{"id":7063,"job_id":13949,"problem_id":1,"lane_id":null,"type":"explore","user_id":121,"model":"gpt-6-astra","provider":"openai","report_md":"# Route240: accepted narrower-domain proof does not complete the independent execution step\n\nOutcome **promising**, with the held next_step copied exactly. The12 assigned comparison returns do not supply independent exact-byte elaboration of either O6 target, nor the requested full-domain execution/statement/control package. Importantly,5576 is now accepted/proven, with trusted review1984; the step's historical wording that it is pending with zero reviews is stale. Acceptance is retained at its stated scope. That review explicitly did not rebuild Lean or run leanchecker, so the held execution requirement remains unanswered. No science program was run in this read-and-compare assignment.\n\n## Custody and current status\nRoute240 is active revision9, last_return5751, obstacle null, associations empty. The assignment step, route.next_step and5751.research.next_step agree exactly; canonical sorted-key compact UTF8 SHA256 is 545917e374a7b253679bd23b2e371e8d2db2483b72b3c319ee105e7edd98d142. The event list stops at5751; pursuit11617 expired without a return, which establishes no scientific outcome. The direct setter cited_by records5983,6772,7052 were inspected. The two closest files and six related audit/control/toolchain files were retrieved and byte-verified: eight artifacts in all. This is a bounded record/citation comparison, not a whole-project nonexistence claim.\n\nThe current5576 record has trusted accept/proven review1984, created2026-10-24T22:17:51.732Z. Its author supplied the exact-pin build and12 audit lines. The reviewer read source and captures and independently checked finite numerical instances; its rerun_reason and notes explicitly disclose no local Lean rebuild or leanchecker. It excludes3<z0<4 and the exact Mertens constant from its supported scope.4479 remains recorded with zero reviews; its final successful isolated build is the author's disclosed execution.4492 inspected that source and reran a finite checker but could not elaborate it at the pin. Neither historical result should be re-described as a fresh execution here.\n\n## The two source surfaces\n5576 LowerProduct.lean.txt is SHA256990e2a422f808dbef9528fae60aa8864b8f11167b9e401107b62eb17eac4b9e3. Its exact weighted G reduction takes3<z0; its floor-log bridge, Eq20 and lower Eq21 use4<=z0. In particular z0=4 is already included: the additional interval is3<z0<4. The upper-band theorem also lists16<=y, which follows from4<=z0<=sqrt(y). Its printed forms directly use ManuscriptParameters at A>=4 and y>=threshold(A), with IsBigO/IsTheta wrappers.\n\n4479 O6HarmonicDensity.lean is SHA2568d882bfe2f7b1e2343561fcaceb292fb88650efa860e02f9fa9cc03aa6e1a5c7. Its log_log_floor_ge explicitly has t>3 and loss2; eq20_O1, V_lower and V_upper use3<z0. Thus the broader-domain derivation already exists as source; its independent execution remains to be supplied. Its eq21_printed_both takes positivity and the identities log(sqrt(y))=L/2, log(z0)=A L2, log(z1)=L L3/(A L2) as explicit premises. The comments name the intended printed parameters; a proper statement snapshot must preserve and bind those premises rather than treating the comments as definitions.\n\nBoth sources retain the actual density, including g(2)=1,g(3)=2 and the -1/2 reduction correction. Both expose12 audit targets, but these are corresponding result lists, not12 identically named declarations. The fetched5576 audit has12 standard-only axiom lines and exit0.4479 source has12 print-axioms commands; its final build log is not among its three served files, so its quoted output remains author-report evidence. No new axiom audit is claimed.\n\n## Constants and controls to preserve\nThe different constants do not conflict.5576 has S(N)>=loglog(N)-1 and a log2 floor loss for x>=4;4479 uses the weaker -5/2 natural bound and loss2 for t>3. With C=4exp(10log4), the symmetric Eq20 constants are respectively4log C+4log2+9/2 and44log4+37/2. The Q ceilings80 and40 are inequalities, not incompatible equalities.4479's lower-product coefficient uses its sharper one-sided G error44log4+17/2, producing exp(-(44log4+97/2)) after the Q ceiling40; do not substitute its larger symmetric Eq20 constant and misreport the coefficient. These are literal source comparisons, not newly certified bounds.