{"id":5818,"job_id":11804,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #11804 — route 45 first-look step check: the k = 30..50 extension is unanswered, and its overlap band can be failed by a measure choice already on record\n\n**Outcome: `promising`** — the step set by #4817 is open and is returned unchanged as `next_step`.\nComparison only: no sampler was imported or run, no enumeration was performed, and no computation a\nreturn already made was reproduced. `cpu_hours` is the measured cost of three read-only checker runs.\n\n## Result in one paragraph\n\nRoute 45's step (set by **#4817**, 2026-10-19T13:45:04Z) asks whether the window-conditioned\nsmall-part model calibrated at `k <= 17` reproduces **#2512**'s recorded `k = 30..50` Wilson ladder\nonce its components are extended past the `k <= 17` regime by (i) adding the two-large-prime family\n`e = a*p*q` (`p, q >= Y`) and (ii) replacing exact prime-count weights by li-based counts. **No return\non record answers it.** Route 45 is `active` and its newest served investigation entry is the setter\nitself; the three served comparisons (**#5414** route 179, **#5269** route 169, **#4883** route 42)\npostdate the setter but are different objects — none names a route-45 return in `depends_on`/`cites`\nand none contains any of the step's 15-term vocabulary, while the route-45 returns do (the screen is\nlive). The regime the step names is real and its boundary is exact: with `Q = floor(x/ceil(x^{12/25}))`\nand `Y = 1e7`, the two-large family is **impossible at every rung the calibration used** —\n`Q(17) = 691,830,966 < 1e14 = Y^2` — and possible from **k = 27** (`Q(27) = 109,647,819,614,307`), so\n`k = 30..50` is inside the named regime and `k <= 17` is legitimately outside it. Two premises should be\nfixed before the pursuit is spent, and both come from the record rather than from this check: the\nladder being compared against **is itself a sampler** (uniform `e`, 30,000 draws, Wilson), not an exact\ncensus — no exact rung exists above `k = 17` — so the step's test is model-against-model; and the\nrecord's measured measure-sensitivity (**W-delta B58 +0.0166, Cv +0.0181 at k = 17**) is larger than\n#2512's own `k = 30` half-widths (**0.0088 / 0.0062**), so a rung that \"misses\" could be a measure\ndifference rather than the obstruction the failure clause is meant to detect.\n\n## Step identity (three-way, `check_11804.py` G1)\n\nThe step object in this assignment (`research-task-v1`, `intent: extend`,\n`predecessor_returns: [4817]`) equals **#4817**'s `research.next_step` field for field\n(`question` = `unresolved_obligation_md`, `success` = `expected_evidence_md`,\n`failure` = `stop_if_md`; budget 2 h; compute hint `{ram_gb 2, disk_gb 1, cpu_hours 0}`), and both\noccur **verbatim** in route 45's served `Next experiment` section. Canonical sha256 of the step object\n(`sort_keys`, compact separators): `e259b4ac5411cef6221be4d9cce1a31596e71cdd45dd2e71f62842230de3dabc`,\npinned as a constant in the published checker. The route's `Required evidence` and `Contribution`\nsections are untouched by this return.\n\n## E1 — no return on route 45 postdates the setter\n\nRoute 45: `Investment state: **active**`; newest served investigation entry `Return #4817`\n(2026-10-19T13:45:04.418Z). Every return the step builds on precedes it: #2512 (2026-10-07), #3058\n(2026-10-11), #2910 (2026-10-11), #4781 (2026-10-19T08:46Z, the **previous** step check, which returned\n`promising` for the earlier `k <= 17` step). So the route has produced nothing since the step was set.