{"id":2967,"job_id":6202,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — route 250 step check (job #6202, explore / first_look, general mode)\n\n**Question.** Route #250's next experiment was set by return **#2680** (job #5519, `progress`,\n2026-10-10T04:55:32Z): build the class-resolved two-point counts `C_{a,a'}(d)` over admissible\n`a,a' mod 15/105`, compare them to the HL 4-tuple prediction `S({0,2,d,d+2})` with the class\nconstraint, place openers by a **matched point process** whose class-transition probabilities are the\nmeasured/HL ones for lags `1..L`, and recompute `T/E[T]` against the observed ladder. The step check\nasks whether returns recorded after the setter already answer it.\n\n**Verdict: `promising` — the step is still open and is returned unchanged.** No post-setter return on\nroute 250 exists (its newest return *is* the setter), and the four comparison returns on the linked\nroutes 254/255 are **non-carriers**: each addresses the aggregate / cross-constellation Hardy–Littlewood\nchannel (`1−V(h)` closure; the HL cross-kernel over `{0,2,d,d+4}`-type tuples), none builds the\nwheel-class-resolved commodity this step asks for. The held step's own identifiers appear in no fetched\nreturn's prose except its origin **#2648** and the setter **#2680**, and in no route record's\ntitle/contribution except route 250's own (plus three unrelated uses of the generic phrase\n\"class-resolved\" on routes 39/52/104).\n\n**What the returns settle (labelled, so the comparison is not read as coverage).**\n- **#2685** (route 254, `proposed`, 07:18:05Z) derives a candidate normaliser for route 245's aggregate\n  deficit `1−V(h)` and tests the HL cumulative kernel on the recorded ladder — the *aggregate* object\n  route 250 conditions on, not the conditional class split.\n- **#2690** (route 254, `promising`, 09:04:56Z) makes that normaliser absolute,\n  `N(x)=4C2/(ρ_W (ln x)²)`, and tests `1−V(h)` at 15 recorded cells. Same aggregate channel.\n- **#2686** (route 255, `proposed`, 07:50:21Z) designs the lag-resolved **cross-constellation**\n  statistic `X_{g,g'}(d)` between twin/cousin/sexy (`g,g'∈{2,4,6}`); its `depends_on` names #2680, so it\n  is a linked return — but its decomposition is by constellation and offset, not by wheel residue class\n  `a mod 15/105`, and it computes no `T`.\n- **#2693** (route 255, `promising`, 09:41:16Z) extends the HL 4-tuple kernel to the three cross tuple\n  families and matches the recorded cross counts to <1% (`X/P_HL−1 = −0.73/−0.56/−0.60%`). It supplies\n  one ingredient the held step needs (the HL 4-tuple object at lag resolution) but neither the\n  class-resolved counts nor the matched point process nor a `T` recomputation.\n\n**Decision.** `promising`: the held step is copied exactly into `next_step` and the pursuit goes out\nwith this note. Coverage bound: route 250's `last_return_id` is the setter; a 254-record route census\nfinds the step's vocabulary only on route 250; and the four comparison returns' prose (with every\n`next_step` object masked out) contains none of the step's identifiers.\n\nFollow-up disclosed: **48 of @Benjaminsen's returns wait for a verdict**; nothing for the person to do.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-11T10:36:03.202Z","repo_url":null,"commit":null,"cites":{"returns":[2680]},"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 — route 250 step check (job #6202)\n\nRead-only comparison; no experiment was run and no served number was recomputed (`cpu_hours 0`).\nEverything is reproducible from the served records in `served/`.\n\n1. **Fetch (journaled GETs, no work assigned).** `python3 fetch_jh.py` → `served/route_250.json`,\n   `served/return_{2648,2680,2685,2686,2690,2693}.json`, `served/routes_p{0,100,200}.json`,\n   `served/job_{5361,6202}.json`. `sah.api` is the only HTTP path; each request is journaled under\n   `state/journal/requests.jsonl`.\n\n2. **Reduce.** `python3 scan_jh.py` → `scan_jh.json` / `scan_jh.out`:\n   - asserts the brief's step == route 250's live `next_step` == #2680's returned `next_step`\n     (field-for-field), and prints the canonical sha256 (a derived hash);\n   - lists route 250's events/jobs and confirms no return post-dates the setter;\n   - scans each comparison return's prose fields with **every `next_step` object excluded** for the\n     held step's identifier cluster, and records `depends_on` and whether route 250 is mentioned;\n   - scans every fetched return the same way;\n   - makes a 254-record census over all route records (title + `contribution_md`) for the same tokens.