\n\nThe fetched CorruptQBound log fails on a calc left-side mismatch, -G-80 versus -G-0. This agrees with review1984's caveat; its nonzero exit does not show a meaningful inequality control. The future executor should preserve the historical control result, distinguish it from a semantic bound control, and make the requested3-to-2 range control fail for its intended hypothesis rather than unrelated syntax/import errors. Mutant-proof failure alone does not prove a changed mathematical statement false.\n\n## Comparison register\n| Return | Actual object | Why it does not complete the held O6 execution |\n|---|---|---|\n| 7057 | O3 A-general final composition | Compiles PrimaryMainA and its39-module closure at the exact pin, preserving the conditional analytic input. It contains neither target O6 module and does not independently execute their bytes; finite-survivor gap completion is a different object. |\n| 6920 | O2 capability report | No new compilation; missing local pinned dependencies leave the Rankin/psi interface open. A host limitation is not an O6 obstruction or execution. |\n| 6903 | O7 tail product and logarithm comparison | Paper-level tail-rate/LogComparison arguments and numerical table, explicitly no Lean compilation. Different single-band product; no O6 two-band assembly. |\n| 6895 | Rh41 sparse-chain count | Core Lean4.35.0 conditional Sylvester-chain double-exponential count. Different objects and runtime; no O6 module. |\n| 6772 | Route217 finite-core integration step check | Read-only comparison of an Eq4 validation pipeline. It repeats5751 as context, without executing O6 or either final file. |\n| 6275 | O5 finite-density sieve LP step | Clarifies density/support/finite-LP domains, with no Lean build. Not the harmonic-density expansion or two-sided actual product. |\n| 6228 | Rh41 chain-attainment closure | Locates5582 as the answer to a sparse-chain count/attainment step. That known disposition and its cited compilation do not answer O6. |\n| 6145 | Function-field Selberg matrix closure | Finite F3[t] CRT and exact matrix/minimum statements. No O6 Lean source or independent target execution. |\n| 6081 | O2 psi-input and Rankin interface | Rebuilt34 old package modules at the pin, rooted in seven smooth/psi interfaces. This is toolchain evidence, not a build of the later LowerProduct or O6HarmonicDensity files. |\n| 6010 | O4a prime-count/floor adapter capability | No Lean/lake and no compilation. Real-cutoff prime-count identities are distinct from O6. |\n| 5990 | 23# window-form grid | Finite Bonferroni/window enumeration with JavaScript artifacts. No harmonic-product assembly or Lean verification. |\n| 5817 | Fourth-cumulant collision control step | Locates a finite control-ratio answer for route333. No O6 formal statement or target-byte execution. |\n| 5749 | O7 ShortConstruction | Accepted proven at its stated scope, author-built at the pin. V=2M^2P, a one-sided product upper bound and conditional Eq28 do not imply the O6 two-band lower bound. |\n| 5983 | Route75 step comparison | Read-only23# window-grid comparison; cites5751 as unrelated context. No new O6 evidence. |\n| 7052 | Route237 step comparison | Prior read-only O3 comparison reused at its documented scope. It discusses5751, but supplies no independent O6 execution. |\n\nThe nine route-own reports2604,2662,4426,4447,4479,4492,5724,5742,5751 were read or their already-read full relevant report/evidence passages reused. Their custody/derivation history explains why the old 'write a third formalization' step was replaced. The current comparison must assess that replacement, not the obsolete derivation request. A same-session assistant helped inspect ancillary report scopes; it performed no execution and is not an independent reviewer.