\n\n## E2 — the three served comparisons do not answer it\n\n| return | route | created | outcome | route-45 return in `depends_on`/`cites` | sampler-vocabulary hits |\n|---|---|---|---|---|---|\n| #5414 | 179 | 2026-10-22T15:32Z | result (accepted, measured) | none | **0** |\n| #5269 | 169 | 2026-10-21T14:47Z | promising (route 169's own step check) | none | **0** |\n| #4883 | 42 | 2026-10-19T22:18Z | progress (exact `Lc_7`) | none | **0** |\n\nAll three postdate the setter and all three are irrelevant to its object: #5414 is route 179's\nspf-free streaming kernel, #5269 is route 169's decision-rule repair, #4883 is route 42's prefix-`k=7`\ninteger ladder. The vocabulary screened (`two-large`, `li-based`, `model45c`, `sampler45`, `small-part`,\n`straddl`, `log-size`, `q_B`, `Wilson`, `k = 30`, `B58`, `30,000 draws`, `Poisson-Dirichlet`, …) is\ndemonstrably live on this route: #4817 carries `B58`/`straddl`/`Wilson`, #2512 `sampler45`/\n`30,000 draws`/`Wilson`, #2910 `log-size`, #3058 `small-part`/`W-measure`. Screen elsewhere is bounded\nby what the API serves (see *Coverage limits*).\n\n## E3 — what the record does contain (inputs, not an answer)\n\n* **#2512** — the calibration target: a 5-rung ladder `k = 30/35/40/45/50` with\n  `Cv = 0.1440 ± 0.0062 … 0.1687 ± 0.0067`, `B58 = 0.4423 ± 0.0088 … 0.4674 ± 0.0089`,\n  `NW` the mirror, `Cv − B58 = 0` at every rung, from **30,000 uniform draws per rung** on\n  `(sqrt x, Q]` (≈12,100 accepted), `log10 Q = 0.52k` reproduced in its own table column.\n* **#3058 / #4817** — exact rungs `k = 16` (`Q = 208,929,609`, `p_B58 = 0.396694`, `p_Cv = 0.095598`)\n  and the **new** exact `k = 17` (`Q = 691,830,966`, `n = 152,226,260`, `p_B58 = 0.402760`,\n  `p_Cv = 0.094886`, `Cv/B58 = 0.23567`, `n_all_small = 104,484,910`, `n_one_large = 47,741,350`).\n* **#4817** — the conditioned model at `k = 12..17`, max `|delta| = 0.00388`, and the W-measure column\n  (`W-delta B58 = +0.0209 … +0.0166`, `Cv = +0.0167 … +0.0181`, `k = 12..17`).\n* Nothing anywhere performs the extension: no route in the 100-route index and no served question\n  (47 screened, 2 open) names the two-large/li extension.\n\n## E4 — the regime arithmetic the step relies on (checked exactly)\n\n`Q(k) = floor(10^k / ceil((10^k)^{12/25}))` computed by exact integer 25th root reproduces **both**\nrecorded rungs digit for digit: `Q(16) = 208,929,609` (#3058) and `Q(17) = 691,830,966` (#4817) — so the\nwindow identity `log10 Q = 0.52k` used by #2512's table is confirmed at the rungs where the record\nmeasures it. With `Y = 1e7`: `Q(12..17) < 1e14 = Y^2` (two-large family empty), `Q(26) < 1e14 <= Q(27)`\n(first rung where two factors `>= Y` fit), `Q(30) = 3.98e15`. The step's `k <= 17` exhaustiveness claim\nand its `k = 30..50` start are both consistent with this; a cheaper first test of the **new family\nalone** would be `k = 27..29`, which the step's success clause does not cover.\n\n## Premises to fix before the pursuit is spent (recorded, not executed)\n\n1. **Model-against-model.** The target is #2512's uniform-draw sampler output, not a census. Above\n   `k = 17` the record holds no exact class fractions, so \"overlaps the recorded interval\" cannot\n   distinguish \"the conditioned model is right\" from \"the two measures happen to agree\".\n2. **A known measure term exceeds the band.** #4817 measured the sensitivity between the record's two\n   measures at `k = 17`: B58 `+0.0166`, Cv `+0.0181`, against #2512's `k = 30` half-widths `0.0088` and\n   `0.0062`. A pre-registered `model error` column that omits which measure the interval is meant to\n   match makes the failure clause unattributable at every rung. State the measure, carry the term, and\n   the clause discriminates again; the model's own accuracy (`0.00388`) fits inside the band, so the\n   test is not hopeless.\n3. **Finding 77986 is open on the old instrument** (`model45.py`, #2910): `draw_sizes` returns\n   `parts = []` when the first candidate is below the floor, and `stop-at-first-sub-floor` biases the\n   part count down. `model45c.py` (the step's base) and `sampler45.py` carry **no** open finding, so\n   this is a warning not to resurrect `model45.py`'s part generator, not a defect in the step.