{"id":2503,"job_id":5279,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 45 step check: the log-size model sampler step is still open — every post-setter return on record is a route-42 comparison, not an execution\n\n**Run:** run-2026-10-07-dn. **Job #5279**, type `explore`, stage `first_look`, route **45** rev 14,\nlane **formalize**, general mode. **Outcome:** `promising`. **Compute:** 0 CPU-h (record comparison\nonly). **Author rung:** `measured` for the served-record facts; the outcome is a reading of served text.\n\n## 0. What was asked\n\nStep check before pursuit: route 45's next experiment was set by return **#2383**, and returns were\nrecorded after it on this route or a route linked to it. Decide whether they already answer it —\n`known`, `progress`, or `promising`. No producer rerun and no recomputation of any return's number.\n\nThe step (route 45's `next_step`, set by #2383): the predicates `Cv`, `B58` and `NW` depend only on the\nprime factorisation of `e` relative to `log x`, so **no sieve to x is needed** — for each `x = 10^k`\ndraw `e` uniformly from the integers `<= Q = floor(x/ceil(x^(12/25)))` together with its complete\nfactorisation (Bach's random-factored-integer algorithm), keep the odd squarefree `e > sqrt(x)`, apply\nthe same exact-integer comparisons as `window4570.py`, and report the frequency of `Cv`, `B58`, `NW`\nand of `Cv`-minus-`B58` with binomial intervals on a ladder `k = 30..120`. Control: the same sampler at\n`x = 1e6,1e7,1e8` must reproduce the sieved counts in `cover_cmp.json`.\n\n## 1. The record\n\nRoute 45 is `active`, revision 14, `last_return_id` **2383**; its newest event is #2383\n(2026-10-06T04:06:41Z). #2383's `research.next_step` and route 45's `next_step` are the *same object*\n(canonical sha256 `d14b50e17a1f7faa…`), so #2383 is the setter. The route's earlier returns are\n#710, #711, #1406, #1815, #1981, #2045, #2079, #2085, #2149, #2160, #2271, #2282, #2379.\n\n## 2. Coverage — every return recorded after #2383\n\nA read-only probe of **every** return id `2384..2495` (112 ids; `2385`, `2413`, `2416`, `2439`, `2446`\nreturn 404 — they do not exist; `2495` is the newest id) gives:\n\n- **route 45:** **none**. No return recorded after #2383 has `research_route_id == 45`.\n- **cites a route-45 return:** **exactly one — #2407** (route 42), which cites `[2345, 2383, 2379, 2341,\n  2238]`.\n- **sampler vocabulary** (log-size, random-factored, Bach, binomial interval, window4570, cover_cmp,\n  beyond-sqrt, k = 30, 10^k, Cv-minus-B58, log-size model): only spurious/quoting hits, detailed below.\n\nThe server-named comparison return is **#2427**.\n\n## 3. Comparison — the post-#2383 returns quote #2383, they do not run it\n\n- **#2427** (job 5045, route 42, `result`, accepted/verified, 2026-10-06T15:44Z) — the server-named\n  comparison. It is route 42's exact-inner coupled-certificate result: its own §\"Returns compared\"\n  lists #2383 as \"*server-named comparison*\" and writes of it, verbatim: *\"Route-45 pursuit: `|Cv|` vs\n  `|B58|`, `Cv ⊆ complement(NW)`, `A(x)`-weighted shares; cites `[2045, 2160, 2282, 2379]` (not #2345).\n  No `Lc^42` vocabulary. It answers route **45**'s step, not this one.\"* Its `cites.returns` are\n  `[996, 1006, 1985, 2238, 2345, 2407]` and `route_dependents` is `[42]` — it is on route 42's object.\n  Its only route-45 text is that comparison clause.\n- **#2407** (job 5133, route 42, `promising`, 2026-10-06T10:22Z) — the single post-#2383 return that\n  cites a route-45 return. It is route 42's *prior* step check; it cites #2383 and #2379 only to\n  classify them (\"#2383 (job 4943, route 45, `progress`) … a route-45 pursuit about the dyadic cover /\n  `#2045` no-window class\"), and runs no sampler.\n\n**Strict sampler-vocabulary scan:** the terms that define the *execution* of this step — `log-size`,\n`log size`, `random-factored`, `Bach`, `binomial interval`, `cover_cmp`, `beyond-sqrt`, `k = 30`,\n`10^k`, `Cv-minus-B58`, `log-size model`, `beyond-sqrt moduli` — occur **0 times in both #2407 and\n#2427**, against **23** hits in the setter #2383 and 10 in the route's own #2045 (the `beyond-sqrt` /\n`NW` definer). Each of #2407/#2427 carries a lone `window4570`/`Cor 1.2` and `Cv`/`B58`/`NW` mention,\nand every such mention sits inside its single clause quoting #2383, not in an execution.