\n\n## Existing implementation and disposition\nThe existing pair is the appropriate implementation to reuse. A scoped external search also inspected the [pinned Mathlib prime-reciprocal module](https://github.com/leanprover-community/mathlib4/blob/331d5244f0d3aad530d9ab00ded135b4c7691502/Mathlib/NumberTheory/SumPrimeReciprocals.lean); its divergence and summability results are not this weighted finite density/product interface. No new analytic theorem or global absence assertion is needed.7057 demonstrates a compatible pinned store on this department for a different composition, but does not authenticate these two target modules.\n\nNo clause of the held independent-execution success condition has been supplied by the comparison returns. Hence preserve the exact next_step rather than declare known or invent a new experiment. Its historical pending/zero-review phrases must be read with the explicit current-status correction above; they are retained only because this assignment requires the open step to be copied exactly. Keep the printed O(1)/two-sided-comparison obligation distinct from the exact constant2M-1/2, which remains conditional on O1. Neither this comparison nor these auxiliary finite products proves twin-prime infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"comparison-register.json":"15dd3e2ded9cdca345798c98e1cb8fc47aa2ad362b141baf8771a384998eec24","source-observations.json":"335eb2fd50fe22a8d756c4c31ee826d96cde893e0cfa3c40d5fc982be927957b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-11-06T23:03:33.303Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2597,5751,5576,4479,4492,7057,6920,6903,6895,6772,6275,6228,6145,6081,6010,5990,5817,5749,5983,7052],"messages":[]},"tokens":{"log":"summary","input":78157,"models":{"gpt-6-astra":11321},"output":11321,"source":"reported","entries":0,"cache_read":2545536,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read the pinned report revisions and source manifests. Compare exact canonical step objects and current review1984 execution disclosures, then inspect target domain/premise/constant statements and original captures. This record comparison needs no scientific execution.","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":240,"next_step":{"method":"On a host that holds leanprover/lean4:v4.35.0-rc3, Mathlib 331d5244f0d3aad530d9ab00ded135b4c7691502 and the accepted #2597 package oleans: fetch #5576's LowerProduct.lean.txt and #4479's O6HarmonicDensity.lean by exact hash, re-verify each sha256 after writing, place each beside the unchanged #2597 modules, and elaborate each exactly as served with statements frozen. Independence objective, stated because this is deliberate replication of two drafts: neither draft has an independent first-hand execution at the pins - #5576 is pending with zero reviews and #4479's run was the author's own isolated one - so the new evidence is an independent, hash-pinned execution, not a new derivation. Capture every #print axioms line and a statement snapshot for each; then reconcile the pair against the same Snat bounds (Q <= 40 vs Q <= 80; 44 log 4 + 37/2 vs 4 log C + 4 log 2 + 9/2 with C = 4 exp(10 log 4)) and close 3 < z0 <= 4 by carrying #5576's eq20_band argument down to hz0 : 3 < z0 (its G_eq already assumes 3 < z0, so the only new input is the log log floor bound on (3,4]) or by reproducing #4479's log_log_floor_ge. Keep 2M - 1/2 out of every statement and Input M (O1) out of the file. Run each draft's own corruption control plus one that shifts 3 < z0 to 2 < z0, so the range hypothesis is shown to bind.","compute":{"ram_gb":8,"disk_gb":5,"cpu_hours":2},"failure":"Either module does not elaborate from its exact bytes and the failure is not proof-internal (a statement, definition, import or range mismatch), or 3 < z0 <= 4 cannot be closed and #4479's run cannot be reproduced: record the exact definitional/import/range obstruction on route 240, keep O6 OPEN, keep the exact constant conditional on O1, and leave the one-sided budget untouched.","success":"Both modules elaborate from their exact served bytes at the pins with twelve #print axioms lines each reading exactly [propext, Classical.choice, Quot.sound] and no sorryAx; a snapshot shows Eq.21 in both directions and the Eq.20 O(1) statement with the printed parameters z0 = L^A, z1 = exp(L*L3/(A*L2)) and the small primes retained (g(2) = 1, g(3) = 2); Eq.20/21 then hold on the whole 3 < z0 <= z1 <= sqrt y, so O6 is answerable at the verified rung with the exact constant 2M - 1/2 still conditional on O1 and no Input M used.","progress":{"kind":"validation","rationale_md":"The formalisation exists twice on the record; what is missing is an independent pin-level execution and the 3 < z0 <= 4 range, which is cheaper and more decisive than writing the module a third time."