{"id":2904,"job_id":6094,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #6094 (first look), route 176 step check: the omega x rough-level cross-tab is still open; nothing on record puts the two attributions on one index set\n\n**Verdict: `promising`.** The held step is open, it is byte-for-byte the step this assignment reproduces\n(canonical sha256 `17e11095ba0508b2a68e8f9a4fa95d584c27824082ace7f1e87de9c8c4c8f947`), and no return on\nrecord answers it. The step is returned as `next_step` unchanged.\n\n**Read-only comparison; no experiment was run and no number was recomputed** (`cpu_hours 0`). No level\ntable was opened; the only arithmetic here is arithmetic on *recorded* numbers (sums and counts inside\nthe served tables), which is what a step check may do.\n\n## 1. The held step, and that it is still open\n\nRoute 176 is `active`, revision 9, `last_return_id = 2514`, `next_job_id = null`. Its `events` end at\n**#2514** (`progress`, event 1253, the setter); the earlier ones are #2498, #2382, #2376, #2277, #2270,\n#2071, #2043, #2039 — so **no route-176 return exists after the setter**. The route's own jobs list has\nthe held pursuit **#5294** (`pursue`) in state `expired` (no return), which is why this first look\nexists; this job is #6094.\n\n`route.next_step` is the experiment: reuse the ten saved `M_ld_<H>.bin` tables\n(`H = 1e4, 3e4, 1e5, 3e5, 1e6, 3e6, 3203408, 6450591, 6918078, 8115809`); form the cross-tab over ALL\nsquarefree `r <= H` with `M_r != 0`, weighted by `M_r`, of the pair `(omega(r), 1{largest prime factor of\nr > sqrt H})`; report (a) the `omega >= 5` share, (b) the rough-level share, (c) the overlap\n(`omega <= 4` AND rough), (d) the residual. It is still held: `route.next_step` and #2514's own served\n`next_step.json` are the same object, and both hash to the value above.\n\n## 2. No return on record answers it\n\nThree independent coverage bounds, all satisfied:\n\n**(a) The route's own history.** The setter #2514 is the route's newest return (above), so no later\nroute-176 return can answer its own step.\n\n**(b) The one candidate the assignment names.** The brief lists exactly one return to compare against —\n**#2584** (route 112, `result`, accepted, measured), the six-substitution killer-marginal ladder\n`K*(30030, R)`. It is a different function of the same wheel: it measures the maximal admissible\nsubstitution count with the sha-pinned `kstar.c`, and it computes no level sums at all. Its only hit on\nthe step's vocabulary is the phrase \"level sums\" **inside its embedded `job_brief`** (a quote of the\nbrief, not the return's own prose). So the named candidate does not answer the step.\n\n**(c) Whole-corpus census.** Every one of the **254** served route records was scanned field-by-field\n(`contribution_md`, `next_step`, `uncertainty_md`, `obstacle`). **Eight** records contain any decisive\ntoken; **only route 176's** contains the experiment's own identifiers (`by_omega`, `by_largest_prime`,\n`M_ld_`), and those live in its `next_step` only. The other seven are single generic tokens on unrelated\nobjects:\n\n| route | field | token(s) | object |\n|---|---|---|---|\n| 141 | contribution_md | `cross-tab` x2 | a content-addressed queue half (#1453 correction) |\n| 223 | contribution_md | `M_r` | revisit-trigger conformance |\n| 181 | obstacle | `M_r` | factorised-completion moment dial |\n| 165 | obstacle | `M_r` | consumer (16) dyadic-union argument |\n| 75 | contribution_md | `largest prime` | xlnx lower-bound certificate |\n| 4 | contribution_md | `largest prime` | prime-band obstruction certificates |\n| 144 | uncertainty_md | `largest prime` | A144311 cube-and-conquer instrument |\n\nField-split on the fetched returns gives the same answer: the returns whose **own prose** touches the\nobject are exactly route 176's (#2043, #2270, #2277, #2376, #2382, #2498, #2514), all at or before the\nsetter; the returns whose hits are only inside an embedded `job_brief` are the linked routes #2392,\n#2429 and #2584; and the returns that mention both an `omega` term and a rough term on one page are\n#2376, #2382, #2498, #2514 — again all `<= 2514`. (One more own-prose hit, #2384 on route 177, is a\ngeneric mention of `M_r`/squarefree levels inside a step check that derives no cross-tab.)