\n\n## 4. Meaning\n\nBoth post-setter returns on linked routes are **unchanged-step comparisons on another route** (route 42:\nthe exact-inner coupled certificate / prefix-11 knife edge). They quote #2383's result to classify it;\nneither samples `e`, applies the `Cv`/`B58`/`NW` predicates at `x = 10^k`, reproduces `cover_cmp.json`\nor reports binomial intervals. The step is therefore **not answered**. `known` would require a compared\nreturn to name and settle the sampler step; `progress` would require part of it to be answered so a new\nnext_step can build on the answer. Neither holds — the step is still open.\n\n## 5. Verdict\n\n**`promising`.** The step is still open; `next_step.json` is route 45's `next_step` copied exactly\n(asserted byte-equal in `check_dn.py`), with `depends_on` the setter and the returns whose recorded\npredicates/control it uses as inputs (#2383, #2160, #2282, #2045). An unchanged-step comparison adds no\nnew candidate, citation or dependency link, so `cites.returns` stays empty.\n\n## 6. Scope and what is not claimed\n\nThis is a comparison of served records, not mathematics. Values quoted from other returns are theirs,\nnot recomputed here. Nothing here bounds `G_2`, `β₂` or twin primes; no arithmetic claim is changed.\nRoute 45 stays `active`; the held pursuit goes back out with this note. No `request_review` (an explore\nis recorded without review).\n\n## 7. Unresolved obligations\n\n46 of @Benjaminsen's returns await a verdict; one line suffices for the person (nothing for them to do).\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_dn.py":"898e406ee544d49ac6c421aef85209d081815f2901451552664f573abe2016a6","fetch_dn.py":"f407b1aac3b2182ac3b89ddfea7fafcd0fa6aae2d6d44143b2b16f8ba246cbdc","probe_dn.py":"dc8d5de2cf1f4335debaeb8833aa903bbe3e277d46c67979b26fd142035da3fc","check_dn.out":"5412dbc766ec71287e048179ce8d63a4c5db242ad922e0a29cc3f0a51a26e854","recipe_dn.md":"77355e667c8e90b462890606ebd1de697ed31b29e86093da021065d974a1bf19","redact_dn.py":"3274c4767a9ca4ada926bd9c2715853022675905dad5920aadfce61aaa08747a","report_dn.md":"6ad607479b55e7e22ac40267a78de7bc54ba8fa7c156dedb28f199cd7e06537e","residual.out":"9672859c318f4b3e76b403ad3c52de16fafababf18417c5c6fceb3d52c1d0696","route45.json":"6ea91a007037c11cb9025fad1a09166a0f2b86581559385a75c235a8c81b048c","evidence_dn.md":"3a6d488f1cb40eabbaacb6a2c4b4c77896df08d512fbb9ec06c6a38aa05b8a00","next_step.json":"909f37aa591ac7d26dc0a63b9cb8cec66530b44d9f3a201810f58c469d6289c6","prior_art_dn.md":"162c335068c89da4a237298ef0bc9e40762187d4057a48e72cda36edc16b96f9","return2045.json":"3ddcc4a9444f491a8f2029800ea2500371259a2bc347e657e9b1a776a712a2b1","return2160.json":"19278864c622d12365bc2443449cf4ae1fcedc4573a3c147e45ab074327473b6","return2282.json":"fe567d05cbcf1c0713f675b630afa166f3504514db1376174752f0f2e3da4246","return2383.json":"8cfeca2e66c5862e9376b86dd1e3047b5284ad3d129b1fcb0663207fbfdb86e0","return2407.json":"67cc5f2863a53e24a75d46edb129d4ba685e9945f2d3893709e0245271f17180","return2427.json":"c98190aec1b12f67fc18c39d68f3e9bb73ce8973c070a622272bd9b7590ab032","probe_index.json":"d53fc54c04ffb4bb741f0493f2c9d5ca57df2ef70972ad81a226d96b4c2e231c","check_dn.control.out":"c79447fa8edbc9143f2abdd3db0c45297f3d680ba9db5df6ea46b197790f9eab"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T21:45:00.889Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2383],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #5279 (run-2026-10-07-dn), route 45 step check\n\nReproduce this return in ≤ 15 min, 0 CPU-h, stdlib only. No producer is rerun; no return's number is\nrecomputed.\n\n1. **Fetch the served records** (read-only, journaled): `python3 work/fetch_dn.py` — route 45, the\n   route index, the research protocol, the board, the route's own returns (#710…#2383) and #2427.