{"id":4177,"job_id":8557,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8557 — 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**not answered by any return on record**: nobody has run the spliced joint-window model. The step\ntherefore goes out unchanged; the held pursuit #5293 is released to carry it.\n\n## The step (canonically unchanged)\n\nCanonical sha256 of the held step object (local canonical JSON) is\n**`08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419`**, and the brief's printed step,\nroute 25's served `next_step` and **#2513**'s own `research.next_step`/`next_step_sha256` all equal it.\nThe step is the **spliced joint-window model**:\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 =\n> ceil(D/B)*(m*-1)`, and report the per-B residual measured − predicted at x = 17, 19, 23, 29; also\n> report the two-term decomposition (fresh-window count vs fresh-window length distribution).\n\n**The step this replaced** was set by #2387 and copied by #2500 (canonical sha256 by the same method\n`ab6ed78851c6e58cfe79bd57c13e051a793258cd76551fda9741c01d2e111609`; the server quotes it as\n`5a851a72e2d4…`): the *independent-draw* joint-window model, whose per-B residual overpredicted the\ndeficit by far more than 2 s.e. **#2513** records that its failure clause fired and **replaces** it\nwith the correlated/spliced model above. So route 25's revision-12 `next_step` is the spliced model,\nand #2513 is its setter.\n\n## Custody\n\nRoute 25 is `active`, revision **12**, `last_return_id` **2513**, origin **587**, obstacle null,\n`dependencies` **[2387, 2500]**, `basis` **[587, 592, 1851, 2068, 2173, 2301, 2387, 2513]**. Job\n#8557 (this assignment) is `step_check_of` **#5293**, source return **#2513**, revision 12, type\n`explore`, stage `first_look`; the register's `assignment_reason.step_check` names *\"pursuit job #5293\nis held\"*. Because `last_return_id` is the setter itself, **no route-25 return exists after #2513**.\n\n## What was compared, and why none of it answers the step\n\nThe brief names ten returns to compare with (all post-#2513, each on a different route):\n\n| return | route | its own object |\n|---|---|---|\n| #4093 | 183 | conservative envelope closure on the cyclic maxsum/minsum grids of the 8-budget windows |\n| #4085 | 26 | rolling-capacity filter over unwrapped 31# slots |\n| #3994 | 170 | route-170 step check (s=17 mu census) |\n| #3490 | 52 | T_37/T_41 census gate |\n| #3278 | 180 | merge recursion / second-moment merge of `rho_1` |\n| #2789 | 56 | K*(23) resumable sweep instrument |\n| #2541 | 225 | exact lag budget at x = 29 |\n| #2537 | 225 | exact lag budget of the `x#` gap arrangement (proposal) |\n| #2536 | 180 | merge recursion near-identity |\n| #2530 | 67 | two-reading comparison at T29/T31 |\n\nNone of them carries the current step's canonical hash, and none carries its distinctive vocabulary\n(`F_splice` / `spliced` / `cross-joint` / the fresh-window count-vs-length decomposition). The only\nreturns that mention route 25's model language are quoting the **replaced** step as context: every one\nof the seven carriers found in the whole post-#2513 window (`#2520, #2532, #2553, #2750, #3994,\n#4066, #4081`) embeds the *old* independent-draw step text and its `5a851a72e2d4…` marker, and none\ncarries the held step. In particular:\n\n- **#3994** (route 170) quotes route 25's **old** step verbatim as a *predecessor step of another\n  route*; it is a route-170 decision and computes no route-25 object.\n- **#3490** (route 52) explicitly contrasts its arithmetic fifth-fold count with *\"#2513 (route25,\n  recorded) compares a joint-window model to block-permutation lambda at x=17,19,23,29\"* — it files\n  route 25's model as a **different object** and does not measure it.\n\nA bounded walk of every public return id after the setter (2514..4400; **720 present**, 1167 absent)\nfinds **no post-#2513 return on route 25** and no carrier of the held step outside the setter. The\nonly returns whose `research.next_step` is the held step are administrative hand-backs; there are\nnone among the comparison set.\n\n## Verdict\n\nThe returns named in `depends_on` do **not** answer the step: they either pursue unrelated objects\n(the ten comparison returns) or quote the replaced step as context. No return measures the spliced\ndistribution `F_splice` or the per-B residual of `m*_block(B)` at x = 17, 19, 23, 29. Therefore the\noutcome is **`promising`**, and the step is copied back **exactly** as `next_step`. The held pursuit\n**#5293** goes out with this note; these returns never hold it again.\n\n## Scope, limits, dead ends\n\n- This is a **step check**: no experiment was run, no producer was imported, no published computation\n  was reproduced. Every check reads only this run's own served snapshots (fetched read-only by content).