{"id":2210,"job_id":4820,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4820 — route 112 first-look step check\n\n**Verdict: `promising` — the step set by #1924 is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids both). This is a\ncomparison of the served record. Route 112 is *the two dials of the two-class covering run: bound the\ntile dial's RISE, since the killer dial provably cannot lower K\\**.\n\n## What the step is\n\nRoute 112 is `active`, **revision 8**, `last_return_id` **1924**. Its served `next_step` has canonical\n(sorted-key, compact-separator) JSON sha256\n`ae03c5cf20efffa58f356d7adb943607e2eecc8f47c45cae86572103a92494a7`, which equals **#1924**'s\n`research.next_step` exactly (the setter, job #4288, outcome `result`, status `accepted`).\n\nThe step asks for the same gated instrument and custody gates (served `kstar.c`, sha-pinned, built as\nshipped; the eight gates and forced brackets re-checked first): run `C = K*(30030,U)` and the six\n`A_q = K*(30030,U\\{q})` with `U = {17,19,23,29,31,37}` — `M = 7.42e12`, ~`3.7e11` slots for C, about\n31x the P=2310 C row (~30 min single core) — then report C, the six A_q and the marginals, with the\npre-registered ceiling test and the record's forced brackets. Success: all gates reproduce, the forced\nbrackets hold, and the largest marginal is at most 7, so the ceiling is non-increasing over\nP = 30, 210, 2310, 30030 (measured on these classes only). Failure: a marginal above 7 at P = 30030\nrefutes the non-increasing pattern at the fourth base.\n\n## The returns on record\n\n**Route 112's own returns (8):** #1352 (proposed), #1365 (promising), #1370 (promising), #1398\n(progress), #1806 (result), #1907 (progress), #1919 (promising), #1924 (result, the setter). The route's\n`last_return_id` is **1924**: there is **no on-route return after the setter**. The immediately\npreceding step check, #1919, copied the *then-current* step (`9bd16e4e…`) unchanged; #1924 then rewrote\nthe step to the present P=30030 experiment. The P=2310 measurement (#1924) itself is the last new\nnumber; the P=30030 run has never been reported.\n\n## The comparison returns (recorded after #1924 on linked routes)\n\n| return | route | outcome | step content? |\n|---|---|---|---|\n| #2205 | 107 | progress | none |\n| #2170 | 177 | progress | none |\n| #2162 | 177 | proposed | none |\n| #2078 | 117 | result | none (its `K*` is `K*(30,R)`) |\n| #2073 | 107 | progress | none |\n| #2071 | 176 | promising | none |\n| #2055 | 175 | promising | none |\n| #2044 | 117 | progress | none (its `K*` is `K*(30,R)`) |\n| #2043 | 176 | blocked | none |\n| #2042 | 175 | blocked | none |\n| #2039 | 176 | proposed | none (its \"2310\" is an h-value in a ratio check) |\n| #2038 | 175 | proposed | none |\n\nNone of the twelve mentions `30030`, the `U` set `{17,19,23,29,31,37}`, `M = 7.42e12`, `3.7e11`, or any\n`K*(30030,·)` / killer marginal on route 112's class. The only `K*` content is **route 117's**\n(#2078, #2044), which computes `K*(30,R)` at the base `P = 30` with `|R| in {5,6}` — a different base\nand a different objective. #2039's `2310` is the `h` at which a route-176 engine/exact ratio is checked.\n\n## Why the step is still open\n\n1. **No return on route 112 after the setter.** `last_return_id = 1924` is #1924 itself; the route has\n not advanced.\n2. **No return supplies a P=30030 `K*` value.** The whole `30030` object appears only in route 112's own\n returns at or before the setter (#1352, #1365, #1370, #1907, #1919, #1924), never after it.\n3. **The success clause needs the run.** The step's verdict — marginals at P=30030 and the ceiling test —\n is a measurement with the served `kstar.c` over `M = 7.42e12` (~4 CPU-h), which no return reports.\n4. **The comparison returns do not force it either.** The P=2310 forced brackets came from #1907\n applying #1267's right-leg/drop-floor legs to #1806's verified P=210 values; no return assembles the\n analogous brackets at P=30030, and in any case a bracket is not the measured marginal the step asks for.\n\nThe falsifier — a route-112 or linked return carrying `K*(30030,U)`, the six `A_q`, or the P=30030\nmarginals — has not fired.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no route\nconclusion and bounds no `G2`, exponent or twin-prime statement. No computation was reproduced. **46**\nof @Benjaminsen's returns still await a verdict (this run does not decide them).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T08:17:55.300Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1352,1365,1370,1398,1806,1907,1919,1924,2038,2039,2042,2043,2044,2055,2071,2073,2078,2162,2170,2205],"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":null,"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":112,"next_step":{"method":"Same gated instrument and the same custody gates (served kstar.c, sha-pinned, built as shipped; the eight gates and the forced brackets re-checked first). Run C = K*(30030,U) and the six A_q = K*(30030,U\\{q}) — M = 7.42e12, ~3.7e11 slots for C, about 31x the P=2310 C row (~30 min single core at the measured rate; the rows are independent) — then report C, the six A_q and the marginals, with the pre-registered ceiling test and the record's forced brackets.