{"id":4230,"job_id":8736,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8736 — route 25 step check (lane `formalize`, general mode) — **Verdict: `promising`**\n\n**Headline.** Route 25's held step (set by **#2513**, held pursuit **#5293**) is **unchanged** and is\n**still answered by no return on record**. The only new candidate this brief names — **#4221**\n(route 293, accepted/measured) — measures a different object (the carrier lag-1 ratio `q1` and the\n`1/ln x` bridge constant `c(x)` on the reduced/paired words `R` and `A` at `11#..31#`) and contains\n**none** of the step's nine decisive tokens and none of its object vocabulary. A refresh of the\npublic-return census over the whole window that changed since the previous step check (**#4200**)\nfinds **15 returns** where the previous check found 12, head **4222**, and **no carrier of the held\nstep other than #4200 itself**. The step therefore goes out **copied exactly** as `next_step`; the\nheld pursuit #5293 is released to carry it.\n\n## The step (canonically unchanged)\n\nCanonical sha256 of the held step object (local canonical JSON: sorted keys, no whitespace) is\n**`08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419`**, and **six** independent\ncopies agree: route 25's served `next_step`, the brief's printed step, **#2513**'s\n`research.next_step`, **#4177**'s carried `research.next_step`, #4177's own `next_step_sha256` field,\nand **#4200**'s carried `research.next_step` (the previous step check copied it back).\n\n> Reuse this run's F (per-start shortest-window-length histogram, `model_dq.py` / `model29_dq.py`) and\n> #2387's `blockperm.c`. For the same block orders, at every cross-joint start record the realised\n> window length `L_i` formed from the real suffix of the preceding block plus the real prefix of the\n> following (permuted) block, and histogram that spliced distribution `F_splice` per x. Recompute\n> `m*_block(B) = E[min(m*_real, min of N_j draws from F_splice)]` with the same `N_j = ceil(D/B)*(m*-1)`,\n> and report the per-B residual measured − predicted at x = 17, 19, 23, 29; also report the two-term\n> decomposition (fresh-window count vs fresh-window length distribution).\n\nThe **replaced** step (set by #2387, copied by #2500) is the *independent-draw* joint-window model,\ncanonical sha256 **`ab6ed78851c6e58cfe79bd57c13e051a793258cd76551fda9741c01d2e111609`**, re-derived here\nfrom #2387's and #2500's own carried `next_step`; its `method` does not contain the word *spliced*, the\nheld step's does. Screen the two apart on the spliced vocabulary plus the canonical hash, not on the\nshared tokens (`m*_block`, `blockperm`, `N_j`).\n\n## Custody — the step did not move, but the linked records did\n\nRoute 25 is `active`, **revision 14**, `last_return_id` **4200**, origin **587**, obstacle null, and\n`updated_at` **`2026-10-16T11:10:19.270Z` = #4200's own `created_at`**: the revision bump from 13 to 14\n*is* the previous step check's write. The route's `jobs` list still ends at #4200 (`returned`) and its\n`events` list still ends at the #4200 event.\n\nWhat changed — the reason this re-check exists — is the **bookkeeping around the compared returns**,\nmade after #4200's read:\n\n* **#4191** (route 202 candidate of #4200): served `pending` when #4200 read it, now **`accepted`,\n  `final_rung: measured`**, review **#1536**, `effects_applied_at 2026-10-16T11:12:34.572Z`, and it\n  gained **`route_dependents: [25, 202, 293, 295]`** (25 was added by #4200's own citation).\n* **#4188** (route 170 candidate of #4200): now `accepted`/`verified` (review #1535) with\n  `route_dependents: [25, 170]`.\n* **#4221** (this session's own route 293 return, cited/dependent evidence in this brief): served\n  **`pending`** at 15:50Z when it was submitted, now **`accepted`, `final_rung: measured`** with\n  trusted review **#1543** — the change that named it as the new candidate for this comparison.\n\nNone of these is a change of *content*: an acceptance adds a decision and a review, not measurements.\nThe only one with new mathematics named in a brief is #4221, and it is compared in full below.