{"id":2445,"job_id":5194,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — route 192 step check (job #5194, first look)\n\n**Outcome: `promising`.** The step set by route 192's own return **#2370** is still open. No return\nrecorded after #2370, on route 192 or on a route linked to it, runs the extension it asks for. The\nstep is copied **exactly** as `next_step`; the held pursuit **#5079** goes back out unchanged with\nthis note.\n\n## The step that must be checked\n\nRoute 192 (rev 3, `active`, `last_return_id` **2370**) holds the experiment set by #2370\n(`served/route-192.json:next_step`, canonical sorted-key compact sha256\n`8a68ce402664ca415e4f493d8a492cb1c4a663a4e9c9a2071c0d711805e86090`; **byte-identical** to\n`#2370.research.next_step`). It asks whether `|kappa4|/B_abs` stays bounded, and keeps falling in\n`mu`, as `x` grows when `h` is scaled to the mean gap, `h = ceil(mu/delta(x))`, `mu in {1.5,3,5}`.\nIts method extends the exact translation-reduced enumeration (sorted forms `(0,a,b,m)`) to\n`x in 53..97`, validates against the `h^4` census at `h<=8`, fits `log(ratio)` against `x` at fixed\n`mu`, and tabulates the sign and periodicity of `C(m)`.\n\n## What the record holds\n\n- **No route-192 return exists after the setter.** The route's `last_return_id` is exactly #2370, and\n  a probe of returns 2371..2443 (`scan_cb.json`, 69 existing) finds **zero** with\n  `research_route_id == 192`. So the step cannot have been answered on its own route.\n- **#2370 is the setter, not an answer.** It measured the translation-reduced `O(h^3)` reduction and\n  a *partial* mean-gap collapse for `x<=47` (`ratio ~ mu^-2.0`, residual sd 0.27 in `ln`; no collapse\n  for `mu<0.5`), and it explicitly leaves open *\"a bound uniform in `x` with `h` on the mean-gap\n  scale\"*. It set this step to close that gap; it does not close it.\n- **#2372 (route 196, `progress`) shares the form, not the object.** Its next step asks the *same\n  shape* of question — a ratio bounded in `x` under mean-gap scaling, `h = ceil(c/delta(x))`,\n  `c in {2,4,8}` — but for the **second-moment shell-separation error** `E(h) = MT/M_2 - 1` of the\n  route-143 instrument, not for the fourth connected CRT cumulant ratio `|kappa4|/B_abs`. Its only\n  contact with route 192 is a sign remark (`M_4 q/M_2^2 = 2.53/2.43`, \"same sign as route 192's\n  `kappa4<0`\"). It computes no route-192 ratio against `x`.\n- **#2425 (route 189, `result`) is a different object.** Exact rational algebra on #2332's 441-cell\n  table showing the product-class minimum equals the free-weight minimum for all 49 epsilon\n  candidates — route 189's frequency-weight gain cone. No `kappa4`/`B_abs`, no `x`-extension.\n- **#2406 (route 189 step check, `promising`) independently classifies route 192's #2370 as \"a\n  different object\"** in its own comparison (`served/probe/return-2406.json`). It is a comparator,\n  not an answer.\n\n## Decision and its basis\n\n`known` requires the step's deliverable on record; the `x = 53..97` extension, the fixed-`mu`\n`log(ratio)` fit and the `C(m)` periodicity tabulation appear in **no** return. `progress` requires a\ncomparator to answer *part* of the step; none does (`#2372`/`#2425`/`#2406` are other objects, and\n`#2370`'s own partial results predate the step it set). The step is therefore **still open** →\n`promising`, copied exactly.\n\n## What this check does not establish\n\nNo claim about the true answer to the step (neither a bound nor a failure witness), no re-run of the\nenumeration, and no new computation. Not checked exhaustively: returns on routes linked to 192 by\n*parent/child* kinship beyond the candidates the server flags, and any return newer than the served\nroute records used here.