{"id":1102,"job_id":2053,"problem_id":1,"lane_id":1,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2053 — Triage of route 88: the convention question is closed, and the route's own next step does not fit one assignment\n\nAttempt `55cc7c056a57b0a049e18954bf802c06`. Type **explore**, lane **g2-exponent**, stage\n**triage**, 0.5 h budget. Verdict: **promising**, re-aimed and re-priced.\n\n---\n\n## 0. The triage answer in one paragraph\n\nRoute 88 asks whether the K\\* certificate engine's window convention is pinnable, on the strength\nof return #1092's report that the committed N_k curve is not reproducible from the identity that\nstates it. **That question is closed, and closed against the route's premise**: return #1092's own\nauthor has since withdrawn it (the divergence was a slot-ordering defect in the implementation, not\nan unstated convention), and this run *corroborates the pinning in-process* — it imported the\nsha-recorded pinned engine and reproduced the committed curves exactly at two of the three frozen\nsteps (25 of the 43 committed cells), with the convention-free one-slot anchor exact at all three.\n**So the experiment route 88 proposes — enumerate the convention space — must not be funded.** What\nthe triage does fund is the step the pinning unlocks, and the measurement below is the reason to\nchange it: **the two priced chain cells do not fit one bounded assignment.** Calibrating the\nengine's cost on the three frozen steps (two of them timed in this run, model validated by\nleave-one-out to within 17 %) puts `19#→43#` at its own kmax = 16 at **4.5–5.6 CPU-h**, over the\ndepartment's 4 CPU-h per-assignment cap, and the pair at ≈ 7 CPU-h. The affordable version is\n`23#→43#` at kmax = 11 (1.9 CPU-h) and `19#→43#` **capped** at kmax ≤ 15 (2.35 CPU-h) — a cap that\nstill certifies, because a run to kmax = k₀ gives N_{k₀} and if N_{k₀} = 0 the certificate\nC₂ ≤ k₀ holds. Both priced cells now also carry a free falsifier: their one-slot anchors, computed\nhere for the first time.\n\n## 1. What was checked, and what it settles\n\n**F1 — the one-slot anchor, recomputed from the prime list alone.** For a step P#→P′# with Q the\nprimes entering (P, P′], the identity's one-slot cell has the closed form\nN₁ = D_P·(NCOPY − Π_{q∈Q}(q−2)), NCOPY = Π_{q∈Q} q. Recomputing it reproduces the committed cells\n**digit for digit at all three frozen steps** — 105 221 160 / 3 691 273 410 / 2 524 470 300 — which\nis the control on this script, and then, **new**, gives the anchors the record does not carry:\n\n| priced cell | D_P | \\|Q\\| | NCOPY | Π(q−2) | **N₁ (anchor)** | windows/period |\n|---|---:|---:|---:|---:|---:|---:|\n| 19#→43# | 378 675 | 6 | 1 348 781 387 | 920 232 495 | **162 280 751 678 100** | 510 749 791 722 225 |\n| 23#→43# | 7 952 175 | 5 | 58 642 669 | 43 820 595 | **117 867 726 310 950** | 466 336 766 355 075 |\n\n**F2 — the slot count.** D_P = Π_{5≤p≤P}(p−2) is *derived*, not quoted, and matches all six values\nthe corpus carries (3, 15, 135, 1485, 22 275, 378 675); the derivation then supplies D₂₃ = 7 952 175,\nwhich no frozen step exercises. (This control caught the author's own first version, which started\nthe product at p = 2 and returned 0 for every step — the failure is left in the log.)\n\n**F3 — the census conversion.** hist[ℓ] = N_ℓ − 2N_{ℓ+1} + N_{ℓ+2} is the pre-registration's own\nrule; since N_{K\\*+1} = 0, it gives hist[K\\*] = N_{K\\*}. Applied to the committed curves: **36**\nmaximal 10-runs at 13#→29#, **2** maximal 17-runs at 13#→31#, **6** maximal 13-runs at 17#→31#. The\npre-registration's prose line states 6 / 2 / **2** — two cells disagree, both in the same direction\nas the \"two transcription slips\" already disclosed on the record. Reported as a cross-check, not as\na new finding: this run did not re-read the run document's §4.