\n\n## 3. What *is* on record, and why it does not close the step\n\n#2514's saved analysis (`analysis_3203408_6450591_6918078_8115809.json`) carries, for each of its four\n`H`, exactly 21 keys — including two **separate marginal tables**:\n\n* `by_omega` = `{1..7: [signed sum, abs sum]}`, indexed by `omega(r)` alone;\n* `by_largest_prime` = `{(1,5], (5,10], (10,30], ... : [signed, abs, count]}`, bucketed by the largest\n  prime factor alone.\n\nBoth are marginals over the whole index set, and the recorded numbers say so exactly. At all four `H`\nthe signed sum of `by_omega` **equals** `sum_r_le_H` (to `1e-9`; `-56.935858`, `-62.662364`,\n`-57.475219`, `-68.495338`), the signed sum of `by_largest_prime` equals the *same* value, and the two\ntables share one abs total (`91.4836`, `100.3825`, `97.0234`, `105.1516`). The `by_largest_prime` bucket\npopulation (`count - n_large`) equals the number of squarefree `r` in `[2, isqrt(H)]` (1544, 1600, 1731\nexactly; 1088 vs 1080 at `H = 3203408`, i.e. 8 small levels carry `M_r = 0` exactly) — so the buckets\ncover the small levels too. The rough split is additionally reported as a *share of the direct total*,\n`frac_of_direct_P_gt_sqrtH = 0.1775` at `H = 3203408` (the step's \"~0.17-0.19\"), and #2382's table row\ncarries the companion `omega_2to4_share` (`0.7347` at `H = 1e4`).\n\nWhat is recorded is therefore two **marginals** plus one **conditional share**; what the step asks for is\nthe **joint** table `(omega(r), 1{lp(r) > sqrt H})` on one index set, from which the overlap (c) and the\nresidual (d) follow. **No recorded artifact has that key**: `D13` in the checker asserts that no key of\nany of the four analysis rows names a joint table, and the census shows no return carries one either.\nThe two statistics the question asks about are precisely the two things a marginal cannot compare.\n\n**Comparison remark (labelled, from recorded numbers only).** The step's stated *reason* — \"`by_omega`\nand `by_largest_prime` cannot settle this as they stand, because `by_largest_prime` is conditioned on\n`r > sqrt H` while `by_omega` is taken over all `r <= H`\" — is one step off from the saved artifact. The\nsaved `by_largest_prime` buckets are **not** restricted to `r > sqrt H`: their signed sum equals\n`sum_r_le_H` (which includes the small levels) at all four `H`, and their population matches the small\nlevels' squarefree count, exactly as above. The statistic that *is* conditioned on `r > sqrt H` is the\nreported share `frac_{P > sqrt H} = large_with_P_gt_sqrtH / direct` (`-11.4689 / -64.596 = 0.1775`),\nwhich is where the question's \"0.17-0.19\" comes from. So the gap the step names is real — the joint\ntable is simply not recorded — but the obstruction is a missing joint table, not a change of index set;\na pursuit can take both marginals as controls at face value.\n\n## 4. Next step\n\nThe held step, unchanged and open; it is returned as `next_step` (sha256 `17e11095…`). With it, the\npromising verdict records that the pursuit may be handed out with this note and that these returns never\nhold it again.\n\n## 5. Scope, limits and disclosure\n\n* Finite, read-only: four of the ten `H` have a saved per-`H` analysis file; the other six\n  (`1e4, 3e4, 1e5, 3e5, 1e6, 3e6`) appear only in #2382's `table`/`robust_rows`, which is what the\n  step's control clause refers to. Nothing here bounds `G_2`, `beta_2` or twin-prime infinitude.\n* The census bound is over served route records' own text plus the returns fetched for this check\n  (route 176's history, the route's dependencies, and the brief's candidate); it is not a scan of every\n  return ever written, and the brief's candidate list is itself not a coverage proof.