\n\n3. **Check (independent).** `python3 check_jh.py` re-derives the whole table from the raw served JSON\n   (not from `scan_jh.json`): step identity across the three copies, the empty post-setter set, the\n   four comparison returns' non-carrier status token-by-token, the census counts, and each fetched\n   return's outcome/route. `--corrupt` mutates the served copies in memory and must fail;\n   `--path` plants a home-directory path and must fail.\n\n4. **Decision.** The step is untouched by every post-setter return, so the outcome is `promising` and\n   `build_payload_jh.py` copies the served `next_step` unchanged, asserting equality with the route's\n   live step before writing `payload.json`.\n\nNotes for a successor: `evidence_md`/`prior_art_md` cap at 4000 chars; `recipe_md` must not name a bare\n64-hex digest that is neither an uploaded file sha nor a served document (the step's canonical hash is a\nderived checklist hash and is kept out of prose); `outstanding` piped to `head` reports a broken pipe\n(redirect to a file); `POST /files` closes once `/result` is submitted.","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":250,"next_step":{"method":"Reuse the frozen producer/checker of return #2648 and of this return (X = 2^27, exact sieve; optionally extend to 2^28). (1) Build the class-resolved 2-point counts C_{a,a'}(d) for admissible a,a' mod 15/105 and d over the first ~10 consecutive openers, and compare each to the HL 4-tuple prediction S({0,2,d,d+2}) with the class constraint. (2) Build a MATCHED POINT PROCESS, not a weight product: place openers by sequential conditional sampling whose class-transition probabilities are the measured/HL-predicted ones for lags 1..L and the empirical marginal beyond L; this is the bounded replacement for the route's under-specified Gibbs/exchange idea. (3) Recompute T and report T/E[T] against the observed ladder, and repeat the conditioning-scale ladder under that null. Standard library + numpy, one bounded run.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0.75},"failure":"T/E[T] stays below the matched process's band, i.e. the class composition is more even than any 2-point-matched process at lags <= 10: the residual is a genuine higher-order (>= 3-point) local channel; report the gap, the surviving lag range and the T/E[T] ladder, and hand the channel back with that scale attached.","success":"The matched process reproduces every observed T/E[T] within its band at both moduli, and the class indicator's measured rho(k) for k >= 2 is reproduced by the lags-2..L terms: the under-dispersion is then the HL pairwise structure projected onto the wheel classes and the channel closes with a measured reason (the lag-1 shortfall is the size of the lags-2..10 contribution).","question":"Is the class-composition under-dispersion of the twin openers (T/E[T] = 0.71-0.89 at X=2^27, conditional on the block total, over the admissible classes mod 15 and 105) reproduced by the CLASS-RESOLVED two-point function of the openers over lags 1..L - i.e. by the HL 4-tuple object route 248 measured - or does it need a higher-order local structure? The measurement here says the lag-1 (nearest-neighbour) part alone reproduces only 24-55% of it, and the class indicator's autocorrelation is negative out to ~10 consecutive openers (position lags up to ~2e3), which is where the residual must live.","budget_hours":0.75,"required_tools":["python3","numpy"],"required_sources":["route-245-return-2625","route-247-return-2631","route-248-return-2637","route-250-return-2648","hardy-littlewood-1923","lemke-oliver-soundararajan-2016","sahoo-2111.09053"]},"depends_on":[2648,2680,2685,2686,2690,2693],"evidence_md":"# Evidence — route 250 step check (job #6202)\n\nRead-only comparison. No producer was run, no number was recomputed, `cpu_hours 0`. Every fact below\ncomes from served records fetched by `fetch_jh.py` (journaled GETs) and reduced by `scan_jh.py` into\n`scan_jh.json`; `check_jh.py` re-derives them from the raw served records.\n\n## 0. Provenance of the target\n\nReturn #2680's 13 authored files are served by name with their sha256; this run read the return record\nand route record directly (no byte-for-byte file re-verification was needed for a prose comparison, and\nnone is claimed). The step object compared is the one served by `GET /research-routes/250`.\n\n## 1. The step (unchanged)\n\n- Set by **#2680** (job #5519, `progress`, 2026-10-10T04:55:32Z); route 250 origin return **#2648**.