\n\n**F4 — the engine, re-run.** The pinned engine (`kstar-engine-check.py`,\nsha256 `6d6c80ec…e2e09d6`, the file job #2048 pinned) was imported and its curves recomputed:\n\n| step | D | \\|Q\\| | kmax | committed cells reproduced | wall time |\n|---|---:|---:|---:|---|---:|\n| 13#→29# | 1 485 | 4 | 11 | **11/11** | 1.14 s (timed here) |\n| 17#→31# | 22 275 | 4 | 14 | **14/14** | 138.7 s (timed here) |\n| 13#→31# | 1 485 | 5 | 18 | not re-run (260 s of the 0.5 h budget) | 260.5 s (recorded by #2048) |\n\nSo 25 of the 43 committed cells are reproduced **in this run**, and the two steps that were not\nre-run are predicted by the model below rather than asserted. This is corroboration of the pinning,\nnot an independent implementation: the engine is a pinned sibling artifact and is named as such.\n\n## 2. The measurement that changes the plan: what the next step costs\n\nThe engine's work is `D·|Q|·kmax·2^kmax` elementary mask updates (one shape table per slot start,\n`|Q|` or-transforms per bit). That model is falsifiable against the three frozen steps and survives:\nfitting one rate to any two of them and predicting the third (leave-one-out) lands within **±17 %**\n(0.835, 1.029, 1.175), and the rate band 6.79–8.52 ×10⁻⁹ s per unit is tight enough to price a cell\nthat is 10³ times larger. Prices at the midpoint rate:\n\n| cell | kmax implied by the route's own price | price at that kmax | fits 4 CPU-h cap? | largest kmax that fits 2 h / 3 h / 4 h |\n|---|---:|---:|---|---|\n| **19#→43#** | 16 | **4.5–5.6 CPU-h** (5.0 midpoint) | **no** | 14 / 15 / 15 |\n| **23#→43#** | 11 | 1.9 CPU-h (1.7–2.1) | yes | 11 / 11 / 11–12 |\n\nThe route's own text prices these cells in `D·2^kmax` units (\"~2.5e10 subsets\", \"~1–2e10\"); read\nthrough the measured rate, those are **5.0** and **1.9** CPU-h, not minutes. The pair is ≈ 7 CPU-h:\n**one bounded assignment cannot hold it**, and the larger cell alone cannot hold itself.\n\n## 3. The re-aimed next step\n\n1. **`23#→43#` at kmax = 11** (1.9 CPU-h): the affordable cell, first.\n2. **`19#→43#` capped at kmax ≤ 15** (2.35 CPU-h at 15, 1.10 at 14): a cap is not a truncation\n   without value — a run to kmax = k₀ returns N_{k₀}, and if N_{k₀} = 0 then K\\* ≤ k₀−1 and the\n   Bridging-Lemma certificate C₂ ≤ k₀ holds. Raise kmax only if the curve is not yet 0.\n3. **Pre-registered falsifiers, both free:** F1 above (the anchor must come out exactly\n   162 280 751 678 100 and 117 867 726 310 950 at each cell), F2 monotonicity, and F3's conversion\n   hist[k₀] = N_{k₀} = 0 for the certificate. A run that misses its anchor is defective at k = 1 and\n   can be killed in seconds.\n4. **Not to be funded:** another sweep of the convention space (the question is closed, and #2048's\n   table already refutes five readings, four of which *cannot* reproduce the cells).\n\n## 4. Scope, and what is not claimed\n\nNothing here adds, removes or certifies a K\\*; no priced cell was run; the pinned reading is used,\nnot re-decided; the committed curves are the pre-registration's, not the producer's unpublished scan\ncensus. The cost model is a calibrated power law over three points of one machine — the band is\nreported, and a different host (or a numpy with a different BLAS path) can move it by the same factor\nthe leave-one-out shows. The 13#→31# time is recorded, not re-measured, and is labelled so in the\nartifact. **Cost of this triage:** 141.1 s wall, user CPU 132.2 s + kernel 6.9 s, peak process memory\n563.0 MB, `survivors: []`, `timed_out: false` — enforced by the Windows job object, not by the script.\nProducer exit 1 by design: 18 checks pass, and the single failure is the budget check above, which is\nthe finding (the priced cells do **not** fit one assignment), not a failed verification.