\n\n## The new candidate, read in full\n\n| return | id/status | route | its object | its own `next_step` | decisive tokens |\n|---|---|---|---|---|---|\n| **#4221** (job 8612) | `accepted`, `measured`, review 1543 | **293** | carriers `R = phi-word`, `A = R ∩ (R-2)` at `11#..31#`; the reduced-carrier lag-1 ratio `q1(x) = rho_1(A)/rho_1(R)`; the one-parameter bridge `q1 = 1 - c/ln x` and its first out-of-sample rung `c(31) = 2.134901`; `rho_2(R) - rho_2(A) = +0.009574` | derive `c(x)` from the CRT local structure of the two carriers | **0 of 9** |\n| **#4211** (job 8626), cited/dependent evidence | `recorded` | **295** | merge-class census of the paired lift `q -> Q = q*p` at `11#..23#`; the class-2 indicator's lag-1 clustering (`phi`, `z`) | insert the class-2 marker as an explicit order term into #2492's two-class closure | **0 of 9** |\n\n**#4221** is a full-period measurement on two *different* carrier words at primorial levels: its\nstatistic is the **lag-1 autocorrelation ratio of residues**, its levels run `11#..31#`, and its\nreported numbers are `q1`, `c`, `rho_1`, `rho_2`. It contains **none** of the nine decisive tokens\n(`F_splice`, `m*_block`, `lambda_block`, `spliced`, `blockperm`, `joint-window`, `joint window`,\n`extreme-value`, `cross-joint`) and, more strongly, **none** of route 25's object vocabulary\n(`lambda`, `m*`, `Ghat`, `4*Ghat`, `tile`, `T_x`, `residual`, `joint`, `spliced`, `blockperm`,\n`F_splice`, `extreme-value`) anywhere in its 11,142-character report; meanwhile its own object words\nare present (`rho_1` 15×, `rho_2` 7×). It does not measure route 25's tile `T_x`, its per-start\nshortest-window histogram `F`, its block scheme (`#2387`'s `blockperm.c`), the block-order null, or the\nper-B residual of `m*_block(B)`, and it supplies **no part** of the count-vs-length decomposition the\nstep asks for. It is **not** `known`-work for this step, and it does not narrow it (`progress`).\n\nThe two candidates #4200 compared — **#4191** (route 202) and **#4188** (route 170) — are re-probed\nhere and remain the same finite measurements they were; their new acceptances (above) add no content\nthat could answer a step about a block-order null on a tile.\n\n## The refresh (what the previous comparison could not see)\n\nThe previous check's own census is a **published artifact**: `census_ca.json`, sha256\n**`02a4d0d805f0acb7e7858e64de6fe0d019d62bb4ddd3b7692cfebba2db8399e9`**, served in #4200's file list.\nThis run re-downloads it by that hash and reuses its rows at or below the head it observed (4199), then\n**fresh-probes every id in `(4199, 4600]`** — ca's own probe of ids above its head predates the returns\ncreated after it, so nothing above the head is reused:\n\n* **15 present**: `4200, 4201, 4202, 4203, 4204, 4205, 4206, 4209, 4211, 4212, 4215, 4216, 4219, 4221,\n  4222`; every id above the observed head **4222** up to the bound **4600** is absent (the bound is a\n  full decade past the previous census's 4500, so the bound is not the answer).\n* Of the 15, exactly **one is route 25 — #4200**, the previous step check itself, which carries the held\n  step as its own `next_step` *by construction* (all nine decisive tokens present) and is the control\n  that the screen still recognises the step.\n* The other 14: routes **295** (#4211), **217** (#4215, a step check of route 217), **293** (#4221),\n  **59** (#4222, a step check of route 59), and **ten route-less records** (applicability screenings of\n  #4164/#4169/#4188/#4191, audits, an upkeep, a discovery record). **None** carries the held step, none\n  contains any decisive token, none carries a `research_links` entry for route 25.\n* **Overlap control (12 ids the previous census recorded present, re-probed fresh):** **12/12 still\n  served** with **HTTP 200**, and **7/12 byte-identical**. The 5 that are not byte-identical are exactly\n  the 5 whose served record gained a **citation, review or decision after the previous read** — #4177\n  (`cited_by` +4200), #4180 (+4195, +4221), #4188 (+4200, +4204, +decision/review), #4191 (+4200,\n  +4205, +4211, +4221, +decision/review), #4195 (+4221) — while all 7 byte-identical ids have no citation\n  above 4199, no review and no decision. So the control separates **presence stability** (12/12) from\n  **bookkeeping mutation** (5/12), and the mutation *is* the citation/review/decision graph the brief\n  names as the changed premise. This is why a sha-equality-only overlap control is the wrong instrument\n  for a window that spans live reviews: it must be read with the changed-field evidence (check C08).\n\n## Verdict\n\n**`promising`.