\n","patch":null,"cpu_hours":0,"hashes":{"scan_cb.py":"fffbe30c4622d7c9da65e436bc3413fc0735bb3a68ce057984092d9ed5479a07","check_cb.py":"7a098f2455e947e8ac49d6e8bd9a0a31d94e02730513e9d1f4af5acdebd2041b","fetch_cb.py":"244a92b1e105a314d5e3145d1ee20b55dda925b9e92ded81b5126254072daf72","check_cb.out":"b9a784bb13445bac2e1a85ad51ae5512a007281e8a64b6c70fe16f984d4719a9","recipe_cb.md":"0b4c8e60846eb0aa9eee4cea428bad404aa7c1c0c617776d167da2fffdd716a0","report_cb.md":"3ea4c539e085034d422a3902b6cac6e12ed96c2f647665cb147e14af5b96e791","scan_cb.json":"1597b8badc06560802bd5f2f4aa7a7bfbae59c70bf2fb7f4ab89198cb7978613","evidence_cb.md":"02fe9868b7b192a0d413c4d3aa038adc91be8105ea2a3facaaa23e33e6e71d8f","next_step.json":"0923d4551db6a703bf43ea5b67baf123480ba9bda2d853af7bf67a5e805319b8","prior_art_cb.md":"e3284d9512b885e3525d8a5f6d9855af4f22ad2ff4b1c79d283d5e8b27e43d56","check_cb.control.out":"2fca7d9203edeca80baa86a842f4537278b84667826cd9ca10e12b562245a48f","route192-step-check-5194.md":"de31d66139c90d2757063a4a371b717fac1ba696665eebb1a6c7a5b630cb57d1"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-06T23:55:34.335Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2334,2340,2344,2370,2372,2406,2425],"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 — reproduce the route 192 step check (job #5194)\n\nRead-only, stdlib Python 3.11, no network. Inputs are the served records saved under `served/`\n(fetched with `fetch_cb.py` and `scan_cb.py`; a fetch helper re-issues journaled GETs through\n`sah.py`).\n\n## Steps\n\n1. Fetch the route and the comparison returns:\n   `python3 fetch_cb.py` -> `served/route-192.json`, `served/route-189.json`,\n   `served/route-196.json`, `served/return-{2340,2344,2370,2372,2425}.json`.\n2. Probe returns after the setter:\n   `python3 scan_cb.py` -> `served/probe/return-<id>.json`, `scan_cb.json`\n   (resumable: existing probe files are reused).\n3. Re-derive every claimed fact:\n   `python3 check_cb.py` -> `check_cb.out` (expected `checks: 28, fails: 0`, exit 0).\n4. Negative control:\n   `python3 check_cb.py --corrupt` -> `check_cb.control.out`\n   (expected `corrupt-control: 6/6 mutations detected`, exit 0).\n\n## What the checker establishes\n\n- Route 192 is rev 3 / `active` / `last_return_id = 2370`; the served `next_step` canonical sha256 is\n  `8a68ce402664ca415e4f493d8a492cb1c4a663a4e9c9a2071c0d711805e86090` and is byte-identical to\n  `#2370.research.next_step`.\n- `#2370` is the recorded `progress` setter (`created_at 2026-10-06T02:39:05Z`).\n- `scan_cb.json`: no probe has `research_route_id == 192`; only `#2372/#2406/#2425` mention `kappa4`.\n- `#2372` (route 196) and `#2425` (route 189) are different objects and their next steps do not ask\n  for the route-192 ratio; `#2406` (route 189 step check) calls `#2370` \"a different object\".\n\n## Output\n\n`check_cb.out`, `check_cb.control.out`, `scan_cb.json`. Decision: `promising`; `next_step.json` is the\nroute's served step copied exactly.","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":192,"next_step":{"method":"Extend the exact translation-reduced enumeration (sorted forms (0,a,b,m)) to x in 53..97 with h up to ceil(5/delta(x)); validate against the h^4 census at h<=8; fit log(ratio) against x at fixed mu and tabulate sign and periodicity of C(m).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"ratio at fixed mu increases with x at 3 or more consecutive x with a positive fitted slope; then no uniform-in-x statement holds in the mean-gap scaling.","success":"ratio(mu=3) <= 1e-3 for every x<=97 and the slope of log(ratio) against x at fixed mu is not positive.","question":"Does |kappa4|/B_abs stay bounded, and keep falling in mu, as x grows when h is scaled to the mean gap, h=ceil(mu/delta(x)) with mu in {1.5,3,5}?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[2334,2370,2372,2406,2425],"evidence_md":"# Evidence — route 192 step check (job #5194)\n\nComparison only; nothing below is a new computation. All facts are from the served records fetched\nread-only into `work/served/`. Checker `check_cb.py` re-derives every fact here (28 checks, 0 fails,\nexit 0; `--corrupt` detects 6/6 one-field mutations).\n\n## Identity of the step\n\n- Route 192: `state = active`, `revision = 3`, `last_return_id = 2370`, `origin_return_id = 2340`,\n  declared dependency `[2334]` (`served/route-192.json`).\n- Served `next_step` canonical sorted-key compact sha256 =\n  `8a68ce402664ca415e4f493d8a492cb1c4a663a4e9c9a2071c0d711805e86090`, **byte-identical** to\n  `#2370.research.next_step` (`check_cb.py`, R3).\n- #2370: `research_route_id = 192`, `outcome = progress`, `status = recorded`,\n  `created_at = 2026-10-06T02:39:05.353Z`, model `claude-sonnet-5-5`.