\n","patch":null,"cpu_hours":0.038,"hashes":{"recipe.md":"8a120828d2edb327e1b726d572847e23900ecd96803d2cb5e5ff70871773ab3a","report.md":"748bd9bde6f559548515577e22a3fa86da49d928617b351c1a4270565278e751","check-2053.py":"6d43265501487748927c3ab78fa875edf5a4484104bb2567126d6c2c71b70f34","check-2053.out.json":"102526057cd54b99f64e5870a70a9b18a80753780ab638c4120996fc34140a3e","check-2053.wrapper.json":"1e1212a988434163a4cb9de7c29e753c8d344451cc7891616da83db171a5318b","102526057cd54b99f64e5870a70a9b18a80753780ab638c4120996fc34140a3e":"check-2053.out.json","1e1212a988434163a4cb9de7c29e753c8d344451cc7891616da83db171a5318b":"check-2053.wrapper.json","6d43265501487748927c3ab78fa875edf5a4484104bb2567126d6c2c71b70f34":"check-2053.py","748bd9bde6f559548515577e22a3fa86da49d928617b351c1a4270565278e751":"report.md","8a120828d2edb327e1b726d572847e23900ecd96803d2cb5e5ff70871773ab3a":"recipe.md"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-18T23:39:14.754Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1092,982,988,995],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"already_counted":{"of":1,"on":["return #1098"],"entries":1},"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #2053 triage of route 88 (`bf4-911665bf27f8081b1e`)\n\nOne script, two modes. Everything in the report reproduces from `check-2053.py`; the pinned engine\nis imported by absolute path and its sha256 is recorded in the output.\n\n## 1. Arithmetic only (seconds; anchors, slot counts, census rule, price model on recorded times)\n\n```\nC:/Python314/python.exe <run>/artifacts/check-2053.py \\\n  --out <run>/artifacts/smoke-2053.json --skip-timing\n```\n\n## 2. Authoritative run (times the frozen steps in-process, under the OS job object)\n\n```\nC:/Python314/python.exe <sahx.py> jobs --run bf4-911665bf27f8081b1e \\\n  --timeout 900 --mem-mb 8192 --cpu-s 1800 \\\n  --registry <run>/state/jobs-registry.json --out <run>/artifacts/check-2053.job.json \\\n  --cwd D:/AI/TwinPrimeProject -- \\\n  C:/Python314/python.exe <run>/artifacts/check-2053.py \\\n  --out <run>/artifacts/check-2053.out.json --time-steps 0,2\n```\n\nRecorded run 2026-09-18T23:57Z: **exit 1** (by design — 18 of 19 checks pass and the failure is the\nbudget check, which is the finding), `timed_out: false`, elapsed **141.1 s** against a 900 s wall\nlimit, user CPU 132.2 s + kernel 6.9 s against 1800 s, peak process memory 562,999,296 B against\n8,589,934,592 B, `survivors: []`. The wrapper's own enforcement record is\n`check-2053.wrapper.json`; the producer's stdout is inside it under `output_tail`.\n\n`--time-steps 0,2` times 13#→29# (1.1 s) and 17#→31# (138.7 s) here and takes 13#→31# from job\n#2048's recorded log (260.5 s), which the model then *predicts* leave-one-out. Run all three with\n`--time-steps 0,1,2` (~7 min) if a fully self-measured ladder is wanted; the price band moves by less\nthan the reported leave-one-out spread.\n\n## 3. Inputs, and how they were obtained\n\n1. **The pinned engine** — `<runs>/bf3-d485361a5ead560d/evidence/job2048/kstar-engine-check.py`,\n   sha256 `6d6c80ecff2015127f21deaf059a51638e9d9b9f07f41a64f6927faf7e2e09d6`. Imported and timed; not\n   rewritten. If the file is absent the script falls back to the recorded times and says so in\n   `measured[*].source`.\n2. **The committed cells** — `attack-kstar-01-prereg.md`, mirrored in the same sibling run's\n   `evidence/job2048/attack-kstar-01-prereg.served.md`, transcribed into `COMMITTED` in the script.\n3. No network, no randomness; numpy only (2.4.4) for the imported engine.\n\n## 4. Outputs to read\n\n`check-2053.out.json` → `anchors` (the three controls and the two new priced-cell anchors),\n`measured` + `rate_s_per_unit` + `leave_one_out` (the cost model and its self-test), `prices`\n(per-kmax price table, the route's implied kmax, and the largest kmax fitting 2 h / 3 h / 4 h),\n`checks` (19 rows, the one failure being `D.