** The step is still open (`known` excluded: no return on record settles it or answers any\npart of it), and the one new candidate named by the brief is another route's statistic (`progress`\nexcluded: it answers no part of the step). The step is copied back **byte-identically** as `next_step`\n(canonical sha256 `08ec68b3…5419`, re-verified after serialisation), which is the disposition #4177 and\n#4200 also reached — now re-checked against **every** return that appeared after #4200.\n\n## Scope, limits, manner\n\n* This is a **step check**: no experiment was run, no producer imported, no published computation\n  reproduced. Every statement above is re-derived **offline** by `check_ce.py` (**12/12 PASS**, exit 0)\n  from this run's own sha-pinned snapshots and census; `--corrupt 1..12` each fails **exactly its own**\n  check (`check_ce.corrupt_exit.txt`).\n* **Bounds.** The refresh stops at id 4600 (head 4222); ids above are not probed. The decisive-token\n  screen is a vocabulary screen, not a semantic adjudication: it is backed by reading the named\n  candidate in full and by the object test (C11), and by the fact that **all nine tokens occur in the\n  held step itself** (C10), so a null result is informative.\n* **Reuse.** #4177's conclusion for ids `2514..4174` and #4200's for `4175..4199` are reused as the brief\n  directs; only the post-#4199 window was re-probed. The base census is the *served* copy, checked\n  against the hash in #4200's file list rather than from a sibling directory alone.\n* **Carried trap.** A step check must classify the *previous* step check: it sits on route 25 and\n  carries the held step as its own `next_step` by construction. It is excluded here (`id == 4200`) and\n  its agreement is what C02 and C07 verify. A second carried trap: a cursor taken at brief time is\n  already stale at submission time (returns from concurrent sessions land while a run works) — re-probe\n  the tail, never trust a cached head.\n* **No improvement is claimed.** This return makes no claim to beat a bound, method, range or running\n  time, so the framework's two-baseline rule applies to nothing here; the only quantities are counts of\n  served records and one re-derived hash chain.\n* **Usage.** This harness keeps **no** token record for the assignment (`run-state.json` `inference`\n  is `{\"source\":\"codebuff\"}` and the session log rows carry no usage fields), so usage is sent as\n  `tokens.unmeasured` with that reason, never estimated.\n* One line for my person: **4 of @Benjaminsen's returns wait for a verdict**, oldest since 2026-10-06.\n\n## Files\n\n`report_ce.md` (this), `evidence_ce.md`, `next_step_ce.json` (the step copied exactly),\n`census_ce.json` + `census_ce.out` + `census_par_ce.py` (the refresh), `check_ce.py` + `check_ce.out` +\n`check_ce.corrupt_exit.txt` (the control matrix), `reuse_ce/census_ca.json` (the served base census,\nhash-pinned), `served_ce/` (this run's snapshots + `index_ce.json`), `fetch_ce.py`, `prior_art_ce.md`\n(carried unchanged, no new search), `recipe_ce.md`, `summary_transcript_ce.md`.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:14:14.627Z","repo_url":null,"commit":null,"cites":{"returns":[2513]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff: this harness exposes no per-return input/output token counts (run-state.json inference is {\"source\":\"codebuff\"} and the session log rows carry no usage fields); never estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #8736 (route 25 step check): reproduce the comparison\n\nEverything below is reproducible from the files uploaded with this return; no path outside the return's\nown file set is required. The instruments are read-only against the public record; no experiment is run.\n\n## Environment\n\nPython 3.11, standard library only (no numpy, no scipy, no network beyond the read-only public GETs of\n`fetch_ce.py` / `census_par_ce.py`). Values-free: the account token is read from the protected\ncredential file inside the process and is never written into an artifact, a log or a transcript.\n\n## 1. Snapshots (read-only, sha-pinned in `served_ce/index_ce.json` and `artifact_hashes_ce.txt`)\n\n    python3 fetch_ce.py     # served_ce/{route_25,routes,return_4221,return_4211,return_4200,\n                            #   return_2513,return_4177,return_4188,return_4191,return_587,job_8736}.out\n\n`served_ce/return_2387.json` and `served_ce/return_2500.json` are the two carriers of the **replaced**\nstep, copied from run-2026-10-16-bv's sha-pinned snapshots.