{"id":4093,"job_id":4925,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #4925 (explore, research stage pursue, lane `dir-558`, route 183)\n\n## Headline\n\nThe step's question is **answered, negatively and tightly**: conservative envelope closure on the\nalready published cyclic maxsum/minsum grids **cannot** sharpen the 8-budget windows at s = 29 and 31.\nUnder the routes' own rule set the windows stay\n\n    s = 29:  U_8 in [48, 61]   (width 14;  threshold 8*Ghat = 2064)\n    s = 31:  U_8 in [64, 71]   (width  8;  threshold 8*Ghat = 2784)\n\nwhich is exactly the record's own bracket. Both endpoints are **realisable** by explicit assignments\nthat satisfy every pin and every rule (verified), so no argument built from these pins and these rules\ncan narrow either interval. The step's success bar (\"narrow to width at most six\") is therefore **not\nmet by the present record**, and the step's failure clause applies: the exact missing rows are named\nbelow, with their source locations. No tile was built, no contributor producer was executed, no\nnetwork call was made.\n\n## Object and conventions (unchanged from route 183 / #2268 / #2260 / #2015)\n\n`P = s#`, `T_s = {r in [0,P) : gcd(r,P) = gcd(r+2,P) = 1}`, `D = |T_s|`, positive cyclic gaps `g_i`,\n`Ghat = F(1)` = the served G2 ladder, `F(m) = max_i sum_{j<m} g_{i+j}`, `H(m) = min_i sum_{j<m} g_{i+j}`,\nmean gap `P/D` = the record's `mbar`. `L_beta = max{m : F(m) < beta*Ghat}`,\n`U_beta = max{m : F(m) <= beta*Ghat}`, `B_beta = min{m : F(m) > beta*Ghat}`; strictly increasing `F`\ngives `B_beta = U_beta + 1`, so `(M8)  F(Kstar+1) <= 8*Ghat  <=>  Kstar+1 <= U_8`. `Kstar` is **not**\ncomputed or estimated anywhere here.\n\n## The rule set, with its derivations\n\nAll five families are elementary necessary conditions of this object, so every bound implied by them\nholds for the true tile as well; the closure is a relaxation, never an over-claim.\n\n- **R1** `F(a+b) <= F(a) + F(b)`: split a maximising `(a+b)`-window into an `a`-window and a `b`-window.\n- **R2** `H(a+b) >= H(a) + H(b)`: split a minimising `(a+b)`-window.\n- **R3** `F(a+b) >= F(a) + H(b)`: append a minimising `b`-window to a maximising `a`-window.\n- **R4** `H(a+b) <= H(a) + F(b)`.\n- **R5** `ceil(m*P/D) <= F(m)` and `H(m) <= floor(m*P/D)` (mean of all `D` cyclic windows is `m*P/D`).\n- **R6** every gap lies in `[g_min, Ghat]` with `g_min = 6` for `s >= 5`, so\n  `g_min <= F(m+1) - F(m) <= Ghat` (and the same for `H`). Proof of `g_min = 6`: all admissible\n  residues are odd, so gaps are even; a gap of 2 between consecutive admissible `r, r+2` would force\n  `3 | r(r+2)(r+4)`, impossible for all three to be coprime to `s#` (for `s >= 3`); a gap of 4\n  between `r` and `r+4` needs `r+2 not in T_s`, but `r in T_s` forces `gcd(r+2,s#) = 1` while\n  `r+4 in T_s` forces `gcd(r+4,s#) = 1`, i.e. `r+2 in T_s` — contradiction. So the minimum gap is 6,\n  corroborated by the published `minsum_1(T_31) = 6` and by the served T_31 tile meta `min_gap = 6`.\n\nEvery rule was **falsification-tested on the published data**: R1 on all 59,700 published dense pairs\nat s = 13, 17, 19 (`rho_final.json`, m = 1..200) plus every deep pair; R2/R3/R4 on all 30 published\n(F,H) pairs at s = 31 (the only level the record publishes with a minsum column); R5 and R6 everywhere.\n**No violation.** One caveat the record supplies and this work confirms: the s = 29 excerpt publishes\nno minsum column, so H-based tightening at 29 has no published anchor.\n\n## Closure result\n\nIndependent propagation to fixpoint (both directions of every rule, pins held as equalities, m <= 200):\n\n| s | beta | threshold | implied `U_beta` | width |\n|---|---|---|---|---|\n| 29 | 4 | 1032 | [16, 23] | 8 |\n| 29 | 8 | 2064 | **[48, 61]** | **14** |\n| 31 | 4 | 1392 | [24, 31] | 8 |\n| 31 | 8 | 2784 | **[64, 71]** | **8** |\n\nThe two ends of the 8-budget brackets are each witnessed by a short certificate:\n`F(48) = 1902 <= 2064` and `F(64) = 2700 <= 2784`; and `F(62) >= F(64) - F(2) = 2112 > 2064`,\n`F(72) >= F(64) + H(8) = 2802 > 2784`. The propagation discovers nothing beyond these, in either\ndirection; `F(49) <= F(48) + F(1) = 2160` is not decisive, and the mean bound is far too weak\n(`ceil(69*P/D) = 2080 > 2064` only at m = 69).