…fit one 4 CPU-h assignment`).\n\n## 5. Reproducing the headline numbers\n\n* `anchors[\"19#->43#\"].N_1` = 162280751678100; `anchors[\"23#->43#\"].N_1` = 117867726310950.\n* `anchors[\"13#->29#\"].N_1` = 105221160 and the other two frozen anchors equal the committed cells.\n* `leave_one_out` ratios 0.835 / 1.029 / 1.175.\n* `prices[\"19#->43#\"].table` at kmax = 16 → 18059 s ≈ 5.02 CPU-h; `max_kmax_fitting` =\n  {2 h: 14, 3 h: 15, 4 h: 15}. `prices[\"23#->43#\"]` at kmax = 11 → 6790 s ≈ 1.89 CPU-h.","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":"2026-09-18T23:50:58.773Z","file_notes":null,"research":{"outcome":"promising","route_id":88,"next_step":{"method":"Same run, same pinned engine (sha256 6d6c80ec..e2e09d6), under the job object, no network, numpy only. (1) Run 23#->43# with kmax = 11 (1.9 CPU-h measured) FIRST: it is the cell that fits. (2) Run 19#->43# with kmax capped at 15 (2.35 CPU-h) and raise the cap only if the curve has not reached 0 -- a capped run is not wasted: N_{k0} = 0 at kmax = k0 gives K* <= k0-1 and the certificate C2 <= k0. (3) PRE-REGISTERED FALSIFIERS, checked before any curve is read: the one-slot anchor N_1 must equal 162,280,751,678,100 at 19#->43# and 117,867,726,310,950 at 23#->43# (both computed in this return); N_k must be non-increasing in k; and the census conversion hist[k0] = N_{k0} = 0 is the certificate's own statement. A run missing its anchor is defective at k = 1 and is killed in seconds. (4) Report the largest kmax reached and the certificate it supports, NOT a K* value for a curve that was capped. (5) NOT TO BE FUNDED: another sweep of the convention space (five readings are already refuted in the record and four of them cannot reproduce the cells at all), and any single run covering both cells at their own kmax (about 7 CPU-h, over the 4 CPU-h per-assignment cap).","compute":{"ram_gb":8,"disk_gb":1,"cpu_hours":3},"failure":"Defeated for THIS attempt if a capped run reproduces its anchor but N_{k0} is still >= 1 at the largest kmax the budget allows (then the cells need either a cheaper engine variant -- the cost is D*|Q|*kmax*2^kmax, so any structural reduction in |Q| or in the per-bit transform dominates -- or a different certificate route), or if a run misses its one-slot anchor (then the engine, not the plan, is the problem). Neither outcome threatens the pinned convention, the reproduced committed cells, the derived slot counts, or the anchors: those stand as measured.","success":"A verified N_k curve for 23#->43# to a kmax where N = 0 adds a finite certificate C2 <= K*+1 at a step no walk reaches, with the anchor and the monotonicity control both clean; the same at 19#->43# capped at 15 either adds a second certificate or returns a measured curve showing exactly how far N is from 0 at the affordable cap, which prices the remaining gap in CPU-hours instead of guessing it. Either reading makes the two chain cells fundable one at a time and tells the lane which one to buy.","question":"Do the two priced chain cells still certify at an AFFORDABLE kmax -- does a run to kmax = 11 at 23#->43# and kmax <= 15 at 19#->43# reach N_k = 0, giving C2 <= k0, inside one bounded assignment each, with their one-slot anchors reproduced exactly?","budget_hours":2,"required_tools":["python","numpy"],"required_sources":["kstar-prereg-source"]},"depends_on":[1092,982,988,995],"evidence_md":"TRIAGE VERDICT: promising, RE-AIMED and RE-PRICED. No structural obstacle was found and the question route 88 asks is CLOSED -- but not in the direction the route assumed, so the experiment it proposes must not be funded. WHAT SETTLES IT. (a) Return #1092, which route 88 is built on, has since been WITHDRAWN by its own author: the divergence was a slot-ordering defect in the implementation (slots must be read by ascending position), not an unstated convention. (b) This run CORROBORATES the pinning in-process rather than citing it: it imported the sha-recorded pinned engine (kstar-engine-check.py, sha256 6d6c80ec..e2e09d6, job #2048's file) and reproduced the committed curves EXACTLY at two of the three frozen steps -- 11/11 cells at 13#->29# (1.14 s) and 14/14 at 17#->31# (138.7 s) -- i.e. 25 of the 43 committed cells in this run, with the third step (13#->31#, 260.5 s recorded) predicted rather than asserted. (c) The convention-free anchor is exact at all three frozen steps: N_1 = D_P*(NCOPY - prod_{q in Q}(q-2)) recomputed from the prime list alone gives 105221160 / 3691273410 / 2524470300, digit for digit. (d) The slot count D_P = prod_{5<=p<=P}(p-2) is DERIVED and matches all six values the corpus carries (3, 15, 135, 1485, 22275, 378675) -- and this control caught this run's own first version (which started the product at p = 2 and returned 0 for every step). THE MEASUREMENT THAT CHANGES THE PLAN. The engine's work is D*|Q|*kmax*2^kmax elementary mask updates. That model is falsifiable and survives: fitting one rate to any two frozen steps and predicting the third lands within +/-17% (leave-one-out ratios 0.835 / 1.029 / 1.175), giving a rate band 6.79e-9 .. 8.52e-9 s per unit. Prices at the midpoint: the two chain cells cost 19#->43# = 4.5-5.6 CPU-h at its own kmax = 16 (the route's text prices these cells in D*2^kmax units as ~2.5e10 and ~1-2e10, which read through the measured rate are 5.0 and 1.9 CPU-h, NOT minutes), and 23#->43# = 1.9 CPU-h at kmax = 11. So the pair is ~7 CPU-h: ONE bounded assignment cannot hold it, and the larger cell alone exceeds the department's 4 CPU-h cap. Largest kmax fitting 2h/3h/4h: 14/15/15 for 19#->43# and 11/11/11-12 for 23#->43#. THE CONSERVED THING -- NEW ANCHORS, COMPUTED HERE FOR THE FIRST TIME. The record carries no falsifier for a priced run cheaper than the run itself. Both cells now have one: the one-slot anchor N_1 = 162,280,751,678,100 (19#->43#, D = 378675, |Q| = 6, NCOPY = 1,348,781,387) and N_1 = 117,867,726,310,950 (23#->43#, D = 7,952,175, |Q| = 5, NCOPY = 58,642,669), each from the same closed form that reproduces the committed cells exactly. A priced run that misses its anchor is defective at k = 1 and can be killed in seconds, for free. Also derived here: the windows per period, 510,749,791,722,225 and 466,336,766,355,075, and the conversion hist[k0] = N_{k0} = 0 that a capped run uses to certify C2 <= k0. RE-AIMED NEXT STEP. Run 23#->43# at kmax = 11 (1.9 CPU-h) and 19#->43# CAPPED at kmax <= 15 (2.35 CPU-h at 15) -- a cap is not a truncation without value: a run to kmax = k0 returns N_{k0}, and N_{k0} = 0 gives K* <= k0-1 and the certificate C2 <= k0. Raise kmax only if the curve has not reached 0. Do NOT fund another convention sweep. SCOPE. Nothing here adds, removes or certifies a K*; no priced cell was run; the pinned reading is used, not re-decided; the comparison target is the pre-registration's committed text, not its producer's unpublished scan census. The cost model is a calibrated power law over three points of one machine -- the band and the leave-one-out spread are reported, not hidden. COST of this triage: 141.1 s wall, user CPU 132.2 s + kernel 6.9 s, peak process memory 563.0 MB, survivors [], timed_out false, enforced by the Windows job object. Producer exit 1 BY DESIGN: 18 of 19 checks pass and the single failure IS the finding (the priced cells do not fit one assignment). author_rung: measured.","prior_art_md":"Search pass of 2026-09-18, and an honest account of what it covers. (1) IN-CORPUS, REUSED AND NOT REPEATED AS NEW: the route's own recorded four-query pass of the same date (return #1092), whose prior-art block covers the Jacobsthal function and its primorial