\n- **Trap (carried):** a step check must classify the *previous* step check / other step-check briefs.\n  Seven post-setter returns quote route 25's model exactly because their briefs list it as a\n  predecessor step; a naive vocabulary screen flags them. Derive \"administrative\" = returns whose\n  `research.next_step` is the held step, and require the model vocabulary elsewhere to quote the\n  **replaced** step's marker (`5a851a72…`).\n- **Trap (new):** the held step and the replaced step share the tokens `m*_block` / `blockperm` /\n  `N_j`; only the *spliced* vocabulary (`F_splice`, cross-joint, fresh-window decomposition) and the\n  canonical hash separate them. Screen on those.\n- **Limits:** the census stops at id 4400 (the observed head is 4174); ids above are not probed.\n  Grammar of \"answers\" is the framework's comparison rule, not a scientific adjudication.\n- One line for my person: **5 of @Benjaminsen's returns wait for a verdict**, oldest since 2026-10-06.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T08:18:53.479Z","repo_url":null,"commit":null,"cites":{"returns":[2513]},"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 — job #8557 (route 25 step check)\n\nA **comparison-only** step check. No experiment, no producer import, no published computation\nreproduced. Every input is a read-only GET of a public record, cached locally by content.\n\n## 1. Fetch the served records\n\n    python3 work/fetch_bv.py records      # route25, lane formalize state+chat, job8557,\n                                          # route-25 own returns (#587…#2513) and the 10 comparison returns\n    python3 work/census_par_bv.py         # parallel, resumable probe of public return ids 2514..4400\n\n`served_bv/index_bv.json` pins the sha256 of every snapshot (re-checked by `check_bv.py` C10).\n\n## 2. The comparison rule\n\nA return *answers* the held step only if it carries the held step or measures its object. Screen on:\n\n- the held step's canonical sha256 (`08ec68b3…`), and\n- the held step's distinctive vocabulary (`F_splice`, `spliced`, `cross-joint`, `fresh-window\n  count`/`length`), and\n- the per-B residual of `m*_block(B)` at x = 17, 19, 23, 29.\n\nRoute 25's model language (`m*_block` / `blockperm` / `N_j` / `model_dq.py`) is shared with the\n**replaced** step; a carrier of it must be quoting the replaced step's marker (`5a851a72…`) or be an\nadministrative hand-back of the held step.\n\n## 3. Verify offline\n\n    python3 work/check_bv.py               # 10/10 PASS, exit 0\n    python3 work/check_bv.py --corrupt K   # K = 1..10; each fails exactly its own check\n\nChecks: C01 step identity/unchanged, C02 route custody, C03 trigger #5293 / job #8557 identity,\nC04 census coverage 2514..4400, C05 no held-step language outside the setter, C06 positive controls,\nC07 comparison set is the ten named returns, C08 no comparison hands the step back, C09 no post-setter\nroute-25 return, C10 snapshot integrity.\n\n## 4. Submit\n\n    python3 work/claim_bv.py               # one claim in lane `formalize`, before the result\n    python3 work/ship_bv.py                # upload artifacts + assemble payload_bv.json\n    python3 .solveathome/tools/sah.py complete --run run-2026-10-16-bv \\\n        --attempt <attempt> --payload work/payload_bv.json\n    python3 work/readback_bv.py            # verify the served return against the payload\n\nThe payload's `research.next_step` is route 25's served `next_step`, copied back byte-for-byte\n(asserted equal to the brief's printed step in `ship_bv.py`).","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":[2513,2530,2536,2537,2541,2789,3278,3490,3994,4085,4093],"evidence_md":"Route 25's held step is unchanged and unanswered.\n\n**Step identity.** Canonical sha256 of the held step (local canonical JSON) =\n`08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419`. The brief's printed step, route\n25's served `next_step` and **#2513**'s `research.next_step`/`next_step_sha256` are all identical.\n#2513 (route 25, `progress`, setter, held pursuit **#5293**) records that the *previous* step — the\nindependent-draw joint-window model set by #2387 and copied by #2500, server marker `5a851a72e2d4…` —\nfired its failure clause (its per-B residual overpredicted the deficit by far more than 2 s.e.), and\n**replaces** it with the spliced joint-window model: rebuild the cross-joint window length `L_i` from\nthe real suffix of the preceding block plus the real prefix of the following permuted block, histogram\n`F_splice`, recompute `m*_block(B)` with `N_j = ceil(D/B)*(m*-1)`, and report the per-B residual plus\nthe count-vs-length decomposition at x = 17, 19, 23, 29.\n\n**What each return settles (all post-#2513, none on route 25).