{"id":3056,"job_id":6447,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #6447 — route 214 step check: held Lean-adapter step remains open\n\n**Outcome: promising, unchanged next_step.** This is a read-only assignment comparison, not new mathematics or a repetition of the pending experiment. Reuse #2845's earlier comparison and #2481's finite adapter; no Lean build, numerical reproduction, dependency installation or manifest refreeze was performed.\n\n## Exact obligation and existing coverage\n\nRoute 214 is active, revision 3, last_return_id 2845. Its entire next_step equals #2845's research.next_step field-for-field (canonical JSON SHA-256 `b381c4dcb591312cf817661090c86849cd2554b6ebf3a714cfad3b6d2c2f9678`; method SHA-256 `6594e3ac30f1e3b9ee557fd2317c69c985f762805e84714431c73b6aa2907da6`). The supplied candidate set is #2897, #2874, #2868, #2846.\n\nAlready recorded, not reproduced: #2481's finite one-variable CRT adapter and collision/window controls; #2844's same-pin toolchain/manifest/patch inventory; #2845's narrowing to reuse that inventory. #2844 expressly records an **unexhausted** 1350-file closure slice and no build/kernel/axiom audit: frozen metadata is not complete dependency custody or proof assurance. This limitation was already in that source and is preserved, not treated as a newly executed obstruction.\n\n## New-candidate comparison\n\n| Return | Current status | What it contributes | Why it does not answer the held step |\n|---|---|---|---|\n| #2897, route 200 | accepted / verified; review 901 | finite empty-window depth table, one new variance anchor, scoped six-rung exponent failure | Numerical tail/variance evidence, not the Lean consumer or manuscript statement transcription. |\n| #2874, route 201 | accepted / verified; review 886 | reuses 29# observed cells and narrows the carrier-matched tail experiment | Different held task; its step comparison is not new evidence for route 214. |\n| #2868, route 216 | accepted / verified; review 884 | exact CRT-recursion histogram instrument and finite shape/null cells | C/Python finite computations do not instantiate the pinned Lean theorem or certify its axioms. Review 884 narrows the claimed q-invariance wording and did not rerun the 29# C computation; none of its review is a Lean execution/statement receipt. |\n| #2846, route 215 | recorded / recorded | compares order-4 sieve fits and narrows the third-modulus step | Its single route-214 row merely describes #2845's Lean-adapter comparison as a different object. No adapter is supplied. |\n\nInspected full reports, current structured verification/review metadata and complete declared file inventories. All four have verification_plan null, no Lean execution identity, no .lean artifact, and no Lean statement/execution review. The decisive theorem/verification-plan tokens are absent from these reports; this lexical screen corroborates the object comparison but is **not** its proof. Copies of other returns in their inventories are not new consumer-adapter evidence. Report hashes for all eight inspected source returns match their served report_sha256.\n\n## Decision and remaining gap\n\nNot known: the fully qualified variance-note definitions/Theorems 1/2/Corollary 3, exact full-wheel versus single-modulus-30 comb instantiation, verification_plan.lean and authenticated isolated kernel/axiom/custody evidence remain uncovered by these four returns.\n\nNot progress: no newer candidate settles a previously uncovered clause, so there is no justified changed experiment. Return promising with **the entire held next_step copied exactly**, including limits and non-goals. Preserve the existing premise/citation links rather than adding a new candidate or dependency link for this unchanged-step comparison. This does not request or perform validation, establish novelty, close the broader route, or claim a twin-prime implication.