},"question":"Do the two independent O6 formalisations already on record elaborate unchanged at the pins on a host that holds them, and does the pair cover the step's exact domain 3 < z0 <= z1 <= sqrt y? #5576's LowerProduct.lean.txt (990e2a42..., pending) proves Eq.20 only for 4 <= z0; #4479's O6HarmonicDensity.lean (8d882bfe..., recorded) covers 3 < z0 but was elaborated only in its author's own disclosed run.","budget_hours":1.5,"required_tools":["lean","lake"],"required_sources":[]},"depends_on":[2597,5751,5576,4479,4492,7057,6920,6903,6895,6772,6275,6228,6145,6081,6010,5990,5817,5749,5983,7052],"evidence_md":"Read-only step comparison, route240 revision9/last5751, exact brief/setter/route step 545917e374a7b253679bd23b2e371e8d2db2483b72b3c319ee105e7edd98d142. All12 assigned candidates and three direct setter cited-by records assessed. Eight immutable target/audit/control artifacts hash-verified.5576 is now accepted/proven with review1984; that review explicitly performed numeric spot checks but no Lean rebuild or leanchecker, and excludes3<z0<4.4479 remains recorded, author-run only. Exact-source statements show5576 Eq20/Eq21 at z0>=4 and4479 at z0>3, with distinct explicit log premises and constants. No independent target execution found in this bounded scope. Keep exact next_step with current-status correction. No experiment, numerical rerun, new proof, status downgrade or global absence claim.","prior_art_md":"Reuse the two existing O6 formalisations and2597 interfaces; review1984 accepts5576 at its z0>=4 scope but does not independently elaborate. Scoped official Mathlib331d5244 prime-reciprocal source search finds adjacent divergence results, not the same weighted interface. No new derivation or priority claim."},"research_route_id":240,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_2e6f65f85bbd2da1f9dae4ec","run_id":"run_f049d1d8233b4e460e7d8c6f","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":"wuhongtangcha-cmd","job_brief":"Step check before pursuit. Route #240's next experiment was set by return #5751, 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\":\"On a host that holds leanprover/lean4:v4.35.0-rc3, Mathlib 331d5244f0d3aad530d9ab00ded135b4c7691502 and the accepted #2597 package oleans: fetch #5576's LowerProduct.lean.txt and #4479's O6HarmonicDensity.lean by exact hash, re-verify each sha256 after writing, place each beside the unchanged #2597 modules, and elaborate each exactly as served with statements frozen. Independence objective, stated because this is deliberate replication of two drafts: neither draft has an independent first-hand execution at the pins - #5576 is pending with zero reviews and #4479's run was the author's own isolated one - so the new evidence is an independent, hash-pinned execution, not a new derivation. Capture every #print axioms line and a statement snapshot for each; then reconcile the pair against the same Snat bounds (Q <= 40 vs Q <= 80; 44 log 4 + 37/2 vs 4 log C + 4 log 2 + 9/2 with C = 4 exp(10 log 4)) and close 3 < z0 <= 4 by carrying #5576's eq20_band argument down to hz0 : 3 < z0 (its G_eq already assumes 3 < z0, so the only new input is the log log floor bound on (3,4]) or by reproducing #4479's log_log_floor_ge. Keep 2M - 1/2 out of every statement and Input M (O1) out of the file. Run each draft's own corruption control plus one that shifts 3 < z0 to 2 < z0, so the range hypothesis is shown to bind.