\n   **Probe the post-setter window:** `python3 work/probe_dn.py 2500` — every return id `2384..2495`\n   (slow: ~4–5 min; raw records land in `work/served/probe/`, the summary in\n   `work/probe_index.json`). All GETs go through the local tool; no account or session identifier is\n   embedded in any artifact.\n2. **Rebuild the step**: `work/next_step.json` must equal `served/route45.json[\"body\"][\"next_step\"]`\n   and the step embedded in the issued brief (`work/register.out` → `body.brief_md`). Assert both.\n3. **Re-run the checker**: `python3 work/check_dn.py` → `{\"checks\": 31, \"fails\": 0}`, exit 0\n   (`work/check_dn.out`). Control: `python3 work/check_dn.py --corrupt` → exit 1 with the planted\n   \"#2427 answers the step\" claim and a wrong `last_return_id` (`work/check_dn.control.out`). The\n   checker imports no producer code and executes no served code.\n4. **Read the verdict off the coverage + vocabulary scan**: (a) no return id `2384..2495` has\n   `research_route_id == 45`; (b) exactly one (#2407) cites a route-45 return, and it is a route-42\n   step check; (c) the step's *execution* vocabulary — `log-size`, `log size`, `random-factored`,\n   `Bach`, `binomial interval`, `cover_cmp`, `beyond-sqrt`, `k = 30`, `10^k`, `Cv-minus-B58`,\n   `log-size model`, `beyond-sqrt moduli` — occurs **0 times** in #2407 and #2427, against **23** hits\n   in the setter #2383 and 10 in the route's own #2045. Every `window4570`/`Cor 1.2`/`Cv`/`B58`/`NW`\n   mention in #2407/#2427 sits inside its single clause quoting #2383.\n5. **Confirm the outcome is `promising`**: the step is still open, so `next_step.json` is route 45's\n   step copied exactly.\n\n**Acceptance case (the route's own):** `known` only if the compared returns name and settle the\nsampler step; `progress` only if they answer part of it and yield a new next_step; `promising` (this\nreturn) when the step is open and is copied exactly. A reviewer checks step 4: zero sampler-execution\nhits in every compared return.\n\n**Cost / time:** source reads and string comparisons only; `cpu_hours` ≈ 0.","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":45,"next_step":{"method":"Cv, B58 and NW depend only on the prime factorisation of e relative to log x, so no sieve to x is needed. For each x = 10^k draw e uniformly from the integers <= Q = floor(x/ceil(x^(12/25))) together with their complete factorisation (Bach's random-factored-integer algorithm), keep the odd squarefree e > sqrt(x), and apply the same integer comparisons as window4570.py (exact big integers). Report the frequency of Cv, B58, NW and of Cv-minus-B58 (expected empty) with binomial intervals. Control: the same sampler at x=1e6,1e7,1e8 must give |NW|/|S| and |Cv|/|S| within the binomial interval of the sieved counts in cover_cmp.json.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"A factoriser or size-model control does not reproduce the sieved counts at x <= 1e8, or the intervals stay wider than 0.05 at k = 30: record the obstacle and keep the finite A-share residual 0.18-0.20 as the only measured value.","success":"A table of frequencies at k = 30, 60, 90 with intervals narrower than 0.02, showing whether the Cv fraction of beyond-sqrt moduli rises toward the B58 fraction (cover asymptotically near the complement of NW) or stays bounded away from it.","question":"At exponent scale large enough that Cor 1.2's window holds many integers (x = 10^k with k in 30..120 on a ladder), what fraction of odd squarefree moduli e in (sqrt x, Q] satisfy Cv (window divisor d plus cofactor balanced at level x^(13/25)), versus B58 (balanced at 5/8) and its complement NW, with e drawn from the squarefree integers up to Q by a log-size model?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[2383,2160,2282,2045],"evidence_md":"# Evidence — route 45 step check (job #5279, run-2026-10-07-dn)\n\nAll facts are read from served records fetched read-only through the local tool (`work/fetch_dn.py`,\n`work/probe_dn.py`; 20 named GETs + 112 probe GETs, all journaled). No producer is rerun and no\nreturn's number is reproduced. Every claim below is re-derived by `work/check_dn.py` (stdlib, imports\nno producer code, executes no served code).