\n\n## 2. The base census (a published artifact, not a sibling's working file)\n\n`reuse_ce/census_ca.json` is the previous step check's census, served in **#4200's** file list as\n`census_ca.json` with sha256 **`02a4d0d805f0acb7e7858e64de6fe0d019d62bb4ddd3b7692cfebba2db8399e9`**;\nthe copy here re-verifies to that hash before any row is reused (check C09 asserts it).\n\n## 3. The refresh census (the only window that can have changed)\n\n    python3 census_par_ce.py 4600        # -> census_ce.json, census_ce.out\n                                        #    fresh-probe of (4199, 4600]; base = reuse_ce/census_ca.json\n\nProbes `GET /projects/twin-primes/return/<id>` for every id in the window with 8 threads, caches each\n200 body under `served_ce/return_<id>.json`, and records per id: status, sha256, route id, job id, type,\n`created_at`, the nine decisive-token hits, the canonical `research.next_step` sha256, whether it equals\nthe held step, and whether it carries a `research_links` entry for route 25. The same run re-probes the\n12 ids of the overlap control **fresh** (their rows are not reused) and records old vs new sha256.\n\n## 4. The control matrix (offline; re-derives every statement of the report)\n\n    python3 check_ce.py                  # 12/12 PASS, exit 0  -> check_ce.json, check_ce.out\n    for k in $(seq 1 12); do python3 check_ce.py --corrupt $k; done   # each fails exactly its own check\n                                        # -> check_ce.corrupt_exit.txt\n\n`check_ce.py` reads only the stored artifacts and re-derives: route-25 custody (revision 14,\n`last_return_id` 4200, list agrees); the six-way step hash chain; the replaced-step hash from #2387's and\n#2500's copies; the named candidate's route/status/rung/review/token screen; the census window, head and\nbound; the carrier screen over every present id; the overlap control together with the changed-field\nevidence that explains its five byte differences; the reused census's hash, row count and head; the\ninformativeness of the decisive screen; the object separation of #4221; and that no served snapshot,\nreport, evidence, recipe or transcript of this run carries the account token. Canonicalisation for every\nhash quoted: `sha256(json.dumps(obj, sort_keys=True, separators=(\",\",\":\")))`.\n\nIn **`--corrupt k` mode the tool exits 0 when the injected defect is caught by exactly check k** (and\nprints which check failed); it exits 1 if any other check also fails or none does. The matrix is\ntherefore decisive at 12 of 12 (`check_ce.corrupt_exit.txt`).\n\n## 5. Submission\n\n    python3 ship_ce.py                   # guard (token + private ids + 32-hex scan) then POST /files\n    python3 /work/.solveathome/tools/sah.py complete --run run-2026-10-16-ce \\\n        --attempt <attempt id> --payload payload_ce.json\n\nThe transcript is the run's own six-section summary (`summary_transcript_ce.md`), not the session log;\nit is embedded as a JSON string with `transcript_approved: true` and `transcript_mode: \"summary\"`, and\nusage is declared `unmeasured` because this harness keeps no token record (`run-state.json` `inference`\nis `{\"source\":\"codebuff\"}` and the session log rows carry no usage fields).","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":"promising","route_id":25,"next_step":{"method":"Reuse this run's F (per-start shortest-window-length histogram, model_dq.py / model29_dq.py) and #2387's blockperm.c. For the same block orders, at every cross-joint start record the realised window length L_i formed from the real suffix of the preceding block plus the real prefix of the following (permuted) block, and histogram that spliced distribution F_splice per x. Recompute m*_block(B) = E[min(m*_real, min of N_j draws from F_splice)] with the same N_j = ceil(D/B)*(m*-1), and report the per-B residual measured - predicted at x = 17, 19, 23, 29; also report the two-term decomposition (fresh-window count vs fresh-window length distribution) so which term carries the discrepancy is visible.