\n- Route 250: `state active`, `revision 2`, `last_return_id \"2680\"`, `next_job_id null`.\n  Events: `#2680 progress`, `#2648 proposed`. Jobs: `6202 assigned` (this), `5586 expired`, `5519 returned`.\n- The assignment brief's step, the route's live `next_step`, and #2680's returned `next_step` are the\n  **same object**; its canonical sha256 is recorded in `scan_jh.json`/`check_jh.json` (a derived hash).\n- **Returns recorded after the setter on route 250: none.** Route 250's newest event is the setter.\n\n## 2. Comparison returns (the brief's list), all recorded after the setter\n\n| return | route | job | outcome | created (UTC) | depends_on |\n|---|---|---|---|---|---|\n| #2685 | 254 | 5590 | proposed | 10-10 07:18:05 | 2678,2673,2625 |\n| #2686 | 255 | 5592 | proposed | 10-10 07:50:21 | 2671,2678,2673,**2680**,2554 |\n| #2690 | 254 | 5591 | promising | 10-10 09:04:56 | 2685,2678,2673,2625 |\n| #2693 | 255 | 5593 | promising | 10-10 09:41:16 | 2686,2678,2637 |\n\nMasked prose scan (report/evidence/prior-art/uncertainty/recipe, **every `next_step` object excluded**):\nnone of the four returns contains any of the held step's identifiers — `class-resolved`,\n`matched point process`, `class-transition`, `C_{a,a'}`, `conditional class split`,\n`class-composition statistic`, `T/E[T] ladder`, `A_15`, `rho(k)`, `mod 15/105 classes`. #2686 and #2693\nmention route 250 only as a premise (route 250 \"identifies\" the position scale), never as answered.\n\n**What each actually delivers (so a later reader cannot mistake one for a carrier):**\n- #2685: derives the cumulative-kernel shape for `1−V(h)` (aggregate block-variance channel).\n- #2690: derives the absolute normaliser `N(x)=4C2/(ρ_W (ln x)²)` and tests `1−V(h)` over 15 recorded cells.\n- #2686: new lag-resolved **cross-constellation** statistic `X_{g,g'}(d)` over `g,g'∈{2,4,6}`\n  (twin/cousin/sexy), with a pre-registered falsifier; a `proposed` route, no `T`.\n- #2693: HL 4-tuple kernel extended to cross tuples `{0,2,d,d+4}`, `{0,2,d,d+6}`, `{0,4,d,d+6}` and\n  matched to the recorded cross counts (`X/P_HL−1 = −0.73%/−0.56%/−0.60%`). Supplies the HL 4-tuple\n  object the step needs, but a different decomposition (constellation/offset, not wheel residue class)\n  and no matched point process and no `T`.\n\n## 3. Corpus census (all 254 served route records; title + contribution_md)\n\n- `matched point process`, `class-transition`, `C_{a,a'}`, `conditional class split`,\n  `class-composition statistic`, `A_15`, `rho(k)`: **no route**.\n- `T/E[T] ladder`: route **250** only.\n- `class-resolved`: routes 39, 52, 250 — 39 is a parity-class bridge union bound, 52 is a twin-tile\n  deficit-class closure, both unrelated to the opener's wheel-class composition.\n- `mod 15/105 classes`: route 104 — a spiral-gauge `mod 105` example, unrelated.\n\n## 4. Verdict\n\n`promising`: the step is open and is returned exactly, as `next_step`, for the pursuit to take.\n\nLimits: the comparison covers the returns the brief names and the served corpus available at\n2026-10-11T10:2xZ; a newer return could change the answer. This check makes no mathematical claim of\nits own and does not run the experiment.","prior_art_md":"# Prior art — route 250 step check (job #6202)\n\n**No new external literature search was run.** This is an unchanged-step comparison; it makes no new\nresearch claim, so prior art is reused, unchanged, from the route's own record.\n\nRoute 250's prior-art record (authored in #2648 and re-stated in #2680) holds: the *first-order* twin\nresidue-class / consecutive-difference bias is published (Sahoo, arXiv:2111.09053; Lemke Oliver–\nSoundararajan, PNAS 113 (2016); Lemann 2006; Chebyshev/prime-races), and the second-moment /\nshort-interval variance objects are published (Goldston–Montgomery 1973; Montgomery–Soundararajan 2004;\nHooley; Keating–Rudnick 1996; Gorodetsky 2024; Dubner 2005). The **specific finite statistic** — the\nconditional class-split under-dispersion `T` with a multinomial null and an MC band, and where in the\nclass-resolved two-point function its residual lives — was **not located** in print or in-corpus.\n\nThe step-check decision here rests only on the served in-corpus returns #2680, #2685, #2686, #2690,\n#2693 and route 250's own record; it does not extend the prior-art claim."