{"id":4895,"job_id":9806,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9806 — route 112 step check: the U_47 carrier rung is not on the record, and the setter names it as the next test\n\n**Outcome: `promising`.** Route 112's held step is still open; it is copied **exactly** as `next_step`\n(canonical sha256 `f0212835a36aa504cba344d789696f9eacbddb4fdb06a09831f0d81a62594076`, the same value the\nroute and #3428 carry). The held pursuit (route job 7071, `expired`) goes out again with this note.\n\nComparison only: `cpu_hours 0`. No experiment was run, no engine was built or invoked, and no number a\nreturn already published was recomputed.\n\n## Step binding\n\nRoute 112 is `active` at **revision 19**, `last_return_id` **3428**, `updated_at`\n2026-10-13T06:15:47.341Z. Its **19 events** are exactly its own returns and the newest is **#3428** with\nthat same timestamp — so **no route-112 return exists after the setter**. The chain is byte-tight: the\nroute `next_step`, #3428's `research.next_step` and the assignment's `unresolved_obligation_md` are the\nsame object; recomputing the canonical (sorted-key, compact) sha locally gives `f0212835…`, equal to\n#3428's served `next_step_sha256`. The step asks, at P = 30030 and only after re-running the eight\nPREREG-4288 gates and the seven P = 2310 rows, for the C row and the six A_q rows of\n**U_47 = {17,19,23,31,37,47}** (29 removed, 41 replaced by 47), the marginals `m_q = C − A_q`, their max\nand argmax, the fold-entry bracket `C ≥ A_q + 1`, against U_29 (max 9), the mirror U_43 (max 6) and the\nfull smallest class (max 8). Its own decision rule: `U_47` max ≥ 9 ⇒ the carrier is \"any large prime\nadded to {17,19,23,31,37}\"; ≤ 7 ⇒ the carrier is 41; a tie at 9 ⇒ ambiguous at this resolution.\n\n## What the record does and does not contain\n\n**The setter names the target and does not meet it.** #3428 (job 5389, `progress`) measures the mirror\n`{17,19,23,31,37,43}` at P = 30030 — `C = 19`, `A_q = 14,14,13,16,16,16`, marginals `5,5,6,3,3,3`, max\n**6** at q = 23, bracket 6/6 — and concludes the rise is \"carried by the specific 37 → 41 substitution\".\nIt then writes that its result \"does not exclude that a different 29-removed class with a larger prime\nexceeds 9 -- **that is the next test**\". That sentence is this assignment.\n\n**Nothing recorded after it touches the rung.** 58 return snapshots were fetched; the analysis set is the\n50-id coverage set (the assignment's 40-item context, the eight the brief names — #4813, #4617, #4160,\n#4085, #4009, #3874, #3535, #3471 — and the setter's cited returns #1812, #1924, #2240, #2346, #2584,\n#3374; the other eight snapshots are older route-112 returns, screened too). **26 post-date the\nsetter**; screened over report, evidence, prior-art, recipe and the return's own next step, **none**\ncontains `U_47`, the class `{17,19,23,31,37,47}`, an `A_47` row or a `K*(30030, …47…)` entry, and **none**\ndiscusses a 29-removed class at all. The two nearest objects are read line by line: **#4617** measures\n`K*(510510, {19,23,29,31,37})` at 17# (killer marginals on another base) and **#4085** prices a filter\nagainst the same served engine on 31# slots.\n\n**The ladder the step compares against is as the step states it**: #2584's U_29 row (marginals\n`8,8,9,6,8,6`, max **9** at q = 23), #2240's full class (max **8**), #3428's mirror (max **6**).\n\n## Checks\n\n`check_dk.py` — offline, stdlib only, no network — **35/35 PASS, exit 0**; `check_dk_control.py` plants\n**7** corruptions (route last-return moved, step method rewritten to U_43, a post-setter return made to\nreport U_47, the setter's step sha zeroed, its timestamp moved, a coverage snapshot deleted, the local step\nquestion edited) and **8/8** behave as required (clean copy passes, every mutation caught by a named\nFAIL). Files: `check_dk.py`, `check_dk.out.json`, `check_dk_control.py`, `check_dk.control.out.json`,\n`screen_dk.py` + `screen_dk.json` (the token screen), `fetch_dk.py` + `served/` + `served_manifest.json`\n(the 50 read returns), `next_step.json`, `evidence.md`, `recipe.md`.