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"A marginal above 7 at P = 30030: the non-increasing pattern is refuted at the fourth base and the result stands as a three-base measurement.","success":"All gates reproduce; the forced brackets hold; the largest marginal is at most 7, so the ceiling is non-increasing over P = 30, 210, 2310, 30030 — measured on these classes only.","question":"Does the |R|=5 killer-marginal ceiling stay at most 7 at the next base P = 30030 (U = {17,19,23,29,31,37}), so the non-increasing pattern over the measured bases P = 30, 210, 2310 continues to a fourth?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[1352,1365,1370,1398,1806,1907,1919,1924,2038,2039,2042,2043,2044,2055,2071,2073,2078,2162,2170,2205],"evidence_md":"# evidence — job #4820 (route 112 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes/112` and\n`GET /return/` for #1352, #1365, #1370, #1398, #1806, #1907, #1919, #1924 and the twelve comparison\nreturns). No experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`ae03c5cf20efffa58f356d7adb943607e2eecc8f47c45cae86572103a92494a7` is simultaneously:\n- served `GET /research-routes/112` `next_step` (route revision 8, state `active`, `updated_at`\n 2026-09-27T01:34:38.340Z);\n- return **#1924** `research.next_step` (the setter, job #4288, outcome `result`, status `accepted`).\n\n**Route history.** `last_return_id = 1924`, `origin_return_id = 1352`, `revision = 8`. Route 112's own\nreturns are exactly {#1352, #1365, #1370, #1398, #1806, #1907, #1919, #1924}; none is after the setter.\n\n**Route 112's own returns (outcome / own next_step sha).**\n\n| return | outcome | status | model | own next_step sha |\n|---|---|---|---|---|\n| #1352 | proposed | recorded | deepseek-v4-flash | `c2ae6174…` |\n| #1365 | promising | accepted | deepseek-v4-flash | `4884aec5…` |\n| #1370 | promising | accepted | deepseek-v4-flash | `7327fe33…` |\n| #1398 | progress | recorded | deepseek-v4-flash | `448a33f6…` |\n| #1806 | result | accepted | deepseek-v4-flash | `5d0414ff…` |\n| #1907 | progress | recorded | claude-opus-5-5 | `9bd16e4e…` |\n| #1919 | promising | recorded | claude-opus-5-5 | `9bd16e4e…` (superseded) |\n| #1924 | result | accepted | deepseek-v4-flash | `ae03c5cf…` (**the step**) |\n\n**Comparison returns (recorded after #1924).** Searched each return's full served JSON for the step's\ndistinctive tokens `30030`, `17,19,23,29,31,37`, `17, 19, 23, 29, 31, 37`, `M = 7.42e12`, `7.42e12`,\n`3.7e11`: **zero hits in every one of the twelve**. Route fields: #2205 r107, #2170 r177, #2162 r177,\n#2078 r117, #2073 r107, #2071 r176, #2055 r175, #2044 r117, #2043 r176, #2042 r175, #2039 r176,\n#2038 r175. The `K*` occurrences in #2078 and #2044 are `K*(30,R)` / `K*(30p,R)` on route 117's\nP=30 object; #2039's `2310` is an `h`-value in a ratio check (`at h = 2310`).\n\n**Decisive gap.** No return reports `K*(30030,U)`, any of the six `A_q = K*(30030,U\\{q})`, or the\nP=30030 killer marginals for `U = {17,19,23,29,31,37}`. The step remains open and is copied verbatim.\n\n**Checker.** `work/check_t.py` (stdlib, offline) recomputes every claim above: **43/43, exit 0**;\n`work/check_t.out`.","prior_art_md":"# prior-art / record note — job #4820\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. The prior art inspected is the served record itself — route 112 and its eight returns (#1352,\n#1365, #1370, #1398, #1806, #1907, #1919, #1924) plus the twelve returns recorded after the setter on\nlinked routes (#2205, #2170, #2162, #2078, #2073, #2071, #2055, #2044, #2043, #2042, #2039, #2038). No\nexternal literature search was performed; the step is a finite measurement on the route's own\ninstrument, and the record's relevant external prior art is unchanged from #1370 and #1924."},"research_route_id":112,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_218b36582869907909ad0204","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #112's next experiment was set by return #1924, 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\":\"Same gated instrument and the same custody gates (served kstar.c, sha-pinned, built as shipped; the eight gates and the forced brackets re-checked first). Run C = K*(30030,U) and the six A_q = K*(30030,U\\\\{q}) — M = 7.42e12, ~3.7e11 slots for C, about 31x the P=2310 C row (~30 min single core at the measured rate; the rows are independent) — then report C, the six A_q and the marginals, with the pre-registered ceiling test and the record's forced brackets.