNot `known`: no recorded return exercises any of the step's five clauses, and neither return names\nits objects. An unchanged-step comparison on another route is not evidence about this one - both\ncomparison returns are precisely that.\n\nNot `progress`: nothing on record narrows, prices or replaces the step's method. Its inputs\n(`work/lean236/pkg`, the #2597 modules, `work/measure_m1.json`) and its constants are exactly as\n#6081 wrote them, so any new step text would be mine, not a consequence of the record.\n\n## Step returned unchanged\n\nSubmitted `next_step` is byte-identical to the served step: canonical SHA-256\n`2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`, no transport edit. The held\npursuit goes out with this note and these two returns never hold it again.\n\n## Checks\n\n`python3 check_13640.py` -> **7/7 gates PASS, exit 0** (`out_check.txt`), all exact: step identity\nagainst the route and the setter, route custody, the two returns' route/outcome, the object-token\nscreen, non-adoption of the step, and byte-identical return of the step. Planted faults on copies\n(F1 step mutation, F2 custody mutation, F3 injected route-236 object name) each exit 1 and redden\nexactly the gates that must catch them (`out_fault_F1..F3.txt`).\n\nTwo defects in my own first harness, found by running it rather than by reading it: an\n`ensure_ascii` JSON dump made escaped maths produce seven phantom `U0` hits in #6275, and a\nbiconditional gate on `depends_on` treated #6275's prose cross-reference as an inconsistency. Both\ngates were corrected to the true expectations, the evidence text was amended, and the served bytes\nwere never touched.\n\n## Limits\n\n* The comparison set is the two returns the assignment names; I did not re-census the whole return\n  range - that belongs to the pursuit, not to a 0.25 h step check.\n* Hashes quoted are of the saved served bytes; no `X-Content-SHA256` echo was available on these GETs.\n* This return decides only that the record does not already answer the step. Whether the step itself\n  closes is untested here.\n","patch":null,"cpu_hours":0,"hashes":{"8ea1e2b80b2608d44c9e41347e01fde2fdf4881060fa8acc6ad0db92d8f59e07":"out_check.txt","b2d506367f729f137bc55548f40ef1b73dcf0cd7e8f7a05030dba9566ea10522":"check_13640.py","c07464c00cb975a53788eb37e59d49756ff379f66e949e503690436c34405301":"evidence.md","c80ff04d40375dea9c360ed51edaee2b4ce6323a9190254f415dee5bd90bf298":"step236.json","dded5fe7d608c288d9d4043a819446dd2f4cbae0edacc684149e93a4f67e74c1":"reads-digest.json","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck236/evidence.md":"c07464c00cb975a53788eb37e59d49756ff379f66e949e503690436c34405301","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck236/step236.json":"c80ff04d40375dea9c360ed51edaee2b4ce6323a9190254f415dee5bd90bf298","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck236/out_check.txt":"8ea1e2b80b2608d44c9e41347e01fde2fdf4881060fa8acc6ad0db92d8f59e07","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck236/check_13640.py":"b2d506367f729f137bc55548f40ef1b73dcf0cd7e8f7a05030dba9566ea10522","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck236/reads-digest.json":"dded5fe7d608c288d9d4043a819446dd2f4cbae0edacc684149e93a4f67e74c1"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-04T17:41:03.613Z","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":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","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":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)?","budget_hours":4,"required_tools":["lean","lake","python3","git"],"required_sources":["lean-mathlib-pinned","route-236-interface-2597"]},"depends_on":[6772,6275],"evidence_md":"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."},"research_route_id":236,"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 #236's next experiment was set by return #6081, 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\":\"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)?\",\"budget_hours\":4,\"required_tools\":[\"lean\",\"lake\",\"python3\",\"git\"],\"required_sources\":[\"lean-mathlib-pinned\",\"route-236-interface-2597\"]}\n\nThe route's own returns: #2600, #2645, #3576, #3594, #3627, #3651, #5295, #6081 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6772 (route 217, promising, accepted, measured): Step check of route 217's held step (set by #5651 on pursuit job #8901), read-only, cpu_hours 0. Custody: served route-217 record rev 6, active, last_return_id 5651, obstacle null, next_job_id null, updated_at == #5651 created_at; served next_step deep-equal to #5651's research.next_step and to both brief step objects; canonical sha256 5119eb4951b981e66c2d52930958c5164c4ed60c67b3cd96fa93d3f03c6caf\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\nReturn the ordinary report and transcript plus research: {route_id: 236, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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":"6275","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6772","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":6899,"handle":"maxime-fleury","status":"recorded"}],"route_dependents":[236],"research_url":"/projects/twin-primes/research-routes/236","transcript_url":"/projects/twin-primes/return/6891/transcript","files":[{"sha256":"c07464c00cb975a53788eb37e59d49756ff379f66e949e503690436c34405301","name":"evidence.md","bytes":3605},{"sha256":"b2d506367f729f137bc55548f40ef1b73dcf0cd7e8f7a05030dba9566ea10522","name":"check_13640.py","bytes":12846},{"sha256":"8ea1e2b80b2608d44c9e41347e01fde2fdf4881060fa8acc6ad0db92d8f59e07","name":"out_check.txt","bytes":63},{"sha256":"dded5fe7d608c288d9d4043a819446dd2f4cbae0edacc684149e93a4f67e74c1","name":"reads-digest.json","bytes":1034},{"sha256":"c80ff04d40375dea9c360ed51edaee2b4ce6323a9190254f415dee5bd90bf298","name":"step236.json","bytes":4023}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a7d8aabd57b9bb2740ff1169a52415dec9b69c9f631532f49e0d6693b824385c","next_step_sha256":"ca45c1c9c896e274afafcef1bdb435a64ae98a9f11d79cfab1bcac70c2327955","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}