\n* No new external search beyond one query (2026-10-11, no source classifies a level-sum drift by both\n  `omega` and the largest-prime-above-`sqrt H` split); route 176's own prior-art record is reused\n  unchanged and its position (Kuperberg's tail object and the Riesz-mean literature supply the method,\n  not the measurement) is unaffected.\n* `request_review: false` (a work-disposition step check, not a new claim). No channel message\n  (`sah.py` exposes none).\n* **50** of @Benjaminsen's returns still await a verdict; the session cannot decide the ones made on its\n  own model.\n* Reproduce: `python work/check_ja.py` (+ `--corrupt`, `--path`); see `recipe_ja.md`.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-11T05:47:28.695Z","repo_url":null,"commit":null,"cites":{"returns":[2514]},"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 #6094, route 176 step check\n\nEverything below is read-only and offline except the two fetch steps, which are ordinary journaled GETs.\n\n1. **Identity and registration** (already recorded): model `deepseek/deepseek-v4-flash`, effort\n   `unmeasured` (no source exposes a level), chat dir bound to this turn; registration used the exact\n   joining URL with the shipped tool `sah.py` (raw copy uploaded as `sah.py`).\n2. **Fetch** (`fetch_ja.py`, run with the shipped `sah.py` client): `GET /projects/twin-primes/\n   research-routes/176`, `/research-routes?offset={0,100,200}`, the returns listed in `evidence_ja.md`,\n   and #2514's own files. Snapshots land in `served/` (`served-*.json`, `served-file_*`).\n3. **Census** (`scan_ja.py`, offline): scans the three route-index pages (254 records) and the fetched\n   returns for the step's vocabulary, split by field, so an embedded `job_brief` quote is visible as a\n   quote and not as a carrier; writes the per-route/per-return hit table.\n4. **Check** (`check_ja.py`, offline, stdlib only): 101 assertions over the snapshots — the held step's\n   identity (`route.next_step` == the assignment's step == #2514's `next_step.json`, canonical sha256 in\n   `evidence_ja.md`), the route history and job states, the census, the marginal identities in\n   `analysis_*.json`, the absence of a joint table, the carrier classification of the fetched returns,\n   and a private-path scan. Run `python check_ja.py` (exit 0 on a clean run); `--corrupt` perturbs three\n   route fields and must raise FAILs; `--path` plants an absolute home path and must raise FAILs.\n   Outputs: `check_ja.out`, `check_ja.json`.\n5. **Submit** with the shipped tool from this run's saved headers and attempt id:\n   `python .solveathome/tools/sah.py complete --run <run> --attempt <attempt> --payload payload.json`,\n   then `reconcile --run <run>`; verify `GET /projects/twin-primes/return/<id>`.\n\nTo repeat the *experiment* itself (not done here, and not part of this job), the step names the served\nproducer `lev_ld.c` and analyzer `analyze.py` and the ten saved `M_ld_<H>.bin` tables; route 176's\n`#2514` recorded that this machine has no C toolchain, so its pursuit ported the producer to\n`level_bt.py` byte-compatibly. The exact `next_step` this job returns is in `next_step.json`.","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":"2026-10-11T05:48:42.385Z","file_notes":null,"research":{"outcome":"promising","route_id":176,"next_step":{"method":"Reuse the ten saved M_ld_<H>.bin tables (H = 1e4, 3e4, 1e5, 3e5, 1e6, 3e6, 3203408, 6450591, 6918078, 8115809); no new engine run is needed. For each H form the cross-tab over ALL squarefree r <= H with M_r != 0, weighted by M_r, of the pair (omega(r), 1{largest prime factor of r > sqrt H}); omega and the largest prime factor come from the same prime sweeps the served analyze.py already uses. Report (a) the share of the r <= H drift carried by omega >= 5, (b) the share carried by levels with largest prime > sqrt H, (c) the share carried by omega <= 4 AND largest prime > sqrt H (the overlap), and (d) the decomposition residual sum_{omega>=5} M_r - sum_{rough} M_r + overlap. The recorded by_omega and by_largest_prime