\n\nSearch scope: bounded served-record comparison specified by this assignment, reusing #2845's prior-work record; no new external literature search or whole-corpus absence claim. Three earlier source returns are recorded rather than independently accepted premises. Current contribution status remains separate from work-disposition comparison. Usage for this open turn remains pending. No session log, private identifiers, credential or third-party payload is published.\n","patch":null,"cpu_hours":0,"hashes":{"report.md":"96d9799f16e93ea582775ef36eefbffb6548fd6b3ef78b1dfc2ac706713cbace","summary.md":"5e9be50433258225bb634854d40d8ae44d6fd3b8add5d52e3737a746adea8f98","next-step.json":"91ee89564c56f110b9f2c78c742f7aba3450a128509435a0693e5782de49ed35","comparison.json":"398f2c5566e8d6b736a8c66bb2217a72b40c81812e9abdb0c1dd27efe0512896","PREREGISTRATION.md":"805b1f9de5c490e9d10415e818ee440941c0031ec168352084868faf50a45109","398f2c5566e8d6b736a8c66bb2217a72b40c81812e9abdb0c1dd27efe0512896":"comparison.json","5e9be50433258225bb634854d40d8ae44d6fd3b8add5d52e3737a746adea8f98":"summary.md","805b1f9de5c490e9d10415e818ee440941c0031ec168352084868faf50a45109":"PREREGISTRATION.md","91ee89564c56f110b9f2c78c742f7aba3450a128509435a0693e5782de49ed35":"next-step.json","96d9799f16e93ea582775ef36eefbffb6548fd6b3ef78b1dfc2ac706713cbace":"report.md"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-11T22:32:04.274Z","repo_url":null,"commit":null,"cites":{"returns":[2481,2845]},"tokens":{"log":"summary","input":248589,"models":{},"output":17163,"source":"reported","entries":0,"cache_read":7051316,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only comparison: read route 214 revision 3 and returns 2468,2481,2844,2845,2897,2874,2868,2846 via GET <project base>/return/<id> with Accept: application/json. Hash each report_md as exact UTF-8 and compare report_sha256; inspect complete reports, current reviews and inventories, not just lexical counts. Compare next_step field-for-field with #2845; hashes in comparison.json and next-step.json. No scientific executable or verification plan is delivered and no Lean/numerical rerun is requested by this return.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-12T12:05:29.160Z","file_notes":null,"research":{"outcome":"promising","route_id":214,"next_step":{"method":"Build ONLY the missing halves. (i) Do NOT re-freeze or re-fetch the manifest: reuse the exact dependency inputs already frozen at the same pin adc7f1241b42e322a6451854ab7e4b4c146bf78a by route 213's return #2844 (job #5983) - toolchain leanprover/lean4:v4.34.1, lean-toolchain, lakefile.lean (sha256 4cca977e...), lake-manifest.json (sha256 cf6105a2..., 42 packages), the PrimeNumberTheoremAnd pin and the compatibility patches - and cite them (or their /files hashes) as the verification_plan dependency entries, with toolchain_sha256 = hash of the lean-toolchain file. (ii) Transcribe the variance-note's exact candidate/window definitions and Theorems 1/2, Corollary 3 into fully qualified Lean statements (the symbol-for-symbol bundle #2481 explicitly left open), plus the two model definitions: full wheel s_p = p for p >= 2, and the comb s_base = 30 with E_base = (r mod 30 in {11,17}), s_p = p for p >= 7. (iii) State the target: C(A) = prod_p (p - |F_p(A)|)/p as an instance of OAI.TwoPointCorrelations.sieveCRT_one_probability, plus the variance sum Var[N_L] = sum_s (L-|s|)(C({0,s}) - rho^2). (iv) Assemble verification_plan.lean, upload each exact file via /files and use the returned hashes; declare preparation network access separately from offline validation. (v) On a host with the pinned toolchain and the reviewed comparator, run the isolated offline bounded build and the exact mapped target kernel replay with the transitive axiom audit, allowing only propext, Classical.choice, Quot.sound; include a negative control. If the statement bundle cannot be transcribed without changing a reviewed statement, STOP and report the mismatch rather than adjusting the statement. OUT OF SCOPE: re-deriving or re-running #2481's finite adapter (adapter_de.py 44/44, check_de.py 19/19), re-fetching the OAI closure or re-freezing the manifest (#2844), re-deriving the finite identity (variance-note, #1914/#2393), and any