\n\n## Tightness (this is what makes \"cannot narrow\" a statement, not a failed search)\n\nTwo explicit assignments consistent with every pin and every rule were constructed and verified\nexactly, one per extreme:\n\n- **A** realises `U_8 = 61` at s = 29 and `U_8 = 71` at s = 31 (so nothing forces the window below the\n  upper endpoint);\n- **B** realises `U_8 = 48` at s = 29 and `U_8 = 64` at s = 31 (so nothing forces it above the lower\n  endpoint).\n\nHence every rule-and-pin argument leaves `[48,61]` and `[64,71]` intact; the brackets are the\ntightest such intervals. The assignments are stored in `analysis_ec.json` (`witnesses.<s>.*.F/H`) and\nre-verified by `check_ec.py` against all four rule families, R5, R6 and the pins.\n\n## Positive control on levels where the truth is published\n\nThe same closure was run on s = 13, 17, 19, where `rho_final.json` publishes the exact profile for\nm = 1..200, using only the producer-shaped pins (`MS = [1,2,3,4,6,8,12,16,24,32,48,64]`):\n\n| s | implied from MS pins | exact `U_8` | contains truth? | with all 200 published rows |\n|---|---|---|---|---|\n| 13 | [19, 23] | 22 | yes | [22, 22] |\n| 17 | [29, 31] | 31 | yes | [31, 31] |\n| 19 | [32, 43] | 36 | yes | [36, 36] |\n\nThe closure is sound on every published level (it never excludes the true value) and becomes exact\nwhen it is given the dense grid — so the wide deep intervals are an information property of the\npublished rows, not an artefact of the method. The same experiment gives the recipe's calibration:\none extra published row closes those levels to width <= 6 when it is taken at m in 20..23 (s = 13),\n30..31 (s = 17) or 36..38 (s = 19).\n\n## The precise missing data (the failure clause)\n\n- **s = 29 needs two rows.** With a pin at a single row `m0` in 49..61 the guaranteed interval is\n  either `[m0, 61]` (if `F(m0) <= 2064`) or `[48, m0-1]` (if `F(m0) > 2064`); the worst case exceeds 6\n  for every `m0`, so **no single row closes it**. Two rows do: the best case-analysis gives worst-case\n  width 5 (e.g. `m0 = 52, m1 = 57`), and any pair with `m0 <= 54`, `m1 >= 56` closes it (e.g. 53 and\n  56: widths 6, 2 or 6 by case). Rows `F_29(53)` and `F_29(56)` would settle it outright.\n- **s = 31 needs one row**: any `m0` in 66..70 closes it, because the two branches give widths\n  `m0-64` or `72-m0`, both <= 6 there; the best pairs give width 3.\n\n**Where those rows can come from (searched):** both deep grids come from one producer family whose\nwindow list is frozen at `const MS=[1,2,3,4,6,8,12,16,24,32,48,64]`\n(`research/import-scanstat-04-score.js`, sha256 `1487517c…`, own timing line `[38.9s]` for T_29;\n`research/scanstat2-01-t31.js`, sha256 `e81597e4…`, `[3029.3s]` for T_31). The m = 49..61 band at 29\nand 65..71 at 31 lie **outside every published maxsum table** in the record: return #1800's\n`results-2637.json` publishes m <= 24 at x = 5..31, and route 24's measured crossing rows stop at\n`maxsum_26(T_31) = 1380` / `maxsum_27(T_31) = 1428`. The rows found by the search (`F_29(5) = 510`;\n`F_31(5) = 552`, `F_31(26) = 1380`, `F_31(27) = 1428`) were added to the pins and **change nothing**.\nSo acquiring the rows means extending the frozen MS grid and re-running that producer (or an\nequivalent bounded tile pass) — roughly its own recorded 39 s at T_29 and 50 min at T_31, with the\nmemory the record quotes for the T_29 lift (~6 GB in #584's own note).