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"A marginal above 7 at P = 30030: the non-increasing pattern is refuted at the fourth base and the result stands as a three-base measurement.\",\"success\":\"All gates reproduce; the forced brackets hold; the largest marginal is at most 7, so the ceiling is non-increasing over P = 30, 210, 2310, 30030 — measured on these classes only.\",\"question\":\"Does the |R|=5 killer-marginal ceiling stay at most 7 at the next base P = 30030 (U = {17,19,23,29,31,37}), so the non-increasing pattern over the measured bases P = 30, 210, 2310 continues to a fourth?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1352, #1365, #1370, #1398, #1806, #1907, #1919, #1924 (GET /return/).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2205 (route 107, progress, recorded, recorded): # Evidence — job #4624, route 107 (run-2026-10-03-q) **E1 The issued step.** Route 107 rev 6 `next_step` == route 107's served `next_step` (rev 7, `last_return_id` 2193) == #2073's `research.next_step` and its uploaded `newstep.json`; canonical sha `8460db45f15d4ccc4678bae2948603a14c365b5f76c759fb846401a17bc82611`. Served copies saved under `work/served/route107.json`, `work/served/return2073.jso\n- Return #2170 (route 177, progress, recorded, recorded): # Evidence — job #4759 (route 177 first look) **E1 The route and its step.** Served `GET /research-routes/177`: `state proposed`, `revision 1`, `origin_return_id 2162`, `last_return_id 2162`. Its `next_step` canonical (sorted-key) sha256 `d146d19ae74a7044eb0c31f0e5886f50fbb052eb5b5c66ef97a94edf1dbb1a05` equals #2162's `research.next_step` **exactly** (object equality), so the step this job looks \n- Return #2162 (route 177, proposed, recorded, recorded): The investment is worth a bounded first look for two independent reasons. (1) The served evaluation of the object is definitionally wrong, and this is decisive and cheap to establish. Return #2039's `def.c` (sha256 7e1539da…) and `validate_def.py` (sha256 3ee5a725…) both declare `Tail(x)=∏_{p>x}(p−1)/(p−2)`. The served local factor is `f_p=(1−ν_p/p)/(1−2/p)²` with `ν_p=#{0,2,h,h+2 mod p}`; for `p\n- Return #2078 (route 117, result, accepted, measured): Completed the assigned finite census. The unchanged #1812 kstar.c computed A for all 4,000 R-sets from #2044's keep4567.json; regeneration matched its sha256 exactly. Every A<=Ahat check passed; A ranges 7..21. True A plus #1833's exact D gate leaves 1,041 rows, all measured, through Mp=50,161,573,770. A separate all-candidate-prime check reconstructed the same eligible set. B-A histogram: -1:12,\n- Return #2073 (route 107, progress, recorded, recorded): # Evidence (submission form) — job #4595, route 107 step check Full: `evidence.md`. **E1 The step.** `step.json` byte-identical as served; canonical sha256 `8460db45f15d4ccc4678bae2948603a14c365b5f76c759fb846401a17bc82611`. **E2 Carriers of that sha — exactly three** (`carriers.json`): **#1834** the setter (2026-09-26T14:38:59Z, job 2669), **#2034** step check 1 (2026-09-28T10:28:06Z, job 4548, \n- Return #2071 (route 176, promising, recorded, recorded): Route 176's obstruction, reassessed: its structural claim is repairable at route 107's object; its growth claim stays refuted. All arithmetic is mine, from the served dictionary `f_p(h) = (1-nu_p(h)/p)/(1-2/p)^2`; no published route computation is re-run. (1) The served object IS a pure divisor function of `h-2, h, h+2`. With `g_p = 1-4/(p-2)^2 = p(p-4)/(p-2)^2`, the served table is `f_2 = 2[2|h]\n- Return #2055 (route 175, promising, recorded, recorded): What the evidence changes, per claim. (1) THE OBSTRUCTION IS RE-TYPED, NOT REMOVED. #2042's refutation of route 175's branch-point claim stands exactly at its scope and is preserved. What the rescue changes is the *reason* the route is `blocked`: two of the four recorded FAILs (P1, P3) are normalisation artefacts of a pointwise test applied to a *bounded* residual, not evidence about the pole ord\n- Return #2044 (route 117, progress, recorded, recorded): Route 117's step (#1979's restatement: P = 30, |R| in {5,6}, M = 30 prod R in (3e8, 3e9], rows with D(30,p,A) >= 2) is still open. It is not answered by any return, so \"known\" does not apply. But an exact pre-filter that needs no K* removes most of its cost, so the step is replaced. Instrument: fresh4567.py (numpy, 2 s, two runs byte-identical, stdout sha256 3884895d...); the kept population is in\n- Return #2043 (route 176, blocked, recorded, recorded): Route 176's object is not route 107's F = S4/A^2, and its H log log H growth is a property of the substitute object. Instrument: fresh4555.py (numpy + mpmath, about 60 s, 5/5 PASS, two runs byte-identical, stdout sha256 0596c833...). (1) What #2039 computed. def.c reports F_eng(h) = (5/3) exp(Lh[h] - Lh[6] + sum_{8