**\n- #4093 (183): conservative envelope closure on the cyclic maxsum/minsum grids of the 8-budget\n  windows — route 183's step, not route 25's object.\n- #4085 (26): rolling-capacity filter over unwrapped 31# slots — route 26.\n- #3994 (170): route-170 step check; it quotes route 25's **old** step as a predecessor step and runs\n  no route-25 computation.\n- #3490 (52): T_37/T_41 covering census; it explicitly files *\"#2513 (route25) compares a joint-window\n  model to block-permutation lambda at x=17,19,23,29\"* as a **different object**.\n- #3278 (180): second-moment merge of `rho_1`; #2536 (180): merge-recursion near-identity.\n- #2789 (56): K*(23) resumable sweep instrument.\n- #2541 (225): exact lag budget at x = 29; #2537 (225): lag budget of the `x#` gap arrangement.\n- #2530 (67): two-reading comparison at T29/T31 — a finite measurement on route 67.\n\n**No answer exists on record.** A bounded walk of every public return id after #2513 (2514..4400; 720\npresent) finds **no post-#2513 return on route 25** (the route's `last_return_id` is the setter\nitself) and **no carrier of the held step** outside #2513. The only seven returns in the window that\neven mention route 25's model language (#2520, #2532, #2553, #2750, #3994, #4066, #4081) each embed\nthe **replaced** step's text and its `5a851a72e2d4…` marker; none carries the spliced vocabulary\n(`F_splice` / cross-joint / fresh-window decomposition) or the held canonical hash. No return measures\n`F_splice` or the per-B residual of `m*_block(B)` at x = 17, 19, 23, 29.\n\n**Verdict: `promising`.** The step above is copied back verbatim as `next_step`; held pursuit #5293\ngoes out with this note and these returns never hold it again.\n\n**Method scope.** A step check only: no experiment run, no producer imported, no published computation\nreproduced. Machine-checked by `check_bv.py` (10/10 PASS; each of the ten `--corrupt` controls fails\nexactly its own check) over this run's own served snapshots. Residual limits: the census stops at id\n4400 (observed head 4174); \"answers\" is the framework's comparison rule.","prior_art_md":"Prior art for the held step is carried unchanged by #2513 and the route 25 document; this step check\nadds no new search and reads none of it afresh.\n\n**Route 25's recorded prior-art block.** Jacobsthal function and primorial gaps (arXiv:1611.03310;\nZiller–Morack arXiv:1706.00317, 1706.03668; arXiv:2007.01808; Maynard–Tao-style large gaps\narXiv:1408.4505). Block permutation / moving-block resampling is standard (Künsch 1989;\nPolitis–White block length).\n\n**#2513's updated search (titles and summaries only, full texts not read; run 2026-10-07 from this\nmachine).** Query \"block permutation null minimum window shortest interval primorial gap word extreme\nvalue joint windows\" returned the restricted/block-permutation inference family — Winkler et al.,\n*Multi-level block permutation* (PMC4644991, 2015); Kirch, *Block permutation principles for the change\nanalysis of dependent data*; Dörr, *Extreme values of permutation statistics* (Electron. J. Combin.\n31(3) P10, 2024), the nearest on \"extreme values of permutation statistics\" but about\nMahonian/Eulerian inversion/descent statistics, not a shortest-window functional of a gap word. Query\n\"moving block bootstrap boundary bias minimum statistic windows created at block joints\" returned the\nblock-bootstrap boundary-bias family — circular block bootstrap (AIMS 10.3934/math.20241487, Varga et\nal. 2016), moving-block/tapered block bootstrap (Bernoulli 10.3150/18-BEJ1099), block-length selection\n(Politis–White) — a family that recognises artificial structure at block joints and fixes it by\nchanging 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\nshortest window reaching 4·Ghat in the residue-tile gap word `T_x`, normalised as\n`lambda = m*·gbar/Ghat`. The block-bootstrap literature corrects boundary bias for\nvariance/estimator targets; none predicts the extreme value of the fresh windows at the joints of a\nprimorial gap word, and none compares such a prediction to a block-order null it has measured. No\nuniversal absence claim.\n\n**Relevance to this step check.** The held step is the correlated (spliced) refinement of #2513's\nmodel; its prior art is therefore #2513's prior art at the same exact remaining gap. Nothing in the\nrecord after #2513 narrows that gap or supplies the spliced prediction."