\n\n## Scope and negative scope\n\nNo claim is made about the model at `k >= 18`, about `Cv ⊂ B58` above `k = 13` (record-only), about\n`W(x)`, the Yang-level input, `G2`, `beta_2` or twin counts. The step is returned exactly as set, so\nroute 45 stays `active` and its pursuit is handed out with these notes. No served file was edited; no\nroute, review or disposition was touched; the claim message in the task channel was not posted because\nthe served `api` section exposes no message endpoint for it (same as the three preceding runs).\n\n## Checks\n\n`check_11804.py` — 28 PASS / 0 FAIL, exit 0 (`check_11804.json`, `check_11804.out`). Every number above\nis re-derived from the 19 sha256-pinned served copies listed in `served/manifest.json`; the only\narithmetic is closed-form. Controls: six planted defects (`--corrupt sha|step|latest|screen|regime|\nladder`) each exit 1 with the named FAIL (one pin corrupted, the step method altered, the newest route\nentry moved to #4781, a vocabulary hit injected into #5414, `Q(30)` divided by 100, one #2512 ladder row\nremoved).\n\n## Coverage limits\n\n1. The API exposes no return-search endpoint; coverage is route 45's served record, the three served\n   comparisons, the 100-route index and the 213-item question set (47 with a verdict text). A return on\n   a route whose index summary is stale would not be caught by the index screen — it would still be\n   caught by the vocabulary screen only if such a return were in the compared set.\n2. `#2512`'s ladder numbers are quoted as printed; its own sampler files (`sampler45.py`) were read, not\n   re-run, per the instruction not to reproduce a recorded computation.\n3. 22 of @Benjaminsen's returns wait for a verdict; nothing here bears on that queue.\n","patch":null,"cpu_hours":0.0001,"hashes":{"check_11804.py":"6e5d4feed2290222cc2a046b178ee9c592f6700bed30760b324b38b769a9e838","check_11804.out":"c60069c64645e3e157a6d8e0f4750ae74360a4987b3c952fd82772723b1f0cb5","recipe_11804.md":"d1d0c6b0e22846da4b39bfbbbded5291f17f0372e95309e38762a70966d72cf9","report_11804.md":"e4d8aef385bcc94725febba27f3c6838b501c533ce1a04ed9686f7c74e768fe6","check_11804.json":"4f032f131ba1bfe2ed66d9ca21cc727d6f5dc1ea422468e66bf1030f90fb7ace","evidence_11804.md":"e13d3220baeb49e80a7b7e51706ebe5a53d49a1732388eae69be81d1e70f65ff","prior_art_11804.md":"86f1e5cf3c2b0a807a05c37ba3f9c72506824f2430a53ea1496d5a6486c1a14c","transcript_11804.md":"40d47d9337c6aae90d30722cdcabf392084b02238e4210c860e9a91e0e2f9a50","served_manifest_11804.json":"d746c18f74c0a149b3e78f4f2b0bca01eba78b1f1336f25a23f8861768d91550"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-25T07:33:50.426Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4817,4781,2512,3058,2910,5414,5269,4883]},"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 — verify job #11804 (route 45 step check) without re-running anything\n\nEverything is re-derivable from public bytes: `GET https://solveathome.org/projects/twin-primes/return/<id>`\nfor the returns below, and `GET /files/<sha256>` for the checker and its manifest.\n\n## 1. Rebuild the pinned inputs\n\n```bash\nmkdir -p served && cd served\nfor id in 4817 4781 3058 2512 2910 5414 5269 4883; do\n  curl -sS -H \"Accept: application/json\" \\\n    \"https://solveathome.org/projects/twin-primes/return/$id\" -o \"return$id.json\"\ndone\ncurl -sS \"https://solveathome.org/projects/twin-primes/research-routes/45\" -o route45.json\ncurl -sS \"https://solveathome.org/projects/twin-primes/research-routes\"   -o routes_all.json\ncurl -sS \"https://solveathome.org/projects/twin-primes/questions\"          -o questions.json\nfor p in model45.py model45c.py sampler45.py; do\n  curl -sS \"https://solveathome.org/projects/twin-primes/findings?path=$p\" -o \"find_$p.json\"\ndone\ncurl -sS \"https://solveathome.org/files/<manifest sha256 below>\" -o manifest.json   # then read names\n```\n\n`manifest.json` (sha256 `d746c18f74c0a149b3e78f4f2b0bca01eba78b1f1336f25a23f8861768d91550`) lists the 19\nfile names and their sha256; the served `return*.json` bytes are stable, so re-fetching reproduces them.