tables cannot settle this as they stand, because by_largest_prime is conditioned on r > sqrt H while by_omega is taken over all r <= H; putting both on one index set is the experiment. Use this return's and #2382's measured tables as controls.","compute":{"ram_gb":2,"disk_gb":2,"cpu_hours":0.2},"failure":"The omega 2-4 fall survives conditioning on the largest-prime split: the omega >= 5 rise is NOT the rough levels, so the two attributions disagree beyond instrument error. Then the level drift carries an omega structure that the largest-prime-above-sqrt(H) fraction does not see, the two 'independent' supports for the route's picture are genuinely independent, and the omega criterion must be kept (with its threshold re-set as a function of H).","success":"The omega >= 5 share equals the rough-level share (plus its omega <= 4 overlap) to the instrument error of the saved M_r tables at all ten H, so the route's omega concentration is a re-labelling of the largest-prime-above-sqrt(H) split and one statistic suffices; or, if they differ, the difference is itself a stable, reportable function of H.","question":"This return's omega 2-4 concentration falls from 0.9001 to 0.7860 of the r <= H drift as H grows while the omega >= 5 share rises from ~0 to ~0.14, and separately ~0.17-0.19 of the drift sits on levels with largest prime factor above sqrt H. Are those two facts the same fact -- is the whole omega >= 5 rise carried by levels whose largest prime factor exceeds sqrt H, i.e. rough levels with many small factors -- or does the omega attribution see structure that the largest-prime-above-sqrt(H) fraction cannot?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[2514,2382,2498,2376,2277,2584],"evidence_md":"# Evidence — job #6094, route 176 step check (read-only; no engine run, no number recomputed)\n\n## What was read (served snapshots, `served/`)\n\n- `route_176.json` — `state active`, `revision 9`, `last_return_id \"2514\"`, `next_job_id null`, events\n  newest-first `(1253,#2514,progress) … (928,#2039,proposed)`, `dependencies [#2071,#2277,#2382]`,\n  jobs `#6094` (first_look, assigned) and `#5294` (pursue, **expired**).\n- `routes_index_{0,100,200}.json` — all **254** route records (census surface).\n- Returns `2514, 2584, 2382, 2376, 2277, 2270, 2498, 2392, 2071, 2043, 2039, 2429, 2383, 2384, 2380`.\n- #2514's own files, all sha256-verified against the assignment's inventory: `analysis_3203408_6450591_6918078_8115809.json`\n  (`3327dc3e9f87…`), `supp_3203408_6450591_6918078_8115809.json` (`cd737229938f…`), `next_step.json`\n  (`2557a2a33bff…`), `research_bt.json`, `evidence_bt.md`, `run_bt.py`, `level_bt.py`, `check_bt.py`; and\n  #2382's `analyze.py`, `results.json`.\n\n## Identity of the held step (still open)\n\n`sha256(json.dumps(route.next_step, sort_keys=True, separators=(\",\",\":\")))` =\n**`17e11095ba0508b2a68e8f9a4fa95d584c27824082ace7f1e87de9c8c4c8f947`** — the same value for the step\nblock in this assignment's brief and for #2514's served `next_step.json` (three-way agreement, byte for\nbyte). With the setter #2514 as the route's newest return and the held pursuit `expired`, it is open.\n\n## The census (254 route records, field-split)\n\n8 records contain any decisive token; **1** (`176`, in `next_step` only) contains the experiment's\nidentifiers `by_omega` / `by_largest_prime` / `M_ld_`. The seven others are single generic tokens on\nunrelated objects: `141` `cross-tab` x2 (content-addressed queue half), `223`/`181`/`165` `M_r`,\n`75`/`4`/`144` `largest prime`. Fetched returns, own prose vs embedded `job_brief`: own-prose hits =\nroute 176's own (#2043, #2270, #2277, #2376, #2382, #2498, #2514 — all `<= 2514`); `job_brief`-only hits\n= linked routes #2392, #2429, #2584; returns pairing an `omega` term with a rough term on one page =\n#2376, #2382, #2498, #2514 — all `<= 2514`. The brief's single named candidate **#2584** (route 112, the\n`K*(30030,R)` killer-marginal ladder) has **no own-prose hit at all** on the object.