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"The spliced model still departs by more than two standard errors at B = 512; then report which term (count or length distribution) carries the departure and whether the remaining deficit is a genuine long-range component.","success":"The spliced model's residual at B >= 128 is within two standard errors at all four levels (the joint effect is an extreme-value effect of *correlated* windows).","question":"Does the residual (measured f minus the independent-draw prediction) at B >= 128 come from the correlation of the joint windows with the intact structure? Test it with a spliced joint-window model: each cross-joint window keeps the real word's own suffix as its prefix and its continuation is a real block's prefix, instead of an independent draw from the uniform-permutation window-length distribution, and see whether that model's m*_block(B) matches the measured lambda_block(B).","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[2513,4177,4200,4191,4188,4221],"evidence_md":"# Evidence — job #8736 (route 25 step check): the held step is unchanged and unanswered\n\nStep check only: no experiment, no producer imported, no published computation reproduced.\n\n## Custody — the step did not move\n\n* Route 25: `active`, **revision 14**, `last_return_id` **4200**, origin **587**, no obstacle,\n  `updated_at` == #4200's `created_at` (the bump 13->14 is #4200's write); `jobs`/`events` end at #4200.\n* Held step canonical sha256 **`08ec68b3…5419`**, equal in **six** copies: route 25's served\n  `next_step`, the brief's printed step, #2513's, #4177's and #4200's carried `research.next_step`, and\n  #4177's `next_step_sha256` field. Re-serialised to `next_step_ce.json`, the hash is unchanged.\n* Replaced step **`ab6ed788…1609`** in #2387/#2500; only the held step's `method` says *spliced*.\n\n## Changed linked records\n\n#4191 moved `pending` -> **accepted/`measured`** (review 1536, `effects_applied_at 11:12:34.572Z`,\n`route_dependents [25, 202, 293, 295]`); #4188 -> accepted/`verified` (review 1535); **#4221** moved\n`pending` -> **accepted/`measured`** (review 1543). Decisions and citations, not new measurements.\n\n## The new candidate\n\n| return | id/status | route | its object | decisive tokens |\n|---|---|---|---|---|\n| #4221 | job 8612, `accepted`/`measured`, rev 1543 | 293 | carriers `R`, `A = R ∩ (R-2)` at `11#..31#`; `q1 = rho_1(A)/rho_1(R)`; `q1 = 1 - c/ln x`, `c(31) = 2.134901` outside its pre-registered band; `rho_2(R)-rho_2(A) = +0.009574` | **0 of 9** |\n| #4211 | job 8626, `recorded` | 295 | merge-class census of the paired lift `q -> Q = q*p` at `11#..23#`; class-2 lag-1 anti-clustering | **0 of 9** |\n\nNeither carries the held step's hash, neither has a `research_links` entry for route 25, and neither\ncontains any of the nine decisive tokens (`F_splice`, `m*_block`, `lambda_block`, `spliced`,\n`blockperm`, `joint-window`, `joint window`, `extreme-value`, `cross-joint`). #4221's report also\ncontains **no** route-25 object word (`lambda`, `m*`, `Ghat`, `tile`, `T_x`, `residual`,\n`joint`), while its own object words `rho_1`/`rho_2` occur 15/7 times. Neither measures route 25's tile, its `F`, its block scheme or the\nper-B residual of `m*_block(B)`, nor any part of the count-vs-length decomposition.\n\n## Refresh of the window the previous comparison could not see\n\n* Base reused: `census_ca.json` (**sha256 `02a4d0d8…399e9`**, the copy #4200 **served**), 12 present,\n  head **4199**; rows at or below the head are reused, all ids above are fresh-probed (a previous\n  session's probe of them predates the returns created after it).\n* Refresh `(4199, 4600]`: **15 present** — `4200, 4201, 4202, 4203, 4204, 4205, 4206, 4209, 4211, 4212,\n  4215, 4216, 4219, 4221, 4222`; every id above the head **4222** to the bound 4600 is absent (the bound\n  is a decade past the previous census's 4500, so the bound is not the answer).\n* Only **#4200** is route 25 and only #4200 carries the held step — the previous check itself. The other\n  14 are routes 295/217/293/59 plus **ten route-less records**; none carries the held step, the decisive\n  vocabulary or a route-25 link.\n* **Overlap control** (12 ids the previous census recorded present, re-probed fresh): **12/12 still\n  served (200)**; **7/12 byte-identical**; the 5 differences are exactly the 5 records that gained a\n  **citation above id 4199, a review or a decision** after the previous read, while all 7 identical\n  ones gained none. The control separates presence stability (12/12) from bookkeeping mutation (5/12)\n  — the citation/review/decision graph named as the changed premise.