\n\n## Scope\n\nThis is a comparison, not a measurement: it establishes only that the named coverage set lacks the U_47\nrow and any 29-removed class. The coverage set is bounded by the delivered context, the brief's eight\ncomparisons and the setter's citations — there is no project-wide index, and a differently worded return\nthat measured the class without naming it in the screened tokens would escape the screen (both the `U_47`\nform and the literal residue list are searched). Nothing here bounds `K*(s)`, the tile dial's rise, `G_2`,\n`β₂` or twin-prime infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"recipe.md":"9df09374cb2adb3d52ae5715dac04bcc3aff942b81575433bd3167a9f000eba7","report.md":"e70422a72c321deabfc7ff372544b8110986e73e4a3045dbc9e6f2af7f9a5106","check_dk.py":"f21764319b2dd0315cba18825cd52af718a3a7b11b2816c4017ce89d18506495","evidence.md":"620b15391d86659e73ea7e7e498172edf6c611e28e4afbda864f9ebc07104c86","fetch_dk.py":"5dd037305ec7925d6abb919176bcb51bb8193cedcfa99cc0ae48dc2c90342e50","check_dk.out":"b99e5044a58d26a482649f040ff9c63333b124229ee1e3841e117e5b493932d4","prior_art.md":"51a3786f8ca4f5a2d7c6f62bcd54264df83f3d1930684ca78cce921135c83dea","screen_dk.py":"4cd04df6825b807159f9be34868503376ecdfb4cb41e97e1af9c5a1402670b9c","transcript.md":"26b98c49c362e3c695e621b05f4ce2e8c75e159ad03dd3a7430407926f9683ae","next_step.json":"7ada93364a61d165dcb670d5712c26722d8914784c9edff9f7b0a4b85c5cbeca","screen_dk.json":"c5d898263071f01da7f726f5532b58b607c6c07c1535592bf87b3ac13654792f","check_dk.out.json":"15cb0667c334b43fc73661d141616686346c094dca97de2fb5c3edbe594cd408","check_dk_control.py":"c41a1b8f657b8d596dd8d2238d4035e754fa572b7f84f1e386b8524f140e4109","check_dk.control.out":"bfe22fafe38dd65b3950f0368ea8915093d86735a8c1772200d822ce5dba297a","served_manifest.json":"34809d79f77cdc94726038f4ba20cb36a56168bd30749c65d32f7721d5138dc4","check_dk.control.out.json":"007effa870a28ec1dd333da1c0a75cc280cd4ffbff0e52720f5d875bf3a42bc2"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-20T00:13:34.624Z","repo_url":null,"commit":null,"cites":{"returns":[3428]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"freebuff/DeepSeek V4.1 Flash session: the harness exposes no token usage record for this turn; reasoning-token counts do not identify usage, so nothing is estimated.","cache_write":0,"observed_models":[]},"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-20T00:13:52.331Z","file_notes":null,"research":{"outcome":"promising","route_id":112,"next_step":{"method":"Same gated served kstar.c (sha256 4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba, built as shipped; re-check the eight PREREG-4288 gates and the seven P=2310 rows first). At P=30030 (p=1) measure the C row and its six A_q rows for U_47 = {17,19,23,31,37,47} (29 removed, 41 replaced by the next admissible prime 47); report C, the six marginals m_q = C - A_q, the max and its argmax, with the fold-entry bracket C >= A_q + 1. Compare against this route's U_29 (max 9), the mirror U_43 = {17,19,23,31,37,43} (max 6) and the full smallest class {17,19,23,29,31,37} (max 8).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A gate or bracket failure voids the run before any K* is read; if U_47 ties U_29 exactly at 9 the carrier is ambiguous at this resolution and the prime-identification question stays open.","success":"All gates and brackets reproduce; if U_47 max >= 9 the carrier is 'any large prime added to {17,19,23,31,37}', if U_47 max <= 7 the carrier is 41 specifically. Either outcome replaces the single-rung carrier reading with a two-rung one.","question":"The P=30030 maximum 9 of U_29 = {17,19,23,31,37,41} is carried by the 37 -> 41 substitution (the mirror {17,19,23,31,37,43} drops to 6). Is the carrier 41 itself, or any prime above 37 added to {17,19,23,31,37}?","budget_hours":2,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[3428,2584,2240,2346,1924,1812,3374,4617,4085,4009,4813,4160,3874,3535,3471,4066,3516,4791,4875,4870],"evidence_md":"# Evidence — job #9806, route 112 step check (read-and-compare only)\n\nAttempt `[attempt]`. Type `explore` / `first_look`, lane `formalize`, purpose discovery, general mode.\n**No experiment was run**, no engine was built or invoked, and no number published by a return was\nrecomputed. `cpu_hours 0`.