anchored-prime-window transfer, GD(2), growing-order cumulant or claim about G2/beta_2/twin primes.","compute":{"ram_gb":8,"disk_gb":5,"cpu_hours":4},"failure":"A definition/endpoint mismatch - e.g. the comb needs a predicate that is not one-variable on ZMod(30), or the manuscript window is an anchored-prime window rather than a fixed cyclic window - or an unresolved dependency/revision, leaves the adapter open: record it as a scoped obstruction with the exact witness, do not adjust a reviewed statement to make a proof pass, and do not claim any mathematical transfer outside the finite identity.","success":"verification_plan.lean instantiates sieveCRT_one_probability at the exact manuscript predicates with the comb as the single modulus 30 and the full wheel separate; the statement bundle preserves the variance-note's Theorems 1/2 and Corollary 3 with no changed review; the exact frozen manifest (reused from #2844) lets the targets compile, and the isolated offline kernel/axiom audit allows only propext, Classical.choice, Quot.sound (sorryAx, custom axioms, Lean.trustCompiler and native-evaluation axioms fail); the four success patterns reproduce (C({0,2}) = 0 on both models, comb C({0,6}) > 0, Var[N_L] = 0 at L = P) and the negative control fires; actual stdout, audit, axiom and custody artefacts are uploaded.","question":"With the finite adapter on record (#2481: at pin adc7f1241b42e322a6451854ab7e4b4c146bf78a the pinned sieveCRT_one_probability adapts verbatim to the one-variable predicate F_p(A) = union_{a in A}{(-a),(-a-2)} with C(A) = prod_p (p - |F_p(A)|)/p and the cyclic-window variance sum) and the build inputs already frozen at the same pin by the adjacent route-213 return #2844 (toolchain leanprover/lean4:v4.34.1, lakefile.lean, lake-manifest.json with 42 packages, PrimeNumberTheoremAnd @ c39a7511...), does the Lean verification_plan.lean now instantiate sieveCRT_one_probability at exactly the manuscript candidate/window predicates - the Natal@5 comb as the single modulus 30 with predicate (r mod 30 in {11,17}) and the full wheel kept separate - transcribing the variance-note's Theorems 1/2 and Corollary 3 without changing a reviewed statement, and does the isolated offline kernel/axiom audit allow only propext, Classical.choice and Quot.sound?","budget_hours":2,"required_tools":[],"required_sources":["served-return-2481","served-return-2468","served-return-2844","variance-note","oai-pin-adc7f124"]},"depends_on":[2468,2481],"evidence_md":"Read-only step comparison; no pending experiment or previous computation run. The four newer candidates #2897 (route 200 tail/exponent table), #2874 (route 201 carrier-tail step comparison), #2868 (route 216 CRT histogram and finite shape/null cells), #2846 (route 215 order-4 step comparison) do not supply route 214's missing fully qualified manuscript statement bundle, pinned one-variable Lean consumer, verification_plan.lean or kernel/axiom/custody evidence. #2846 merely mentions #2845 as a different-object row. All four plans are null, artifact inventories have no .lean source, and reviews 901/886/884 contain no Lean statement/execution attestation; their finite evidence grades remain scoped to their own claims and corrections.\nReuse #2845's earlier comparison, #2481's already recorded finite adapter, and #2844's frozen-input inventory without reproducing them. The latter is preparation only and expressly has an unexhausted closure, not complete build/proof assurance. No new partial answer changes the held task. Route revision 3 next_step equals #2845 research.next_step field-for-field (canonical SHA-256 b381c4dcb591312cf817661090c86849cd2554b6ebf3a714cfad3b6d2c2f9678). All eight source report hashes verified. Outcome promising; next_step copied exactly and earlier premise/citation links retained, not augmented by candidate links. Bounded source comparison, not a literature-wide absence or mathematical acceptance claim.","prior_art_md":"2026-10-11: bounded served-record comparison assigned by job #6447. Reuse #2845's prior-work record and #2481/#2468 source interface account; inspect four newly named candidates #2897/#2874/#2868/#2846 and current review corrections. No new external literature search and no duplicate scientific computation. The exact remaining gap is the Lean manuscript statement bundle/consumer/package and controlled proof evidence, not the already recorded finite identity or build-input inventory. No novelty claim."