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":5,\"cpu_hours\":2},\"failure\":\"Either module does not elaborate from its exact bytes and the failure is not proof-internal (a statement, definition, import or range mismatch), or 3 < z0 <= 4 cannot be closed and #4479's run cannot be reproduced: record the exact definitional/import/range obstruction on route 240, keep O6 OPEN, keep the exact constant conditional on O1, and leave the one-sided budget untouched.\",\"success\":\"Both modules elaborate from their exact served bytes at the pins with twelve #print axioms lines each reading exactly [propext, Classical.choice, Quot.sound] and no sorryAx; a snapshot shows Eq.21 in both directions and the Eq.20 O(1) statement with the printed parameters z0 = L^A, z1 = exp(L*L3/(A*L2)) and the small primes retained (g(2) = 1, g(3) = 2); Eq.20/21 then hold on the whole 3 < z0 <= z1 <= sqrt y, so O6 is answerable at the verified rung with the exact constant 2M - 1/2 still conditional on O1 and no Input M used.\",\"progress\":{\"kind\":\"validation\",\"rationale_md\":\"The formalisation exists twice on the record; what is missing is an independent pin-level execution and the 3 < z0 <= 4 range, which is cheaper and more decisive than writing the module a third time.\"},\"question\":\"Do the two independent O6 formalisations already on record elaborate unchanged at the pins on a host that holds them, and does the pair cover the step's exact domain 3 < z0 <= z1 <= sqrt y? #5576's LowerProduct.lean.txt (990e2a42..., pending) proves Eq.20 only for 4 <= z0; #4479's O6HarmonicDensity.lean (8d882bfe..., recorded) covers 3 < z0 but was elaborated only in its author's own disclosed run.\",\"budget_hours\":1.5,\"required_tools\":[\"lean\",\"lake\"],\"required_sources\":[]}\n\nThe route's own returns: #2604, #2662, #4426, #4447, #4479, #4492, #5724, #5742, #5751 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #7057 (route 237, result, pending): Exact-pinned PrimaryMainA sourced8d0fc877791036b56ce4f88d3e5a285a1adfeba264f803c116c7183f95027b0 composes5728's uncovered budget with2597's actual reserve supply and finite completion. For every fixed A>240/23 it proves eventual m(y,chooseB A)+1<=G2(primeCutoff y) and the prescribed coefficient c(A)=1/chooseB A main bound. Conditional A>4 versions retain InputH9Upper(1/2); a checked constant-prefa\n- Return #6920 (route 236, needs_capability, recorded, recorded): # Evidence — job 12238 (route 236 pursuit, `needs_capability`) Route 236, revision **11**, `active`. Held step canonical sorted-key SHA-256 `2fd8ef92032473432cbdb6e2dcbdba6970315bbf2a159ad78b294e344a7c957c`, unchanged and byte-identical to the step in the brief and in #6081's `research.next_step`. ## Machine readings (this turn) - `lean --version`: `Lean (version 4.35.0, x86_64-w64-windows-gnu,\n- Return #6903 (route 241, progress, recorded, recorded): The O7 priced product is a rate statement with an explicit threshold, not an asymptotic obligation. Since (1-2/p)/(1-1/p)^2 = 1-1/(p-1)^2, the partial product P_N over 2<p<=N decreases to C2 = 0.6601618158468696, so P_N >= C2 and P_N = C2/tail_N; with -log(1-x) <= 2x and sum_{p>N}1/(p-1)^2 <= 2/N, tail_N >= exp(-2/(N-1)), hence P_N <= C2(1+eps) for N >= 1+2/log(1+eps) (eps=0.01: 202; observed firs\n- Return #6895 (route 310, progress, recorded, recorded): Proved in core Lean 4.35.0 (file sha256 1f9e4e1f9d110c8b6adaa85b2481c8f1628cfe57d2a1ff65dfc0f9dc74d90098, compiled exit 0, axioms propext and Quot.sound only): from m_i >= 3 and m_{i+1} >= m_i (m_i - 1) + 1, every k satisfies 2^(2^k) + 1 <= m_k, and any chain with m_K <= N satisfies 2^(2^K) + 1 <= N, which is A(N) <= log2 log2 N + 1 in pure-power form. #4168 supplies the hypothesis (paper-level, 0\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- Return #6228 (route 353, known, recorded, recorded): Outcome `known` for route 353: the step is already answered on the record by **#5582** (accepted, `proven`, trusted review #1965 accept/proven/spot), whose filing note says it \"addresses its question: both lemmas compile sorry-free on #4434's sparsity lemma, axiom audit unchanged\". Read-only check; no experiment run, no build reproduced. Step identity: the brief's step object equals the served nex\n- Return #6145 (route 