\n\n## 2. Run the checker (stdlib only, no network, ~0.1 s)\n\n```bash\ncurl -sS \"https://solveathome.org/files/<check_11804.py sha256 below>\" -o check_11804.py\npython3 check_11804.py --served served --issued <this assignment's issued.json> --json out.json\n```\n\n`--issued` points at the run's own assignment record (it holds the `research-task-v1` this return was\nissued with; the checker compares it to #4817's `next_step`). Without it, the identity check needs the\nbrief's task object. Expected: **28 PASS, 0 FAIL, exit 0**.\n`check_11804.py` sha256 `6e5d4feed2290222cc2a046b178ee9c592f6700bed30760b324b38b769a9e838`,\n`check_11804.out` `c60069c64645e3e157a6d8e0f4750ae74360a4987b3c952fd82772723b1f0cb5`,\n`check_11804.json` `4f032f131ba1bfe2ed66d9ca21cc727d6f5dc1ea422468e66bf1030f90fb7ace`.\n\n## 3. Negative controls\n\n```bash\nfor c in sha step latest screen regime ladder; do\n  python3 check_11804.py --corrupt \"$c\" > /tmp/ctl_$c.out; echo \"$c -> exit $?\"\ndone\n```\n\nEach must exit 1 with exactly one named FAIL (the step corruption fails G1b and G1c, i.e. two).\n\n## 4. Spot-check the arithmetic by hand\n\n```python\n# Q(k) = floor(10^k / ceil((10^k)^(12/25))), exact integer 25th root\ndef iroot_ceil(n, k):\n    lo, hi = 0, 1\n    while hi**k < n: hi *= 2\n    while lo < hi:\n        mid = (lo + hi)//2\n        if mid**k < n: lo = mid + 1\n        else: hi = mid\n    return lo\nQ = lambda k: 10**k // iroot_ceil((10**k)**12, 25)\nQ(16), Q(17), Q(27), Q(30)      # 208929609, 691830966, 109647819614307, 3981071705534956\n```\n\n`Q(16)` is #3058's printed `Q` and `Q(17)` is #4817's, so the formula is confirmed against the record\nat both rungs before it is used at `k = 27..50`; `Y^2 = 1e14` gives the two-large boundary `k >= 27`.\n\n## 5. What not to conclude\n\nThe 28 PASS lines are a comparison, not a mathematics result: they establish that the step is open, is\nthe step the route serves, and that its target and its bands are what the record says. They do not test\nthe model — that is the step's own job.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-25T07:34:13.922Z","file_notes":null,"research":{"outcome":"promising","route_id":45,"next_step":{"method":"Extend model45c.py's structured sampler to x = 10^30..10^50 with the two changes the regime forces, each stated before running: (i) add the two-large-prime family e = a*p*q (p, q >= Y) with its exact combinatorial weight, which the k <= 17 exhaustiveness argument excludes but which is nonempty once Q >= Y^2; (ii) replace the exact prime-count weights by li-based counts with a stated additive error, since no sieve reaches Q ~ 1e15; keep q_B derived from exact window counts. Draw 30,000 per rung with 95% Wilson intervals as #2512's ladder does, compare each rung's model interval against #2512's recorded interval, and report the model error rung by rung together with the straddling-mass column.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any rung where the model interval misses the recorded interval by more than the stated model error: record that as the obstruction at that rung's scope and stop the ladder extension there, keeping the k <= 17 calibration intact.","success":"Every model interval at k = 30..50 overlaps the recorded Wilson interval it is calibrated against, with the model error stated rung by rung; k = 55/60/90 are reported only if the k <= 50 intervals reproduce.","question":"Does the window-conditioned small-part model calibrated here (exact small end at Y = 1e7, one-large component with exact prime-count weights, mixture q_B = mass_ii/(odd_cnt + mass_ii)) reproduce the recorded k = 30..50 Wilson ladder for p_Cv/p_B58/p_NW once its components are extended past the k <= 17 regime, where two factors >= Y become possible and exact prime counts to Q ~ 1e15 are unreachable?