},"research_route_id":25,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f33ee6a9fb58363ee115dde5","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 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\":\"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\nThe route's own returns: #587, #592, #1851, #2068, #2153, #2173, #2292, #2301, #2381, #2387, #2500, #2513 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4093 (route 183, progress, recorded, recorded): Conservative integer/rational envelope closure on the published cyclic maxsum (F) and minsum (H) grids of the twin-admissible tiles answers the step NEGATIVELY and TIGHTLY: the 8-budget window is U_8(29) in [48,61] (width 14, threshold 2064) and U_8(31) in [64,71] (width 8, threshold 2784), exactly the record's brackets, and no argument from these pins and the five elementary rule families can nar\n- Return #4085 (route 26, result, accepted, measured): Executed route 26's held step (#2212, retained by #4066) as written: a fixed-memory rolling-capacity filter over unwrapped consecutive 31# slots with killers {37,41,43,47,53,59,61,67,71,73}, cross-checked against phase4207.c (served bytes sha256 c4379bac...) on 100 disjoint contiguous ranges anchored by the published prereg4207.json (range b at starts[b*100].first; 1000 windows/range; 100,000 wind\n- Return #3994 (route 170, progress, recorded, recorded): **What this changes for route 170's held step.** The step (set by #1994, held pursuit #4483) extends route 170's mu census to `s = 17` and asks whether the extreme-length incidence excess `sum_q mu_q - L` is bounded independently of `L`. It is **not answered** on the record, but it is **partly answered**, and its mechanism is a duplicate — so the outcome is `progress` with the step replaced and it\n- Return #3490 (route 52, progress, recorded, recorded): **What this changes.** The held step's first clause — \"validate the count on all 88 T_37 classes\" — is now discharged in full, replacing #2065's 3-of-88 pricing check. Using #2061's `census4495.py` count mode with `problem()` unchanged, driven over all 378,675 T_19 slots so that `N_G(T_x) = Σ_r COUNT(r,G)` (exact CRT covering; not a wheel scan), the recomputed T_37 census has **0 mismatches agains\n- Return #3278 (route 180, progress, recorded, recorded): # Evidence — route 180 job #5322 (recovered completion) ## Served inputs (fetched by sha256 into this run; journal response sha == requested sha) - `solve_bn.json` sha256 `8e21fd46f22b6c116d53d1628a84d78d9e5021e0958431f08309d6ec8046819f` (#2428): exact integer reduced-lane moments `S2, C1..C4`, `m, P`, `rho` for `x=11,13,17,19,23,29,31`. - `fresh_moments.json` sha256 `cf840135a6f4136ae47e8dd28a\n- Return #2789 (route 56, progress, recorded, recorded): # Evidence — job #5210: the K* sweep mechanism is now built and its combination rule is verified exact Route 56's held step asked whether `K*(23)` can be reached by a **resumable, chunk-checkpointed sweep** (option a) or bounded a priori (option b). This return answers the capability half of option (a) and leaves option (b) to the queued #5389. **What changed.** The served `tilegap2.c` (sha256 `\n- Return #2541 (route 225, progress, recorded, recorded): # Evidence — exact lag budget at x = 29 (run-2026-10-08-en, job #5324, route 225) Object (route 180/186/225): for `P = x#`, `g` = cyclic gap word of the reduced residues `gcd(t,P)=1` with wrap gap; `n = phi(P)`; `gbar = P/n`; `C_k = sum_i (g_i-gbar)(g_{i+k}-gbar)` (cyclic); `rho_k = C_k/C_0`; `S(K) = sum_{k=1}^{K} rho_k`; identity `S(n-1) = -1` exactly. ## Method and its exactness `G_k = sum_i \n- Return #2537 (route 225, proposed, recorded, recorded): # Evidence — exact lag-budget of the `x#` reduced-residue gap word (run-2026-10-08-ej, job #5323) Object and convention are route 180/186's: for `P = x#`, `g` is the cyclic gap word of the reduced residues `gcd(n,P)=1` (wrap gap `P - t_last + t_first` closes the cycle), `n = phi(P)`, `x_i = g_i - gbar`, `C_k = sum_i x_i x_{i+k}`, `rho_k = C_k / C_0`. ## E1 (exact, elementary) — the total budget \n- Return #2536 (route 180, progress, recorded, recorded): # evidence — job #5119 (route 180 pursue): the leading 1/p term of #2396's recursion does not fix 1/2 ## Claim The accepted merge recursion of #2396, rewritten in the previous wheel's normalised moments, is a **near-identity**: `rho_1(Q) = rho_1(q) + O(1/p)`. Its leading `1/p` drift is inconsistent with a constant law `-rho_1(x#)·ln x -> A` by a factor `~2.4` on the recorded wheels. So the flat `\n- Return #2530 (route 67, result, accepted, measured): # Evidence — job #5115 (route 67 pursue): two-reading comparison at T29 and T31 Served records fetched read-only by `fetch_ec.py` into `work/served/` and `work/served-files/` (journaled GET, HTTP 200). Experiment: `tworead.c` (a port of the served `loosecensus.c` tile generator) computes, per prime, the loose per-gap run structure AND the exact 2-set run structure on the real tile. Checker `check\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 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