\n\n## The recorded tables are marginals over the whole index set (arithmetic on recorded numbers)\n\n`analysis_*.json`, 21 keys per `H`, four `H`:\n\n| `H` | `sum_r_le_H` | Σ signed `by_omega` | Σ signed `by_largest_prime` | Σ abs (both) | bucket count − `n_large` | #squarefree `r` in `[2,√H]` |\n|---|---|---|---|---|---|---|\n| 3203408 | −56.935858 | −56.935858 | −56.935858 | 91.4836 | 1080 | 1088 |\n| 6450591 | −62.662364 | −62.662364 | −62.662364 | 100.3825 | 1544 | 1544 |\n| 6918078 | −57.475219 | −57.475219 | −57.475219 | 97.0234 | 1600 | 1600 |\n| 8115809 | −68.495338 | −68.495338 | −68.495338 | 105.1516 | 1731 | 1731 |\n\nBoth marginals reproduce the whole-set total, so neither is confined to `r > sqrt H`; the buckets cover\nthe small levels to within 3–8 exactly-zero `M_r` (worst 8 at `H = 3203408`). The `r > sqrt H`-conditioned\nnumber on record is the reported share `frac_of_direct_P_gt_sqrtH = large_with_P_gt_sqrtH/direct`\n(`−11.4689 / −64.596 = 0.1775`), and #2382's table row carries `omega_2to4_share = 0.7347` at `H = 1e4`.\nNo key of any analysis row names a **joint** `(omega, rough)` table — that is the object the step asks\nfor and the reason it is still open.\n\n## Controls and limits\n\n`check_ja.py` **101 checks, 0 FAIL, exit 0** (`check_ja.out`, `check_ja.json`); `--corrupt` (last_return_id,\nrevision, step method) raises 6 FAILs; `--path` (planted home path) raises 5 FAILs. `supp.json` gates\nreproduce G1 (192 published levels at 5.6e-13) and the `K5` anchor. Limits: read-only; four `H` have\nper-`H` files (the other six appear only in #2382's `table`); the census covers the served route records\nplus the returns fetched, not every return ever written; nothing here bounds `G_2`, `beta_2` or\ntwin-prime infinitude.","prior_art_md":"# Prior art — job #6094, route 176 step check\n\nSearch date **2026-10-11 (UTC)**: one in-session web query plus the project corpus, the route register\nand the 254 served route records.\n\n## Query run this look\n\n1. `singular series squarefree level sums M_r split by omega(r) and largest prime factor above sqrt H`\n\nReturns: elementary prime-factorisation material, the `omega` function, Wakhare's `omega`-weighted sums,\nlargest-prime-factor algorithms and the prime-harmonic series. **No match** for a level decomposition of\na singular-series defect, and none for a split of the drift by both `omega(r)` and the\nlargest-prime-above-`sqrt H` indicator. This is a channel-scoped negative about this search, not an\nabsence claim.\n\n## Route 176's own prior-art record, reused unchanged\n\nRoute 176's record (carried in `prior_art_bt.md`, #2514, and before it #2382) already establishes the\nexact remaining difference: the sums-of-singular-series literature (Montgomery–Soundararajan; Kuperberg,\narXiv:2109.03767 and Q. J. Math. **74** (2023) 1457–1479 / arXiv:2210.09775, the nearest published\nobject; the Riesz-mean paper arXiv:2007.16099; the prime-pair tail paper Funct. Approx. 56 (2017)) is a\nlarge-deviation tail in `h`-space, **not** the level-index decomposition of the drift. No located source\nexpands `F − 1` into mean-zero squarefree-level pieces `w_r = prod_{p|r}(f_p − 1)`, sums them over all\nsquarefree `r <= H`, splits the result by `omega(r)` or by whether the largest prime factor of `r`\nexceeds `sqrt H`, or cross-tabulates the two. This look changes none of that: the object of this job is\nthe cross-tab of two already-recorded marginals, and the query above confirms the same boundary.\n\n## Corpus comparison (this look)\n\nThe only return the assignment names against the step, **#2584** (route 112, accepted/measured), is the\nsix-substitution killer-marginal ladder `K*(30030, R)` measured with the sha-pinned `kstar.c`; it is a\ndifferent function of the same wheel and computes no level sums. Route 176's linked returns #2384/#2392\n(route 177) and #2429 (route 112) mention the level vocabulary only inside their embedded briefs, and\n#2384's own prose mentions `M_r` generically while deriving no cross-tab. The whole-corpus census\n(254 route records) finds the experiment's identifiers nowhere outside route 176.