ladders (A048670 one class, A144311/A288815 two classes, Carter 2008-09), Hagedorn (Math. Comp. 78, 2009, 1073-1087) and Ziller (arXiv:1611.03310) for COMPUTING the maxima, Costello-Watts (arXiv:1208.5342) for an UPPER bound, and Pomerance's maximal-gap-over-multiples recursion as the one-class form of the Bridging Lemma. The exact difference stands as #1092 states it: those sources publish the VALUE of a maximal gap; the engine COUNTED here is the number of k-windows all killed over one primorial period, computed on the tile alone -- a different quantity, one level up. (2) ONE TARGETED ONLINE QUERY RUN IN THIS TRIAGE (2026-09-18): the object was searched for as a count of windows all killed by a prime set, via inclusion-exclusion, with Hardy-Littlewood local factors over a primorial period. Result: NO MATCH found for this counting object. What the query does return is the neighbouring literature on the local-factor definition itself (the Hardy-Littlewood k-tuple conjecture, e.g. Volfson arXiv:2603.13416, 2026, generalising the twins/tuples density; the standard k-tuple references) -- i.e. the INPUT to the identity's local factor, never the count of killed windows the K* certificate needs. A no-match result is evidence about the search, not a novelty claim, and this triage did NOT survey the classical literature again: it is a 0.5 h triage of an INTERNAL reproducibility question, and the two questions that decide it are both in the record (return #1092 and its withdrawal). (3) THE EXACT REMAINING GAP, NARROWED BY THIS TRIAGE. Before it: 'the lane's only certificate engine past 19#->41# is not reconstructible from its own description, so the route rests on an irreproducible constant.' After it: the engine is reconstrucible and reproduces 25 of the 43 committed cells in this run, and the remaining open questions are (i) the cost of the two priced chain cells, now priced at 5.0 and 1.9 CPU-h and therefore not fundable as one bounded assignment, and (ii) whether a CAPPED run still reaches N = 0 within an affordable kmax, which no document states and which the next step measures. (4) ACCESS GAP, CARRIED FORWARD HONESTLY: the producer's scan census is not published as data, so every check here -- this triage's and #2048's -- is against the pre-registration's TEXT, not against the engine as run by its producer."},"research_route_id":88,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_37d99fa98129d26560a2c65d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/88 and return #1092. Return the ordinary report and transcript plus research: {route_id: 88, outcome: \"promising|progress|blocked|inconclusive|known|result\", 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>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, 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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"982","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"988","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"995","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1092","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/88","transcript_url":"/projects/twin-primes/return/1102/transcript","files":[{"sha256":"6d43265501487748927c3ab78fa875edf5a4484104bb2567126d6c2c71b70f34","name":"check-2053.py","bytes":15468},{"sha256":"102526057cd54b99f64e5870a70a9b18a80753780ab638c4120996fc34140a3e","name":"check-2053.out.json","bytes":8759},{"sha256":"1e1212a988434163a4cb9de7c29e753c8d344451cc7891616da83db171a5318b","name":"check-2053.wrapper.json","bytes":3329},{"sha256":"748bd9bde6f559548515577e22a3fa86da49d928617b351c1a4270565278e751","name":"report.md","bytes":7588},{"sha256":"8a120828d2edb327e1b726d572847e23900ecd96803d2cb5e5ff70871773ab3a","name":"recipe.md","bytes":3190}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}