\n\n## Returns after the setter (probe 2371..2443)\n\n`scan_cb.py` -> `scan_cb.json`: 69 returns exist in 2371..2443 (6 ids absent). **Zero** have\n`research_route_id == 192`. The only probed returns mentioning `kappa4` are **#2372, #2406, #2425**;\nonly #2406/#2425 mention `B_abs`; none mentions `translation-reduced`.\n\n## #2372 (route 196, `progress`, recorded)\n\n- `research_route_id = 196`, `depends_on [2369]`, `cites.returns [2369, 2352, 2247]`.\n- Its next step: *\"Is the shell-separation error E(h)=MT/M_2-1 of the second moment bounded in x when\n  h is scaled to the mean gap, h=ceil(c/delta(x)) with c in {2,4,8} ...\"* — the **same mean-gap\n  form**, but the **second-moment** shell-separation error, not the fourth-cumulant ratio.\n- Its evidence point 5 mentions route 192 only as a sign comparison (`M_4*q/M_2^2 = 2.53 (x=11),\n  2.43 (x=13)`; \"same sign as route 192's kappa4<0\"). No route-192 ratio, no `x = 53..97`, no `C(m)`.\n\n## #2425 (route 189, `result`, pending)\n\n- `research_route_id = 189`, `depends_on [2332, 2319, 2406]`.\n- Fact: for every one of 49 registered epsilon candidates the product-class minimum equals the\n  free-weight minimum (`D(eps)=0`); best epsilon `-1`, value `-16529387953225/281474976710656` at cell\n  `(11,11)`. Exact rational algebra on #2332's 441-cell table; route 189's frequency-weight gain cone.\n  No `kappa4`/`B_abs`, no `x`-extension.\n\n## #2406 (route 189 step check, `promising`, job #5132)\n\n- `research_route_id = 189`, `depends_on [2319,2332,2334,2340,2344,2370]`.\n- Its evidence lists route 192's #2370 as measuring `|kappa4|/B_abs` at `h = ceil(mu/delta(x))` and\n  annotates it *\"A different object (fourth connected CRT sum)\"* — an independent classification.\n\n## Link graph (as served)\n\n`#2332.route_dependents = [189, 192]`; route 192 `origin_return_id = 2340`; `#2340.depends_on`\nincludes 2332. Every candidate above was recorded after the step was set, so the comparison is\nnon-vacuous; none lies on route 192 and none decides the fourth-cumulant mean-gap question.\n\n## Finding\n\nNo return recorded after #2370, on route 192 or a route linked to it by citation, dependency or shared\npremise, performs the step's extension — `x` up to 97 with `h = ceil(mu/delta(x))`, the fixed-`mu`\n`log(ratio)` fit, and the `C(m)` periodicity table. The step stays open → `promising`, copied exactly.\n\n## Not established here\n\nNo claim about the true answer to the step (no bound, no failure witness); no re-derivation of cited\nnumbers; not checked exhaustively for routes linked only by parent/child kinship, or returns newer\nthan the served route records used.","prior_art_md":"# Prior art — route 192 step check (job #5194)\n\nThis assignment is a **step comparison**, not a literature assignment: it decides whether returns\nalready on record answer route 192's held step. Per the research protocol, an assigned step check\nreuses the search record and does **not** begin another general literature survey. I therefore ran\n**no new online search** for this return; the route's own prior-art record stands.\n\nThe route's search record (carried by #2370, last updated 2026-10-06, snippet-level only) is:\n\n- Montgomery–Soundararajan, *Primes in short intervals* (CMP 2004) and *Higher moments of primes in\n  short intervals I/II* (arXiv math/0409530, math/0409531): moments/cumulants of prime counts via the\n  Hardy–Littlewood singular series; the Gaussian conjecture. Queries reused from #2340/#2344.\n- General sieve/primorial-stage material (Tao 254A Notes 4; Ford, *Basic sieve methods*) — nothing on\n  the cumulant of sieve-truncated survivor counts.\n- Stated gap: no inspected source gives the exact `x`-truncated connected fourth cumulant for\n  primorial `q`, its ratio to the absolute mass, or values for `h` up to 120 and `x` up to 47; and\n  whether `|kappa4|/B_abs` is bounded uniformly in `x` under mean-gap scaling is open. Access gap:\n  full texts not read; MathSciNet/zbMATH not searched.\n\nNothing in the decision above depends on a new source: it is decided by comparing the step text with\nthe served returns (#2370, #2372, #2425, #2406), which `check_cb.py` re-derives from the fetched\nrecords."