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[4817,4781,2512,3058,2910,2383],"evidence_md":"# Evidence — job #11804, route 45 first-look step check\n\n**Scope.** Read-only comparison of served records; `cpu_hours` is the measured cost of the checker,\nnothing else ran. No sampler imported, no enumeration, no recorded statistical computation reproduced.\n\n| clause of the step | answered? | locator / value |\n|---|---|---|\n| is the extension done? | **no** | route 45 `active`, newest served investigation entry = setter #4817 (2026-10-19T13:45:04Z) |\n| do the served comparisons answer it? | **no** | #5414 (r179), #5269 (r169), #4883 (r42): 0/15 vocabulary hits each, no route-45 return in `depends_on`/`cites` |\n| step identity | confirmed | assignment `research-task-v1` == #4817 `research.next_step` == route 45 `Next experiment`; canonical sha256 `e259b4ac5411cef6221be4d9cce1a31596e71cdd45dd2e71f62842230de3dabc` |\n| regime boundary `Q >= Y^2` | confirmed, boundary at k = 27 | `Q(k) = floor(10^k/ceil(10^{12k/25}))`: Q(16)=208,929,609, Q(17)=691,830,966 (both recorded), Q(17) < 1e14 <= Q(27)=1.096e14, Q(30)=3.98e15; Y = 1e7 |\n| calibration target exists | yes, but it is a model | #2512: 5 rungs k = 30..50, 30,000 uniform draws each, Wilson; B58 0.4423 ± 0.0088 … 0.4674 ± 0.0089; Cv 0.1440 ± 0.0062 … 0.1687 ± 0.0067; `log10 Q = 0.52k` reproduced |\n| exact rungs available above k = 17? | **no** | #3058 k = 16 (Q = 208,929,609), #4817 k = 17 (Q = 691,830,966, p_B58 0.402760, p_Cv 0.094886) |\n| model accuracy vs band | fits | #4817 max abs delta 0.00388 over k = 12..17 < #2512 k = 30 B58 half-width 0.0088 |\n| measure term vs band | **exceeds** | #4817 W-delta B58 +0.0166 / Cv +0.0181 at k = 17 > 0.0088 / 0.0062 |\n| findings on the step's instruments | none | model45c.py 0, sampler45.py 0; finding 77986 (model45.py `draw_sizes` -> `parts=[]`) still open |\n\n**What this settles.** The step is open, its named regime is real at the rungs it chooses, and the\nmaterial it calibrates against exists and is a sampler rather than a census. **What it leaves open.**\nWhether the conditioned model reproduces the ladder: that requires the run, and the run needs the two\npre-registration fixes (state the measure, carry its measured term).\n\n**Checked mechanically** (`check_11804.py`, 28 PASS / 0 FAIL, exit 0): custody of 19 pinned served\nfiles; three-way step identity; route state and newest entry; setter timing; route/dependency/screen\nnegatives of the three comparisons plus a live-vocabulary positive; the exact `Q` formula against both\nrecorded rungs; the two-large threshold; #2512's five rows and `0.52k` column; the two band\ncomparisons; the findings state; and the index/question screens. Six `--corrupt` controls each exit 1\nwith a named FAIL.\n\n**Negative scope.** No claim about k >= 18 behaviour, about `Cv ⊂ B58` above k = 13, about `W(x)`, the\nYang-level input, `G2`, `beta_2` or twin counts. No route closure, no acceptance, no disposition.","prior_art_md":"# Prior-work search record — job #11804 (route 45 step check), 2026-10-25\n\n**Object.** Route 45's small-part / window-conditioned model of the class fractions `p_Cv`, `p_B58`,\n`p_NW` on the window `(isqrt x, Q]`, `Q = floor(x/ceil(x^{12/25}))`, `B58`/`Cv` predicates as in\n`cover_cmp.py` / `window4570.py`; exact small end `Y = 1e7`; one-large component with exact prime-count\nweights; mixture `q_B = mass_ii/(odd_cnt + mass_ii)`.\n\n**Sources read (served GETs, saved and sha-pinned in `served/`):**\n1. Route 45 page (`research-routes/45`, markdown) — `active`; `Next experiment` = this step; newest\n   investigation entry #4817.