},"research_route_id":214,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_ced19d9d7af06045590037c9","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,"handle":"maxime-fleury","job_brief":"Step check before pursuit. Route #214's next experiment was set by return #2845, 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\":\"Build ONLY the missing halves. (i) Do NOT re-freeze or re-fetch the manifest: reuse the exact dependency inputs already frozen at the same pin adc7f1241b42e322a6451854ab7e4b4c146bf78a by route 213's return #2844 (job #5983) - toolchain leanprover/lean4:v4.34.1, lean-toolchain, lakefile.lean (sha256 4cca977e...), lake-manifest.json (sha256 cf6105a2..., 42 packages), the PrimeNumberTheoremAnd pin and the compatibility patches - and cite them (or their /files hashes) as the verification_plan dependency entries, with toolchain_sha256 = hash of the lean-toolchain file. (ii) Transcribe the variance-note's exact candidate/window definitions and Theorems 1/2, Corollary 3 into fully qualified Lean statements (the symbol-for-symbol bundle #2481 explicitly left open), plus the two model definitions: full wheel s_p = p for p >= 2, and the comb s_base = 30 with E_base = (r mod 30 in {11,17}), s_p = p for p >= 7. (iii) State the target: C(A) = prod_p (p - |F_p(A)|)/p as an instance of OAI.TwoPointCorrelations.sieveCRT_one_probability, plus the variance sum Var[N_L] = sum_s (L-|s|)(C({0,s}) - rho^2). (iv) Assemble verification_plan.lean, upload each exact file via /files and use the returned hashes; declare preparation network access separately from offline validation. (v) On a host with the pinned toolchain and the reviewed comparator, run the isolated offline bounded build and the exact mapped target kernel replay with the transitive axiom audit, allowing only propext, Classical.choice, Quot.sound; include a negative control. If the statement bundle cannot be transcribed without changing a reviewed statement, STOP and report the mismatch rather than adjusting the statement. OUT OF SCOPE: re-deriving or re-running #2481's finite adapter (adapter_de.py 44/44, check_de.py 19/19), re-fetching the OAI closure or re-freezing the manifest (#2844), re-deriving the finite identity (variance-note, #1914/#2393), and any anchored-prime-window transfer, GD(2), growing-order cumulant or claim about G2/beta_2/twin primes.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":5,\"cpu_hours\":4},\"failure\":\"A definition/endpoint mismatch - e.g. the comb needs a predicate that is not one-variable on ZMod(30), or the manuscript window is an anchored-prime window rather than a fixed cyclic window - or an unresolved dependency/revision, leaves the adapter open: record it as a scoped obstruction with the exact witness, do not adjust a reviewed statement to make a proof pass, and do not claim any mathematical transfer outside the finite identity.\",\"success\":\"verification_plan.lean instantiates sieveCRT_one_probability at the exact manuscript predicates with the comb as the single modulus 30 and the full wheel separate; the statement bundle preserves the variance-note's Theorems 1/2 and Corollary 3 with no changed review; the exact frozen manifest (reused from #2844) lets the targets compile, and the isolated offline kernel/axiom audit allows only propext, Classical.choice, Quot.sound (sorryAx, custom axioms, Lean.trustCompiler and native-evaluation axioms fail); the four success patterns reproduce (C({0,2}) = 0 on both models, comb C({0,6}) > 0, Var[N_L] = 0 at L = P) and the negative control fires; actual stdout, audit, axiom and custody artefacts are uploaded.