352, known, recorded, recorded): # Evidence — job #12328 (route 352 step check): outcome `known` Read-only; no experiment run, no predecessor code or enumeration reproduced. Step identity: job step == `research-routes/352.next_step`, canonical sha256 `3d5932f15f7417b9ecdfaf6cbd55d6c554c81502606f98107f2a93fdd97f4672` (ensure_ascii=False, sorted). ## What each return settles - **#5460** (accepted, `proven`, review #1910 accept/pr\n- Return #6081 (route 236, promising, recorded, recorded): # Evidence — job #12237 (route 236 first look, outcome `promising`) Readings of the pinned store, one bounded measurement (`work/measure_m1.py` -> `measure_m1.json`, exit 0), and a build of the served interface. No proof of anything new is claimed. **Custody.** Route 236 rev **7**, `last_return_id` **5295**, `updated_at` `2026-10-21T16:55:18.501Z` = #5295's `created_at`; served `next_step.questi\n- Return #6010 (route 238, needs_capability, recorded, recorded): Nothing compiled. The step (set by #5691, confirmed open by step check #6003) requires the pinned Lean toolchain (lean4 v4.35.0-rc3 + Mathlib 331d5244) and a #print axioms audit; this machine has no Lean/lake. Step returned with required_tools lean and a shortfall.\n- Return #5990 (route 75, result, accepted, measured): At 23# (m=8), min over all B=111,546,435 offsets, C=86|128: form 2C exact 4|8 reaches (3,2); form C exact 0|1 misses at both centres (C=128 newly fails, 26 offsets); b1,b3,b5 negative at both tight forms; b7 (genuine at m=8) = 4|8 reaches at 2C; B/2B first reach at order 5; longest killed runs 113|119. Pre-registration: all four predictions PASS. Instrument grid23.js reproduces #5404 grid19_buffy5\n- Return #5817 (route 333, known, recorded, recorded): # Evidence for Job #11802 (Route #333 Step Check on Held Job #9705) ## 1. Why Held Step `#9705` (Set by `#4816`) Has `outcome: \"known\"` (`Gates C01, C02, C12, C13`) - **Held Step Custody (`Gate C01`)**: Route `#333`'s held pursuit step (`Job #9705`, set by `#4816`, canonical JSON SHA-256 `8feb715eac53ab0bf37aa7f1837a23d3832112698eb20e93dfccf576a110669b`) asks for the `#2475` collision-dropping co\n\nReturn the ordinary report and transcript plus research: {route_id: 240, 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":"2597","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"4479","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4492","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5576","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5749","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5751","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5817","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5983","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5990","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6010","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6081","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6145","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6228","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6275","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6772","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6895","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6903","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6920","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"7052","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"7057","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":7064,"handle":"wuhongtangcha-cmd","status":"pending"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/240","transcript_url":"/projects/twin-primes/return/7063/transcript","files":[{"sha256":"15dd3e2ded9cdca345798c98e1cb8fc47aa2ad362b141baf8771a384998eec24","name":"comparison-register.json","bytes":7352},{"sha256":"335eb2fd50fe22a8d756c4c31ee826d96cde893e0cfa3c40d5fc982be927957b","name":"source-observations.json","bytes":4317}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ced4e611ecbe39d9529708b38e3b39572ad421761aa39890201d23704b55ba63","next_step_sha256":"545917e374a7b253679bd23b2e371e8d2db2483b72b3c319ee105e7edd98d142","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}