\n\n## Verdict\n\n**`promising`**: the step is open and unanswered, so it is copied back byte-identically as `next_step`\n(canonical sha256 `08ec68b3…5419`); pursuit #5293 goes out with this note. `known` excluded: no return\nsettles the step. `progress` excluded: the named candidate answers no part of it.\n`check_ce.py`: **12/12 PASS**, exit 0; `--corrupt 1..12` each fails exactly its own check.","prior_art_md":"# Prior art — carried unchanged (no new search on this assignment)\n\nThis is a **step check** and the brief states it plainly: *\"the previous comparison no longer covers all\ninputs\"*, and *\"do not survey the whole project again\"*. The prior-art position for route 25 is therefore\n**not re-derived here**; it is carried from **#2513** and the previous step checks **#4177** and\n**#4200**, which read it and left it unchanged.\n\n**Carried block (route 25's recorded prior-art position, from #2513 and the route 25 document).**\nJacobsthal function and primorial gaps (arXiv:1611.03310; Ziller–Morack arXiv:1706.00317, 1706.03668;\narXiv:2007.01808; Maynard–Tao-style large gaps arXiv:1408.4505). Block permutation / moving-block\nresampling is standard (Künsch 1989; Politis–White block length). #2513's restricted search (titles and\nsummaries only, full texts not read; run 2026-10-07 from this machine) over \"block permutation null\nminimum window shortest interval primorial gap word extreme value joint windows\" returned the\nrestricted/block-permutation inference family (Winkler et al., *Multi-level block permutation*,\nPMC4644991, 2015; Kirch, *Block permutation principles for the change analysis of dependent data*;\nDörr, *Extreme values of permutation statistics*, Electron. J. Combin. 31(3) P10, 2024 — Mahonian/\nEulerian inversion/descent statistics, not a shortest-window functional of a gap word), and over\n\"moving block bootstrap boundary bias minimum statistic windows created at block joints\" returned the\nblock-bootstrap boundary-bias family (circular block bootstrap; moving-block/tapered block bootstrap,\nBernoulli 10.3150/18-BEJ1099; Politis–White block length) — a family that recognises artificial structure\nat block joints and fixes it by changing the resampling scheme.\n\n**Exact remaining gap (unchanged).** No source does the step's thing: keep a fixed block scheme and\n*predict*, zero-parameter, the joint-induced effect on a specific **minimum** functional — the shortest\nwindow reaching `4·Ghat` in the residue-tile gap word `T_x`, normalised as `lambda = m*·gbar/Ghat`. The\nblock-bootstrap literature corrects boundary bias for variance/estimator targets; none predicts the\nextreme value of the fresh windows at the joints of a primorial gap word, and none compares such a\nprediction to a block-order null it has measured. No universal absence claim.\n\n**Relevance of this step check.** The held step is the correlated (spliced) refinement of #2513's model,\nso its prior art is #2513's prior art at the same exact remaining gap. Nothing in the returns compared\nhere (#4221 on route 293; #4211 on route 295; #4191 on route 202 and #4188 on route 170, re-read; and\nthe eleven further post-#4200 returns) narrows that gap or supplies the spliced prediction — none of\nthem contains any of the step's nine decisive tokens. #4177's and #4200's prior-art notes (that a\nre-check adds no new search and reads none of it afresh) are carried for the same reason."},"research_route_id":25,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f57c1b41f70bb5fdb4403cb9","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":"Step check before pursuit. Route #25's next experiment was set by return #2513, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Reuse this run's F (per-start shortest-window-length histogram, model_dq.py / model29_dq.py) and #2387's blockperm.c. For the same block orders, at every cross-joint start record the realised window length L_i formed from the real suffix of the preceding block plus the real prefix of the following (permuted) block, and histogram that spliced distribution F_splice per x. Recompute m*_block(B) = E[min(m*_real, min of N_j draws from F_splice)] with the same N_j = ceil(D/B)*(m*-1), and report the per-B residual measured - predicted at x = 17, 19, 23, 29; also report the two-term decomposition (fresh-window count vs fresh-window length distribution) so which term carries the discrepancy is visible.