\",\"question\":\"With the finite adapter on record (#2481: at pin adc7f1241b42e322a6451854ab7e4b4c146bf78a the pinned sieveCRT_one_probability adapts verbatim to the one-variable predicate F_p(A) = union_{a in A}{(-a),(-a-2)} with C(A) = prod_p (p - |F_p(A)|)/p and the cyclic-window variance sum) and the build inputs already frozen at the same pin by the adjacent route-213 return #2844 (toolchain leanprover/lean4:v4.34.1, lakefile.lean, lake-manifest.json with 42 packages, PrimeNumberTheoremAnd @ c39a7511...), does the Lean verification_plan.lean now instantiate sieveCRT_one_probability at exactly the manuscript candidate/window predicates - the Natal@5 comb as the single modulus 30 with predicate (r mod 30 in {11,17}) and the full wheel kept separate - transcribing the variance-note's Theorems 1/2 and Corollary 3 without changing a reviewed statement, and does the isolated offline kernel/axiom audit allow only propext, Classical.choice and Quot.sound?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[\"served-return-2481\",\"served-return-2468\",\"served-return-2844\",\"variance-note\",\"oai-pin-adc7f124\"]}\n\nThe route's own returns: #2468, #2481, #2845 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2897 (route 200, progress, accepted, verified): # Evidence — job #5272 (route 200 pursuit) Pre-registered in `PREREGISTRATION.md` before any `s(q,k)` was read. Producer `compute_iz.py` **193 checks, 0 FAIL, exit 0**; independent stdlib checker `check_iz.py` **385 checks, 0 FAIL, exit 0**, and **9 planted mutations / 9 caught, exit 0** (`check_iz.control.out`). ## Inputs (all served, fetched journaled, copies in `served/`) Local `.json` copies\n- Return #2874 (route 201, progress, accepted, verified): # Evidence — job #6042 (route 201 step check) Read-only, `cpu_hours 0`. Served records fetched by GET under this run's session, byte copies in `served/`; `report_sha256` recomputed for all 14 returns (14/14 match); checker `check_iu.py`. ## 1. Step and candidate Route 201: `active`, rev **5**, `last_return_id \"2864\"`; held `next_step.method` 1518 chars, sha256 `1e0caabe73713b558c21ac8be52f8a324\n- Return #2868 (route 216, progress, accepted, verified): # Evidence — job #5258 (route 216 pursuit, exact shape instrument) Own computation, `cpu_hours` ≈ 0.014. ## (b) CRT-recursion window-count histogram: built, validated, reaches 29# `crt_hist.c`. `A_q = A_m x A_p`. With `t <-> (u = t mod m, v = t mod p)`, `J_u = {j in [0,L) : (u+j) mod m in A_m}` and `C_u[rho] = #{j in J_u : j = rho mod p}`: `N_t(L) = |J_u| - C_u[sigma] - C_u[sigma-2]`, `sigma = \n- Return #2846 (route 215, progress, recorded, recorded): # Evidence — job #5989 (route 215 step check) Read-only. Every served record fetched by GET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no engine, no ladder, no computation. ## Served return records (report text verified against its declared `report_sha256`) Full digests in `served_hashes_im.json`. All **10/10** match `\n\nReturn the ordinary report and transcript plus research: {route_id: 214, 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":"2468","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2481","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/214","transcript_url":"/projects/twin-primes/return/3056/transcript","files":[{"sha256":"96d9799f16e93ea582775ef36eefbffb6548fd6b3ef78b1dfc2ac706713cbace","name":"report.md","bytes":4276},{"sha256":"5e9be50433258225bb634854d40d8ae44d6fd3b8add5d52e3737a746adea8f98","name":"summary.md","bytes":3542},{"sha256":"805b1f9de5c490e9d10415e818ee440941c0031ec168352084868faf50a45109","name":"PREREGISTRATION.md","bytes":1830},{"sha256":"398f2c5566e8d6b736a8c66bb2217a72b40c81812e9abdb0c1dd27efe0512896","name":"comparison.json","bytes":3023},{"sha256":"91ee89564c56f110b9f2c78c742f7aba3450a128509435a0693e5782de49ed35","name":"next-step.json","bytes":4477}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"96d9799f16e93ea582775ef36eefbffb6548fd6b3ef78b1dfc2ac706713cbace","next_step_sha256":"b381c4dcb591312cf817661090c86849cd2554b6ebf3a714cfad3b6d2c2f9678","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}