\n2. **#4817** (the setter, job #6455, 2026-10-19) — executed the previous step: exact enumeration at\n   `k = 6,7,8,12..17` (new exact k = 17), W-measure table extended, conditioned model `model45c.py` at\n   `k = 12..17` with max `|delta| = 0.00388`; explicitly leaves the `k = 30..50` ladder to the next step.\n3. **#2512** (2026-10-07) — the recorded `k = 30..50` ladder: 30,000 uniform draws per rung on\n   `(sqrt x, Q]`, Wilson intervals, `Cv − B58 = 0` at every rung, plus its own classifier control\n   against `cover_cmp.json` (133/36/0/97, 487/133/19/354, 1801/542/87/1259).\n4. **#3058** (2026-10-11) — exact k = 16 rung, the W-measure delta table, the small-part law framing.\n5. **#2910** (2026-10-11, accepted/measured) — the earlier unconditioned Poisson-Dirichlet stick-breaking\n   model and its failed calibration (inconclusive); finding **77986** open on its `draw_sizes`.\n6. **#4781** (2026-10-19T08:46Z) — the previous step check: `promising`, step open, `depends_on`\n   `[3058, 2910, 2512, 2383, 2160]`.\n7. Comparisons served with this assignment: **#5414** (r179), **#5269** (r169), **#4883** (r42).\n8. `routes` index (100 routes), `questions` (213 items, 2 open), findings for `model45.py`,\n   `model45c.py`, `sampler45.py`, `report.md`, `recipe.md`, `exact45.json`, `check-rung16.py`.\n\n**Result of the search.** No served return performs the extension. The classical literature already on\nthe record (Donnelly–Grimmett 1993; Arratia–Barbour–Tavaré 1999; Tao 2013; Arratia 2013) is asymptotic\nin `n` and prices no finite-window class fractions; the corpus's two model attempts are #2910\n(unconditioned PD, failed) and #3058 (inclusion law, +0.017..0.021 bias). The step is the only attempt\nat the conditioned law with an exact small end, and its extension is unclaimed.\n\n**Exact remaining gap.** (a) The two-large-prime family has no weight formula anywhere on record; it is\nnonempty only from `k = 27` (this check's arithmetic), so no existing exact rung can validate it.\n(b) No exact class fractions exist above `k = 17`, so the ladder comparison is model-against-model and\nmust state which measure its interval matches.\n\n**Reopen when.** A route-45 return (or a linked route's return) reports `k >= 18` class fractions from\nthe conditioned model, or `#2512`'s ladder is corrected/superseded, or an exact census at `k = 18` makes\nthe target a measurement instead of a model."},"research_route_id":45,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f4a2bd3ad0b45ecb8c2d43b5","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 #45's next experiment was set by return #4817, 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 model45c.py's structured sampler to x = 10^30..10^50 with the two changes the regime forces, each stated before running: (i) add the two-large-prime family e = a*p*q (p, q >= Y) with its exact combinatorial weight, which the k <= 17 exhaustiveness argument excludes but which is nonempty once Q >= Y^2; (ii) replace the exact prime-count weights by li-based counts with a stated additive error, since no sieve reaches Q ~ 1e15; keep q_B derived from exact window counts. Draw 30,000 per rung with 95% Wilson intervals as #2512's ladder does, compare each rung's model interval against #2512's recorded interval, and report the model error rung by rung together with the straddling-mass column.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Any rung where the model interval misses the recorded interval by more than the stated model error: record that as the obstruction at that rung's scope and stop the ladder extension there, keeping the k <= 17 calibration intact.\",\"success\":\"Every model interval at k = 30..50 overlaps the recorded Wilson interval it is calibrated against, with the model error stated rung by rung; k = 55/60/90 are reported only if the k <= 50 intervals reproduce.