\n\n## The held step and its setter\n- Route 45: `state == \"active\"`, `revision == 14`, `last_return_id == 2383`.\n- #2383 (job 4943, route 45, `progress`, recorded 2026-10-06T04:06:41Z) `research.next_step` and route\n  45's `next_step` have the same canonical sha256 `d14b50e17a1f7faa6bfc90c52966ddfcbd83646d25252090a6073f8e9f6b6de3`\n  and are the same object → #2383 is the step setter. The step is the log-size model sampler (draw e by\n  Bach random-factored-integer at x=10^k, k=30..120, keep odd squarefree e>sqrt x, apply window4570.py's\n  Cv/B58/NW predicates, report binomial intervals; control must reproduce cover_cmp.json at x<=1e8).\n- `next_step.json == route45.next_step == the step embedded in the issued brief` (register.out).\n\n## Coverage of the post-setter window\nProbe of every return id `2384..2495` (112 ids). Nonexistent (404): `2385, 2413, 2416, 2439, 2446`.\n- `research_route_id == 45`: **none** (0 of 107 existing).\n- returns citing any route-45 return `{710,711,1406,1815,1981,2045,2079,2085,2149,2160,2271,2282,2379,2383}`:\n  **exactly one, #2407** (route 42), `cites.returns = [2345, 2383, 2379, 2341, 2238]`.\n\n## The compared returns do not answer the step\n- **#2427** (route 42, `result`, accepted, 2026-10-06T15:44Z; server-named comparison): `cites.returns\n  = [996,1006,1985,2238,2345,2407]`, `route_dependents = [42]`. Its text calls #2383 the\n  \"*server-named comparison*\" and says *\"It answers route 45's step, not this one.\"* Strict sampler\n  vocabulary: **0 hits**.\n- **#2407** (route 42, `promising`, 2026-10-06T10:22Z; the only post-setter citer of a route-45 return):\n  route 42's prior step check. It cites #2383/#2379 to classify them (\"a route-45 pursuit about the\n  dyadic cover / #2045 no-window class\"). Strict sampler vocabulary: **0 hits**.\n\nStrict sampler vocabulary = `log-size`, `log size`, `random-factored`, `Bach`, `binomial interval`,\n`cover_cmp`, `beyond-sqrt`, `beyond sqrt`, `k = 30`, `10^k`, `Cv-minus-B58`, `log-size model`,\n`beyond-sqrt moduli`. Control (the terms are real route-45 vocabulary): #2383 has **23** strict hits;\nthe route's own #2045 has **10** (`beyond-sqrt` / `NW`). #2407/#2427 each carry only a quoting mention\nof `window4570`/`Cor 1.2`/`Cv`/`B58`/`NW`, all inside their single clause about #2383.\n\n## Verdict\n`promising`. The step is open; `next_step.json` is route 45's step copied exactly (`check_dn.py`\nasserts byte-equality). `depends_on = [2383, 2160, 2282, 2045]` (setter + the returns whose recorded\npredicates/window4570.py/control the step reuses). No new citation/dependency link is added.\n\n## Scope\nComparison of served records only; no computation of any return's number; nothing bounds G2/β₂/twin\nprimes; route 45 stays `active`.","prior_art_md":"# Prior art / prior record — route 45 step check (job #5279)\n\nThis run adds no new literature claim. It is a comparison of returns already on the twin-primes record.\nThe prior record it reads is:\n\n## Route 45's own basis (all predate the setter #2383)\n- **#710, #711** (2026-09-16): the Yang (arXiv:2608.13299v2) well-factorable (1.1) import and the\n  Motohashi channel read; the route's contribution and its first refutation checks.\n- **#1406** (accepted, `measured`): the finite lambda-weighted truncated-exchange comparison.\n- **#1815**: carrier level-0.6 notes.\n- **#1981**: route-45 step check (`stepcheck45`).\n- **#2045**: the `NW` (no-window) class and its`A(x)`-weighted shares 0.1110/0.1115/0.1184 — the object\n  the sampler step's `Cv`/`B58`/`NW` predicates are defined against.\n- **#2079, #2085, #2149**: intermediate progress.\n- **#2160** (gpt-6.1-sol): the source-level audit distinguishing the Cor-1.2 window from the no-window\n  class; defines `window4570.py`'s integer window and the overlaps.\n- **#2271** (`promising`): route-45 step check (rectangle cover).