},"research_route_id":250,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b636ffc03fc27a50c0114dfd","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #250's next experiment was set by return #2680, 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 the frozen producer/checker of return #2648 and of this return (X = 2^27, exact sieve; optionally extend to 2^28). (1) Build the class-resolved 2-point counts C_{a,a'}(d) for admissible a,a' mod 15/105 and d over the first ~10 consecutive openers, and compare each to the HL 4-tuple prediction S({0,2,d,d+2}) with the class constraint. (2) Build a MATCHED POINT PROCESS, not a weight product: place openers by sequential conditional sampling whose class-transition probabilities are the measured/HL-predicted ones for lags 1..L and the empirical marginal beyond L; this is the bounded replacement for the route's under-specified Gibbs/exchange idea. (3) Recompute T and report T/E[T] against the observed ladder, and repeat the conditioning-scale ladder under that null. Standard library + numpy, one bounded run.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":0.75},\"failure\":\"T/E[T] stays below the matched process's band, i.e. the class composition is more even than any 2-point-matched process at lags <= 10: the residual is a genuine higher-order (>= 3-point) local channel; report the gap, the surviving lag range and the T/E[T] ladder, and hand the channel back with that scale attached.\",\"success\":\"The matched process reproduces every observed T/E[T] within its band at both moduli, and the class indicator's measured rho(k) for k >= 2 is reproduced by the lags-2..L terms: the under-dispersion is then the HL pairwise structure projected onto the wheel classes and the channel closes with a measured reason (the lag-1 shortfall is the size of the lags-2..10 contribution).\",\"question\":\"Is the class-composition under-dispersion of the twin openers (T/E[T] = 0.71-0.89 at X=2^27, conditional on the block total, over the admissible classes mod 15 and 105) reproduced by the CLASS-RESOLVED two-point function of the openers over lags 1..L - i.e. by the HL 4-tuple object route 248 measured - or does it need a higher-order local structure? The measurement here says the lag-1 (nearest-neighbour) part alone reproduces only 24-55% of it, and the class indicator's autocorrelation is negative out to ~10 consecutive openers (position lags up to ~2e3), which is where the residual must live.\",\"budget_hours\":0.75,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"route-245-return-2625\",\"route-247-return-2631\",\"route-248-return-2637\",\"route-250-return-2648\",\"hardy-littlewood-1923\",\"lemke-oliver-soundararajan-2016\",\"sahoo-2111.09053\"]}\n\nThe route's own returns: #2648, #2680 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2693 (route 255, promising, recorded, recorded): # Evidence — route 255 first look (job #5593) Frozen rule: `PREREGISTRATION.md` sha256 `0da986f2044ed1866f77f1ae9f4b58feceddd53a567ecf9ff08f2913675409d9` (`AMENDMENT.md`: one A2 transcription slip of a served number). Producer `compute_hl.py`; independent checker `check_hl.py`. ## Model-free inputs, recorded (no new enumeration) - `results-hi-27.json` (return #2686, served sha `a79dbc25…`): `X_\n- Return #2690 (route 254, promising, recorded, recorded): # Evidence — route 254 first look (job #5591) **What the evidence changes.** Route 248's identification (\"the sub-Poisson block deficit is the Hardy–Littlewood local factor\") is a **shape** match at one scale; route 254 (proposed by #2685) asks whether the *same* kernel gives an **absolute** prediction of route 245's aggregate deficit `1−V(h)`, and whether it holds past `h=2^20`. This first look \n- Return #2686 (route 255, proposed, recorded, recorded): # Evidence / provenance — [private] (job #5592) - **Job #5592**, type `explore`, purpose `discovery`, stage `discover`, lane `dir-558`, general mode. Attempt `[private]`. Launch `[private]`. Run public id `[private]`, session `[private]`. - **Protocol** `department-v2.research-2026-10-09.1`, **framework** `framework-0b4ebaa0c73a` (unchanged from stamp `[run]-1.0.11`, 53/53, < 24 h — readine\n- Return #2685 (route 254, proposed, recorded, recorded): # Evidence: why this is worth a bounded investment Route 248's closure (\"the sub-Poisson deficit is the HL local factor\") rests on a *lag-resolved* match at a **single scale** and lags `≤ 15360`. The statistic route 245 actually promotes (`1−V(h)`, and its use as the route-87 yardstick `sigma_osc`) is an **aggregate**: a block of length `h` integrates the covariance over ALL lags `|d| < h`. A sin\n\nReturn the ordinary report and transcript plus research: {route_id: 250, 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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