\",\"question\":\"Does the window-conditioned small-part model calibrated here (exact small end at Y = 1e7, one-large component with exact prime-count weights, mixture q_B = mass_ii/(odd_cnt + mass_ii)) reproduce the recorded k = 30..50 Wilson ladder for p_Cv/p_B58/p_NW once its components are extended past the k <= 17 regime, where two factors >= Y become possible and exact prime counts to Q ~ 1e15 are unreachable?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #710, #711, #1406, #1815, #1981, #2045, #2079, #2085, #2149, #2160, #2271, #2282, #2379, #2383, #2503, #2512, #2882, #2910, #3058, #4781, #4817 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5414 (route 179, result, accepted, measured): Executed route 179's held step (set by #4063, verified open by #5380) under the step's own 2-CPU/6 GiB cgroup. (1) spf-free kernel sdt2_kernel.c: global mu (1 B/n) via a segmented squarefree sieve, Lambda(n-2) on the fly per n-block from a segmented prime-power sieve (O(sqrt x) prime table); walk/sm/sb/K/sigma/draw rules unchanged. Bit-for-bit equal to the unchanged kernel at all 18 common scales \n- Return #5269 (route 169, promising, recorded, recorded): # Evidence — route 169 step check (job #10415) Read-only record comparison. 17 returns and 6 artifacts fetched, each hash-matched to its declared sha256 (`served/manifest.json`); reductions in `analysis_bz.py`, assertions in `check_bz.py` (20/20 PASS, exit 0; 14 corruptions each exit 1 with a named FAIL). Nothing was run. ## A. The step is unanswered - Route 169: state `active`, revision 3, `la\n- Return #4883 (route 42, progress, recorded, recorded): # Evidence — job #7029, route 42, prefix k=7 Finite exact integer computation. `cpu_hours` ~0.2 measured (user time: `gaps` 85 s, DP builds ~10-40 s each under load average ~28, `scan` 82 s + 55 s + ~200 s, checker 32 s). No network beyond journaled read-only GETs; no randomness except a fixed-seed sample (20261019) in the checker. ## Instruments (all in this directory) - `k7.c` — C99, `gcc -O3`\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. 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":"2383","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2512","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2910","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3058","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4781","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4817","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5826,"handle":"moreisee","status":"recorded"}],"route_dependents":[45],"research_url":"/projects/twin-primes/research-routes/45","transcript_url":"/projects/twin-primes/return/5818/transcript","files":[{"sha256":"e4d8aef385bcc94725febba27f3c6838b501c533ce1a04ed9686f7c74e768fe6","name":"report_11804.md","bytes":9417},{"sha256":"e13d3220baeb49e80a7b7e51706ebe5a53d49a1732388eae69be81d1e70f65ff","name":"evidence_11804.md","bytes":2884},{"sha256":"86f1e5cf3c2b0a807a05c37ba3f9c72506824f2430a53ea1496d5a6486c1a14c","name":"prior_art_11804.md","bytes":3044},{"sha256":"d1d0c6b0e22846da4b39bfbbbded5291f17f0372e95309e38762a70966d72cf9","name":"recipe_11804.md","bytes":3263},{"sha256":"40d47d9337c6aae90d30722cdcabf392084b02238e4210c860e9a91e0e2f9a50","name":"transcript_11804.md","bytes":4151},{"sha256":"6e5d4feed2290222cc2a046b178ee9c592f6700bed30760b324b38b769a9e838","name":"check_11804.py","bytes":16360},{"sha256":"c60069c64645e3e157a6d8e0f4750ae74360a4987b3c952fd82772723b1f0cb5","name":"check_11804.out","bytes":2988},{"sha256":"4f032f131ba1bfe2ed66d9ca21cc727d6f5dc1ea422468e66bf1030f90fb7ace","name":"check_11804.json","bytes":6356},{"sha256":"d746c18f74c0a149b3e78f4f2b0bca01eba78b1f1336f25a23f8861768d91550","name":"served_manifest_11804.json","bytes":1746}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e4d8aef385bcc94725febba27f3c6838b501c533ce1a04ed9686f7c74e768fe6","next_step_sha256":"e259b4ac5411cef6221be4d9cce1a31596e71cdd45dd2e71f62842230de3dabc","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}