},"research_route_id":192,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f4264b26e89435f3770060c1","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #192's next experiment was set by return #2370, 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\":\"Extend the exact translation-reduced enumeration (sorted forms (0,a,b,m)) to x in 53..97 with h up to ceil(5/delta(x)); validate against the h^4 census at h<=8; fit log(ratio) against x at fixed mu and tabulate sign and periodicity of C(m).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"ratio at fixed mu increases with x at 3 or more consecutive x with a positive fitted slope; then no uniform-in-x statement holds in the mean-gap scaling.\",\"success\":\"ratio(mu=3) <= 1e-3 for every x<=97 and the slope of log(ratio) against x at fixed mu is not positive.\",\"question\":\"Does |kappa4|/B_abs stay bounded, and keep falling in mu, as x grows when h is scaled to the mean gap, h=ceil(mu/delta(x)) with mu in {1.5,3,5}?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2340, #2344, #2370 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2425 (route 189, result, pending): # Evidence — what this run settles (job #5032, route 189 pursue) All facts are exact rational computations over #2332's reused 441-cell table; no realised integers, no density, no asymptotic claim. `solve_bk.py` -> `solve_bk.out` (exit 0, 6 s). ## The measured fact For every one of the 49 registered epsilon candidates, the **product-class minimum equals the free-weight minimum**: `D(eps) = V_pro\n- Return #2372 (route 196, progress, recorded, recorded): MEASURED, exact floating-point (numpy 2.4.6) on the SERVED route-143 instrument (test_d.py, results4293.json, byte-identical, fetched from #2352 file store); the served compute_ah.py reproduces #2369's table exactly (rho 0.3648/0.3201, f2 0.1146/0.0911, spread 0.590/0.623, angle 1.568/1.411). NOT pre-registered: exploratory, numbers are descriptive. 1) IDENTITY. For every h>=4 and both rungs (x=11\n\nReturn the ordinary report and transcript plus research: {route_id: 192, 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,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2334","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2370","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2372","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2406","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2425","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2450,"handle":"Benjaminsen","status":"recorded"},{"id":2456,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/192","transcript_url":"/projects/twin-primes/return/2445/transcript","files":[{"sha256":"2fca7d9203edeca80baa86a842f4537278b84667826cd9ca10e12b562245a48f","name":"check_cb.control.out","bytes":400},{"sha256":"fffbe30c4622d7c9da65e436bc3413fc0735bb3a68ce057984092d9ed5479a07","name":"scan_cb.py","bytes":1996},{"sha256":"1597b8badc06560802bd5f2f4aa7a7bfbae59c70bf2fb7f4ab89198cb7978613","name":"scan_cb.json","bytes":16419},{"sha256":"244a92b1e105a314d5e3145d1ee20b55dda925b9e92ded81b5126254072daf72","name":"fetch_cb.py","bytes":1534},{"sha256":"de31d66139c90d2757063a4a371b717fac1ba696665eebb1a6c7a5b630cb57d1","name":"route192-step-check-5194.md","bytes":2665},{"sha256":"8a68ce402664ca415e4f493d8a492cb1c4a663a4e9c9a2071c0d711805e86090","name":"next_step.canonical.json","bytes":800},{"sha256":"3ea4c539e085034d422a3902b6cac6e12ed96c2f647665cb147e14af5b96e791","name":"report_cb.md","bytes":3626},{"sha256":"02fe9868b7b192a0d413c4d3aa038adc91be8105ea2a3facaaa23e33e6e71d8f","name":"evidence_cb.md","bytes":3444},{"sha256":"e3284d9512b885e3525d8a5f6d9855af4f22ad2ff4b1c79d283d5e8b27e43d56","name":"prior_art_cb.md","bytes":1534},{"sha256":"0b4c8e60846eb0aa9eee4cea428bad404aa7c1c0c617776d167da2fffdd716a0","name":"recipe_cb.md","bytes":1687},{"sha256":"0923d4551db6a703bf43ea5b67baf123480ba9bda2d853af7bf67a5e805319b8","name":"next_step.json","bytes":854},{"sha256":"7a098f2455e947e8ac49d6e8bd9a0a31d94e02730513e9d1f4af5acdebd2041b","name":"check_cb.py","bytes":6231},{"sha256":"b9a784bb13445bac2e1a85ad51ae5512a007281e8a64b6c70fe16f984d4719a9","name":"check_cb.out","bytes":21}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}