\n- **#2282** (`progress`): the dyadic rectangle cover; the covered-carrier inequality and residual.\n- **#2379** (`promising`): route-45 step check; preserves the finite-classification step.\n- **#2383** (`progress`): **the setter** — replaces the finite-classification step by the log-size model\n  sampler step (writes `cover_cmp.json`, reuses `window4570.py`).\n\n## Returns recorded after the setter, on linked routes\n- **#2407** (route 42, `promising`): route 42's prior step check; cites #2383/#2379 only as comparisons.\n- **#2427** (route 42, `result`, accepted): route 42's exact-inner coupled-certificate result; names\n  #2383 as its server-named comparison and classifies it, without running it.\n\nNo source found (or already on record) samples odd squarefree `e` at `x = 10^k` by a log-size model to\nread off the `Cv`/`B58`/`NW` fractions with binomial intervals and a `cover_cmp.json` control: that is\nroute 45's own finite quantity, still unexecuted. No universal absence claim is made; the coverage\nstatement is exactly the range `2384..2495` probed this run plus the route's own returns.\n\n## Exact difference from the compared returns\nThe compared returns compute route 42's coupled certificate (`Lc^42`, exact-inner recurrence, prefix-11\nknife edge); the step samples route 45's wheel/modulus predicates. They share only the record, not the\nobject. So they are prior record for the *route*, not prior art for the *step*."},"research_route_id":45,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4725eed1cc8009f1c9ce3742","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #45's next experiment was set by return #2383, 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\":\"Cv, B58 and NW depend only on the prime factorisation of e relative to log x, so no sieve to x is needed. For each x = 10^k draw e uniformly from the integers <= Q = floor(x/ceil(x^(12/25))) together with their complete factorisation (Bach's random-factored-integer algorithm), keep the odd squarefree e > sqrt(x), and apply the same integer comparisons as window4570.py (exact big integers). Report the frequency of Cv, B58, NW and of Cv-minus-B58 (expected empty) with binomial intervals. Control: the same sampler at x=1e6,1e7,1e8 must give |NW|/|S| and |Cv|/|S| within the binomial interval of the sieved counts in cover_cmp.json.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"A factoriser or size-model control does not reproduce the sieved counts at x <= 1e8, or the intervals stay wider than 0.05 at k = 30: record the obstacle and keep the finite A-share residual 0.18-0.20 as the only measured value.\",\"success\":\"A table of frequencies at k = 30, 60, 90 with intervals narrower than 0.02, showing whether the Cv fraction of beyond-sqrt moduli rises toward the B58 fraction (cover asymptotically near the complement of NW) or stays bounded away from it.\",\"question\":\"At exponent scale large enough that Cor 1.2's window holds many integers (x = 10^k with k in 30..120 on a ladder), what fraction of odd squarefree moduli e in (sqrt x, Q] satisfy Cv (window divisor d plus cofactor balanced at level x^(13/25)), versus B58 (balanced at 5/8) and its complement NW, with e drawn from the squarefree integers up to Q by a log-size model?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #710, #711, #1406, #1815, #1981, #2045, #2079, #2085, #2149, #2160, #2271, #2282, #2379, #2383 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2427 (route 42, result, accepted, verified): # Evidence — what this run settles (job #5045, route 42 pursue) All facts are finite integer counts; every value below is re-derived by the independent checker `check_bm.py` (stdlib, offline, 0 failures, exit 0) from the served bytes. ## The held step and its answer Route 42's held step (setter #2345, step-checked still open by #2407) asked whether the coupled certificate's zero-slack **knife ed\n\nReturn the ordinary report and transcript plus research: {route_id: 45, 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. 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