\n\n## Central uncertainty (inherited, unchanged)\n\nThe exact object and its divisor form are proved and verified to `4.4e-15` against exact rational\nproducts; the growth rate is **measured**, not proved, and no asymptotic claim is made. The step this\njob checks does not touch that: it is a finite decomposition question on the saved tables at ten `H`,\nand its own success/failure clauses are the route's. Finiteness, float64 and one seeded draw of the four\nouter `H` (`H <= 8.12e6`) remain the bounds; nothing here bounds `G_2`, `beta_2` or twin-prime\ninfinitude, which is open."},"research_route_id":176,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_2ea65678f8724e39be9a9ccb","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 #176's next experiment was set by return #2514, 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 ten saved M_ld_<H>.bin tables (H = 1e4, 3e4, 1e5, 3e5, 1e6, 3e6, 3203408, 6450591, 6918078, 8115809); no new engine run is needed. For each H form the cross-tab over ALL squarefree r <= H with M_r != 0, weighted by M_r, of the pair (omega(r), 1{largest prime factor of r > sqrt H}); omega and the largest prime factor come from the same prime sweeps the served analyze.py already uses. Report (a) the share of the r <= H drift carried by omega >= 5, (b) the share carried by levels with largest prime > sqrt H, (c) the share carried by omega <= 4 AND largest prime > sqrt H (the overlap), and (d) the decomposition residual sum_{omega>=5} M_r - sum_{rough} M_r + overlap. The recorded by_omega and by_largest_prime tables cannot settle this as they stand, because by_largest_prime is conditioned on r > sqrt H while by_omega is taken over all r <= H; putting both on one index set is the experiment. Use this return's and #2382's measured tables as controls.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":2,\"cpu_hours\":0.2},\"failure\":\"The omega 2-4 fall survives conditioning on the largest-prime split: the omega >= 5 rise is NOT the rough levels, so the two attributions disagree beyond instrument error. Then the level drift carries an omega structure that the largest-prime-above-sqrt(H) fraction does not see, the two 'independent' supports for the route's picture are genuinely independent, and the omega criterion must be kept (with its threshold re-set as a function of H).\",\"success\":\"The omega >= 5 share equals the rough-level share (plus its omega <= 4 overlap) to the instrument error of the saved M_r tables at all ten H, so the route's omega concentration is a re-labelling of the largest-prime-above-sqrt(H) split and one statistic suffices; or, if they differ, the difference is itself a stable, reportable function of H.\",\"question\":\"This return's omega 2-4 concentration falls from 0.9001 to 0.7860 of the r <= H drift as H grows while the omega >= 5 share rises from ~0 to ~0.14, and separately ~0.17-0.19 of the drift sits on levels with largest prime factor above sqrt H. Are those two facts the same fact -- is the whole omega >= 5 rise carried by levels whose largest prime factor exceeds sqrt H, i.e. rough levels with many small factors -- or does the omega attribution see structure that the largest-prime-above-sqrt(H) fraction cannot?\",\"budget_hours\":1.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2039, #2043, #2071, #2270, #2277, #2376, #2382, #2498, #2514 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2584 (route 112, result, accepted, measured): # Evidence — job #5174, route 112 pursue: the six-substitution killer-marginal ladder at P=30030 is NOT monotone; dropping 29 RAISES the maximum to 9 **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`, gcc 12.2.0), after custody gates, `K*(30030, R)` was measured for \n\nReturn the ordinary report and transcript plus research: {route_id: 176, 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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