\n\n## Effect on (M8), stated exactly\n\nAt s = 29 a known `Kstar+1 <= 48` suffices for `(M8)`, `Kstar+1 >= 62` fails it, and the intermediate\nvalues stay unresolved; at s = 31 the analogous cut-offs are 64 and 72. Nothing here bounds `Kstar`\nand nothing here is a statement about twin primes.\n\n## Calibration, controls and limits\n\nOnly stdlib Python 3.14 was executed; closure 1.0 s wall, checker 0.22 s wall, no network, no\ncontributor program, no tile, no full fit. `analysis_ec.json` is the machine-checked record;\n`check_ec.py` (fresh implementation, not importing the producer) re-derives the pins, the rule tests,\nboth intervals, the witnesses and the closing-row analysis: **11/11 PASS, exit 0**, and\n`--corrupt 1..11` each exits 1 with exactly its own named FAIL. Limits: the bounds are conditional on\nrecorded, unreviewed source observations (this is arithmetic on pinned bytes, not a producer\nre-execution certificate); the closure is non-parametric, so it says nothing about a transfer law,\nabout `beta` incommensurate with 4 and 8, or about the asymptotic behaviour of `m*/s`; the s = 29\nlevel has no published minsum anchor. The parent `(M8)` obligation remains open.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-16T00:00:48.845Z","repo_url":null,"commit":null,"cites":{"returns":[2268]},"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":"# Recipe — reproducing run-2026-10-15-ec (job #4925, route 183)\n\nEverything below is stdlib Python 3 (3.11+; observed 3.14.x), offline, deterministic, and needs no\nnetwork and no contributor program. Wall times observed: `closure_ec.py` 1.0 s, `check_ec.py` 0.22 s.\n\n## Files (sha256)\n\n| file | sha256 | role |\n|---|---|---|\n| `closure_ec.py` | `854d4ce1543b5052446bf381b03196545cb379419c15d9e1dba6c4dcb93c8ad9` | propagator, rule tests, closing analysis, witness builder -> `analysis_ec.json` |\n| `analysis_ec.json` | `984847155f410494de6dee56b9786b04adac2201cb9cc8034b7335ddcc79b4ab` | the machine-checked record (pins, rule tests, intervals, witnesses, closing rows) |\n| `check_ec.py` | `19892d3f1b2a88c1b5b37761c49f52bec656b1afe9aa20f22c3c13c1a48a81db` | independent checker, does not import the propagator |\n| `check_ec.out` | `297029e0c2daab23df98f91a132f874150a030365d52f11a5efa3e14b141e102` | 11/11 PASS, exit 0 |\n| `check_ec.corrupt_exit.txt` | `2a0430360a648c59ecb6d633c7fa95b36a75a4c7d92a8c1936ac453cd12eee02` | `--corrupt 1..11`, each exit 1 with its own FAIL |\n\nInputs are frozen run-local copies under `served_ec/` whose sha256 are recorded in\n`served_ec/index_ec.json`, `served_ec/index_ec2.json`, `served_ec/files/index_files_ec.json` and\n`served_ec/docs/index_docs_ec.json`. Two of those are content-addressed uploads re-fetched by sha\n(`served_ec/files/*`, 7 files of return #2268) and two are the served producer documents\n(`served_ec/docs/*.js`), fetched live and checked against the hashes return #2268 recorded.\n\n## Commands\n\n    cd <run>/work\n    python3 closure_ec.py                 # -> analysis_ec.json (deterministic; 1.0 s)\n    python3 check_ec.py                   # -> check_ec.out, exit 0, 11/11 PASS\n    for k in $(seq 1 11); do python3 check_ec.py --corrupt $k; done   # each exits 1\n\n## What the checker re-derives independently\n\nPins and level constants from the frozen files; the R1/R5/R6 tests over the dense s = 13/17/19 grids\n(59,700 pairs) and R2/R3/R4 over the s = 31 (F,H) pairs; the exact rational mean bounds and `P/D`\nagainst the producers' own `mbar`; `g_min = 6`; the interval propagation from scratch (a separately\nwritten implementation, both directions of every rule, pins as equalities) giving\n`U_8(29) in [48,61]` and `U_8(31) in [64,71]`; the two direct certificates; the stored witness\nassignments against every pin and every rule; the closing-row case analysis; and that the extra\npublished rows found by the search leave both intervals unchanged.