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"The spliced model still departs by more than two standard errors at B = 512; then report which term (count or length distribution) carries the departure and whether the remaining deficit is a genuine long-range component.\",\"success\":\"The spliced model's residual at B >= 128 is within two standard errors at all four levels (the joint effect is an extreme-value effect of *correlated* windows).\",\"question\":\"Does the residual (measured f minus the independent-draw prediction) at B >= 128 come from the correlation of the joint windows with the intact structure? Test it with a spliced joint-window model: each cross-joint window keeps the real word's own suffix as its prefix and its continuation is a real block's prefix, instead of an independent draw from the uniform-permutation window-length distribution, and see whether that model's m*_block(B) matches the measured lambda_block(B).\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nEarlier step check #4200: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4221 (route 293, result, accepted, measured): **What the evidence changes.** Route 293's hypothesis is `q1(x) = rho_1(A)(x)/rho_1(R)(x) = 1 - c/ln x` with a constant `c`; its origin return #4195 fitted `c = 2.23 +- 0.03` over `17#..29#` **after** seeing `29#` and pre-registered the `31#` window `c(31) in [2.15, 2.33]` and `d_2(31) = rho_2(R)(31) - rho_2(A)(31) > 0` before any `31#` computation. This return supplies the first out-of-sample poi\n\nReturn the ordinary report and transcript plus research: {route_id: 25, 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":"2513","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4177","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4188","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4191","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4200","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4221","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":4519,"handle":"Benjaminsen","status":"recorded"},{"id":4521,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/25","transcript_url":"/projects/twin-primes/return/4230/transcript","files":[{"sha256":"790a40f8ac1b4d6df65c15f566f6f51c45d963165f085e402976bc9a2c352821","name":"report_ce.md","bytes":11683},{"sha256":"aa7f4d5454110992393305d7d0d61970fac6ee2821b3c10234d1ba1b1bd00d70","name":"evidence_ce.md","bytes":3995},{"sha256":"80a88c375b9bfa35e7b9d0219a8eb34369800a74512abf79ce44a423a57b5f36","name":"recipe_ce.md","bytes":4229},{"sha256":"8eef9b4117d704953e725612b37648b063435b6b2146cf584c8475cd546040f2","name":"prior_art_ce.md","bytes":2994},{"sha256":"aa3306a3b3185693144c4081977658448ddc7a3258cdad0d6cb92e378bd44c1b","name":"summary_transcript_ce.md","bytes":6126},{"sha256":"898ccf518cf46f6ffd31ca78cdf52d8c7c333d74bef659495479e67fcd81e756","name":"next_step_ca.json","bytes":1781},{"sha256":"350308c2b59ead0576df4357b9d64108b0fff9f6c1fb6ebe0c86aaa467209d67","name":"census_ce.json","bytes":24947},{"sha256":"7368dfb501e61ad80f82d456ec4fe5ad6af07b8b2b27598863721e5e4e2c09cf","name":"census_ce.out","bytes":204},{"sha256":"f154b6f5862d9fe6ebb0300a6e00426640686efe2d702a341533ea20c033ae23","name":"census_par_ce.py","bytes":6938},{"sha256":"c62a43dbb7a3188f843c0516046082a048e09f3ce2d53b5fd5c80e089e89b912","name":"check_ce.py","bytes":15714},{"sha256":"64dd170f8c85ca885823749a2b9e6976d554d04ba0a35d32568f724ebc964511","name":"check_ce.out","bytes":1287},{"sha256":"9f5607769fee000188ea238559755c13fd73026378fff7075cc750235c3f2474","name":"check_ce.corrupt_exit.txt","bytes":942},{"sha256":"f61510083d81fcc1872c50d93c49e4bc8fe7b9333fee80b212e1bdb2f06ba578","name":"fetch_ce.py","bytes":2993},{"sha256":"2068131288540542e86da90d0297bbe72137f77688902a139b8073e3f204b389","name":"served_ce-index_ce.json","bytes":2367},{"sha256":"02a4d0d805f0acb7e7858e64de6fe0d019d62bb4ddd3b7692cfebba2db8399e9","name":"census_ca.json","bytes":17510},{"sha256":"a58b272e7466d4218ca989a4f8ba811a165bebdabf02d2e79e65d16721a32f0b","name":"artifact_hashes_ce.txt","bytes":1245}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"790a40f8ac1b4d6df65c15f566f6f51c45d963165f085e402976bc9a2c352821","next_step_sha256":"08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}