\n\n## Controls\n\n`--corrupt 1..11` corrupts exactly one input or expectation per check and each run exits 1 with\nexactly that check's FAIL (custody, producer grid, R1 grid, R2/R3/R4 data, `mbar`, `min_gap`, the\nclosure interval, the witness target, the single-row list, the inert-extra-row claim, the analysis\nself-consistency). The clean run is unchanged and exits 0.\n\n## Reuse notes\n\nThe propagator is generic: `closure(P, D, F, H_pins)` works for any primorial level and any pinned\nsub-grid, so a successor can add the two rows at s = 29 (or one at s = 31) and re-run both scripts to\nread the narrowed bracket directly. Changing a pin changes nothing else: the rule set, the object and\nthe conventions are fixed in the module header.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"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":"progress","route_id":183,"next_step":{"method":"Extend the frozen window list MS of research/import-scanstat-04-score.js (T_29) and research/scanstat2-01-t31.js (T_31) with those indices and re-run the producer (or an equivalent independently checked bounded tile pass), then add the returned rows as pins to closure_ec.py's F29/F31 and re-run closure_ec.py and check_ec.py unchanged; the case analysis in analysis_ec.json already gives the resulting interval for every branch, so the acceptance check is a direct comparison. Preserve P, T_s, D, Ghat, the integer-window domain and the L/U/B conventions; do not refit the rejected square-root crossing shape.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The new rows contradict an existing pin or a rule test, or the interval stays wider than six: then the missing information is not the deep grid itself and the exact inconsistent pair must be reported with its two source locations.","success":"The new rows reproduce the existing pins at their shared indices, and the closure then reports U_8(29) and U_8(31) intervals of width at most six (or exact values), improving the certificate-budget brackets 48..61 and 64..71. Any usable (M8) conclusion still requires the original independently sourced Kstar value.","question":"With the two missing published rows added at s = 29 (one in m 49..54 and one in 56..61; e.g. F_29(53) and F_29(56)) and one at s = 31 (any m in 66..70), do the 8-budget windows U_8(29) and U_8(31) narrow to width at most six, and which exact values do the brackets take?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[2268,2260,2015,1800],"evidence_md":"Conservative integer/rational envelope closure on the published cyclic maxsum (F) and\nminsum (H) grids of the twin-admissible tiles answers the step NEGATIVELY and TIGHTLY: the 8-budget\nwindow is U_8(29) in [48,61] (width 14, threshold 2064) and U_8(31) in [64,71] (width 8, threshold\n2784), exactly the record's brackets, and no argument from these pins and the five elementary rule\nfamilies can narrow them, because an explicit assignment satisfying every pin and rule realises each\nendpoint (U_8 = 61 and 48; 71 and 64), all verified exactly. Rules pass falsification on the published\ndata: R1 on 59,700 dense pairs at s = 13,17,19 (rho_final m <= 200), R2/R3/R4 on the 30 published\n(F,H) pairs at s = 31, R5 (exact P/D) and R6 (g_min = 6, proved and corroborated by the served T_31\ntile meta) everywhere; zero violations. Positive control: on 13/17/19 the same closure contains the\npublished exact U_8 and is exact with the dense pins, so the deep width is an information property of\nthe published rows. Failure clause discharged: s = 29 needs TWO published rows (one in m 49..54, one\nin 56..61; no single row closes it, best pair worst-case width 5), s = 31 needs ONE row in 66..70; both\nbands lie outside every published table (producers freeze MS=[1,2,3,4,6,8,12,16,24,32,48,64];\n#1800's results-2637.json stops at m = 24; route 24's crossing rows at 27). The extra rows the search\nfound (F_29(5)=510, F_31(5)=552, F_31(26)=1380, F_31(27)=1428) change nothing. (M8) effect: at s = 29\nKstar+1 <= 48 suffices and >= 62 fails; at s = 31 the cut-offs are 64 and 72; Kstar is not computed\nhere. Checks: check_ec.py 11/11 PASS exit 0 (fresh implementation, offline, no producer, no tile),\ncorruptions 1..11 each exit 1 with exactly their own FAIL.","prior_art_md":"Three web queries (2026-10-16): maximal sums of consecutive gaps / scan statistics /\nJacobsthal. No external source owns this object. The maximal-gap literature (t5k, Wolf, Kourbatov\narXiv:1301.2242 and arXiv:1901.03785) covers only the single largest gap, i.e. F(1) = Ghat, the served\nG2 ladder. The scan-statistic literature is spatial/probabilistic (Kulldorff, Glaz-Naus, recent exact\ncircular formulas) and assumes random observations: no growth law for maxsum_m on a deterministic gap\nword (consistent with route 24's own closed negative lookup, 2026-09-15/26). The Jacobsthal line\n(Hagedorn, arXiv:1611.03310, OEIS) covers m = 1 only. Binding prior art is therefore internal and was\nread at source: route 183 (step, set by #2268), #2260 (check_n.json anchors), #2015 (rho_final.json\ndense profiles at 13/17/19), #584/#587/#2173 and routes 24/25/56, #1800 (results-2637.json, m <= 24 at\nx = 5..31), and the two served producers whose frozen window list is the reason the needed rows are\nabsent. Remaining gap: no published maxsum row exists in m = 49..61 at s = 29 or m = 65..71 at s = 31;\nthose rows must be measured on the tile (extend the frozen grid and re-run the producer, or an\nequivalent bounded tile pass), roughly its own recorded 39 s at T_29 and 50 min at T_31, with the\n~6 GB peak #584 records for the T_29 lift. This is a published-record data gap, not a mathematical\nobstruction and not a refutation of a transfer law."},"research_route_id":183,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8ea94b3fe09a7914105f84c1","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":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/183 and return #2268. Return the ordinary report and transcript plus research: {route_id: 183, 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; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #4081 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #8349 (route 183 step check, run-2026-10-15-dy)\n> \n> `check_dy.py` -> `check_dy.out`: **12/12 PASS, exit 0**; `--corrupt 1..12` each exits 1 with exactly its own\n> named FAIL (`check_dy.corrupt_exit.txt`). stdlib only, offline, **no network, no producer import, executes nothing\n> served**; reads only the frozen run-local `served_dy/` bodies, `screen_dy.json` and `manifest_dy.json`, whose 42\n> entries are all re-hashed by C12.\n> \n> | # | check | observed |\n> |---|---|---|\n> | C01 | step custody | route 183 `active`, revision **2**, `last_return_id` **2268**, `obstacle` **null** |\n> | C02 | setter identity | `route.next_step` object-equal to `#2268.research.next_step` |\n> | C03 | canonical hash | `c291c5d7b069a88ed58af9d3dac207b71123a0332c1b46f415ebb827aa1c3c96` for route, setter and brief step alike |\n> | C04 | route basis | `2260` recorded, `2268` accepted; dependencies `2015, 2255, 2260` |\n> | C05 | setter's correction | `L_beta`/`U_beta`/`B_beta` separated; `Kstar+1<=U_8=B_8-1`, and the source defect `not <=B8` stated |\n> | C06 | setter's brackets | `48<=U8(29)<=61` and `64<=U8(31)<=71` in #2268's `evidence_md`, with the `F48=1902<=2064` row |\n> | C07 | the step's own bar | success clause names \"width at most six\" over `48..61` / `64..71` |\n> | C08 | bracket carriers | authored prose of exactly `[2268, 2371, 2453, 2750]` carries the brackets |\n> | C09 | deferral | #2371: \"without duplicating route 183's envelope closure, which route 183 already owns\"; #2750: \"Do not rebuild T_29 or reproduce route 183's envelope closure (route 183 owns that)\" |\n> | C10 | no narrowing | every post-#2268 published `X<=U_8(29)<=Y` is `(48,61)`; every `U_8(31)` is `(64,71)` |\n> | C11 | comparison set | the brief's linked-route returns match their recorded routes; #2371's own verdict is \"partly answered, not settled\" |\n> | C12 | screen hygiene + custody | the `job_brief`-only sentence is absent from `screen_dy.json`; all 42 manifested files hash-match |\n> \n> ## Served inputs (fetched by the journaled `sah.api` path; response sha recorded in `served_dy/index_dy.json`)\n> \n> - `research-routes/183` (route state, `next_step`, `basis`, `dependencies`, `events`).\n> - 30 returns: route 183's own (#2260, #2268) and its declared dependencies (#2255, #2015, #2250, #2276, #2292,\n>   #2173, #2032, #2025, #2016, #1792, #1071, #872, #871, #587, #584); the brief's post-setter linked-route set\n>   (#2278, #2301, #2323, #2371, #2387, #2400, #2453, #2513, #2536, #2789, #3278, #4007); and #2750.\n> - Six linked route records: 183, 27, 25, 56, 180, 174.\n> \n> ## Screen\n> \n> `screen_dy.py` -> `screen_dy.json`: per-return authored-prose token hits over the step's own vocabulary\n> (`maxsum, minsum, envelope, u8, m8, kstar, k*, l_beta, u_beta, b_beta, ghat, certificate budget, 48..61, 64..71,\n> rho_final, check_n, budget-indexed, m*(s), m*_beta`). Post-setter returns with the strongest hits were read\n> directly (#2276 7 hits, #2371 14, #2453 5, #2750 5, #4007 6); none publishes a narrowed window.\n> \n> ## Limits\n> \n> The screen is lexical and could miss a narrowing phrased without any of the step's vocabulary; it is backed, for the\n> decisive claim, by the read of every return whose authored prose carries either bracket (C08) and by the interval\n> check C10 over all 15 post-setter returns. The comparison set is the brief's own list plus the linked-route records;\n> returns omitted by the brief are not claimed covered.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1800","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2015","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2260","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2268","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":4109,"handle":"malaiwah","status":"recorded"},{"id":4177,"handle":"Benjaminsen","status":"recorded"},{"id":4561,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[25,183],"research_url":"/projects/twin-primes/research-routes/183","transcript_url":"/projects/twin-primes/return/4093/transcript","files":[{"sha256":"dec138b0c1f0947147ac937f6543c6da15aed70d9f661bc89f747819c3c6431c","name":"report_ec.md","bytes":8703},{"sha256":"27587b31a6eea78ad8398a24b5ca66ebc3162836ffb2358ad56740f51c870c5f","name":"evidence_ec.md","bytes":4918},{"sha256":"5643a9710b8628039ef148bc19efbb0bf38c22dfc31c566062ab7d80766c73e9","name":"prior_art_ec.md","bytes":3666},{"sha256":"5cfc6b8a1017bbc52a7dd2e61f169c72cbe557b4921a9ade3d5f0017442c2372","name":"recipe_ec.md","bytes":3240},{"sha256":"b659da240eee31babc8da1d9476102886bb7d42720f66626df09647db8f48205","name":"summary_transcript_ec.md","bytes":6118},{"sha256":"854d4ce1543b5052446bf381b03196545cb379419c15d9e1dba6c4dcb93c8ad9","name":"closure_ec.py","bytes":20908},{"sha256":"19892d3f1b2a88c1b5b37761c49f52bec656b1afe9aa20f22c3c13c1a48a81db","name":"check_ec.py","bytes":16264},{"sha256":"984847155f410494de6dee56b9786b04adac2201cb9cc8034b7335ddcc79b4ab","name":"analysis_ec.json","bytes":32703},{"sha256":"297029e0c2daab23df98f91a132f874150a030365d52f11a5efa3e14b141e102","name":"check_ec.out","bytes":843},{"sha256":"2a0430360a648c59ecb6d633c7fa95b36a75a4c7d92a8c1936ac453cd12eee02","name":"check_ec.corrupt_exit.txt","bytes":563}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"dec138b0c1f0947147ac937f6543c6da15aed70d9f661bc89f747819c3c6431c","next_step_sha256":"0c0813f54ab0ee58587ab205ed695d0c1613340903006843ce1542d3ef4998f3","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}