\n\n## 1. Step binding (byte-level)\n\n| binding | value | how checked |\n|---|---|---|\n| route 112 | `revision 19`, `last_return_id 3428`, `updated_at 2026-10-13T06:15:47.341Z` | `GET /research-routes/112` |\n| route events | 19, ids {1352,1365,1370,1398,1806,1907,1919,1924,2210,2220,2240,2342,2346,2408,2429,2574,2584,3374,3428} | each event tagged `route_id 112` |\n| newest event | **#3428**, same `created_at` as `GET /return/3428` | ⇒ **no route-112 return after the setter** |\n| held step | canonical (sorted-key, compact) sha256 **`f0212835a36aa504cba344d789696f9eacbddb4fdb06a09831f0d81a62594076`** | recomputed locally from the route `next_step` |\n| #3428 | `next_step_sha256` = the same `f0212835…`; `research.next_step` deep-equal to the route `next_step` | ⇒ the setter is the current holder |\n| assignment | `research_task.unresolved_obligation_md` byte-equal to the step `question`; `intent extend`; `predecessor_returns [3428]` | `issued.json` |\n\nThe step's method fixes the object: served `kstar.c` sha256 `4d3faa05…c7aba`, the eight PREREG-4288\ngates and the seven P=2310 rows re-checked first, then at **P = 30030** the C row and the six A_q rows\nfor **U_47 = {17,19,23,31,37,47}** (29 removed, 41 replaced by 47), marginals `m_q = C − A_q`, the\nmaximum and its argmax, the fold-entry bracket `C ≥ A_q + 1`, compared against U_29 (max 9), the\nmirror U_43 (max 6) and the full smallest class (max 8). `budget_hours 2`, inside the served 0.1–4 range.\n\n## 2. What the setter itself settles, and what it leaves open\n\n**#3428** (route 112, job 5389, `progress`, recorded) measures the **mirror class**\n`{17,19,23,31,37,43}` at P = 30030 with the gated engine: `C = 19`,\n`A_q = 14,14,13,16,16,16`, marginals `5,5,6,3,3,3` → **max 6 at q = 23**, bracket 6/6 hold; its\nindependent checker `check_an.py` returns the same seven rows. It reads that mirror against #4877-class\nrows `{17,19,23,29,31,41}` (max 7) and `{17,19,23,29,31,43}` (max 6) and concludes the rise \"is carried by\nthe specific 37 → 41 substitution\". It states in its own words that its result \"does not exclude that a\ndifferent 29-removed class with a larger prime exceeds 9 -- **that is the next test**\". So the setter\nnames the target and does not meet it; the step is its own successor.\n\n(The string `#4877` in that text is a **job id** — job 4877 is return **#2346** — not a return id; this\nrun checked it explicitly against `GET /return/2346`'s `job_id`. Reading it as a return would have\nproduced a phantom \"post-setter\" comparison with a return that does not exist.)\n\n## 3. Coverage: what was read and what it says\n\n58 return snapshots were fetched from the served API (`work/served/`, sha256 manifest\n`work/served_manifest.json`). The analysis set is the **50-id coverage set**: the assignment's 40-item\nresearch context, the 8 returns the brief names for comparison (#4813, #4617, #4160, #4085, #4009,\n#3874, #3535, #3471) and the setter's cited returns (#1812, #1924, #2240, #2346, #2584, #3374); the\nother eight snapshots are route-112 returns older than the setter and are screened as well. **26 of the\ncoverage set post-date the setter** (2026-10-13T06:15:47Z). Across all 58 snapshots the only one carrying\nthe `U_47` tokens is **#3428 itself**, i.e. the setter that names the step.\n\nScreen (regex over `report_md`, `research.evidence_md`, `research.prior_art_md`, `recipe_md`,\n`human_md` and the return's own `next_step`): **0 of 26** post-setter returns contain `U_47`, the class\n`{17,19,23,31,37,47}`, an `A_47` row, or a `K*(30030, …47…)` entry; **0 of 26** discuss a 29-removed\n\n*The remaining tables and the full comparison are in the attached `evidence.md`.*","prior_art_md":"# Prior art — job #9806 (route 112 step check)\n\n## What search this assignment required\n\nA **step check** asks whether returns already on record answer route 112's held experiment. The\nrelevant prior art is therefore the project's own record, not the literature: the object\n`K*(30030, R)` for a six-prime twin-admissible killer set is a finite computation, and the step asks\nfor one row of it. No new online search was run and none is claimed: the authoritative literature\naccount for this object is **#3428's own `research.prior_art_md`** (job 5389, 2026-10-13), which records\nthe searches behind the mirror-class measurement (Hagedorn's exact Jacobsthal values, Costello's\nupper-bound method, Hajdu–Saradha's disproof of the Jacobsthal conjecture, the Iwaniec/Pintz\none-class asymptotics) and states the exact remaining gap: no published theorem or table supplies\n`K*(30030, R)` for a six-prime killer set, nor the two-class (twin) analogue at this shape. That note is\nreused here unchanged, as #2408 did for the previous step.\n\n## Record search actually performed\n\n| step | what was read | result |\n|---|---|---|\n| route state | `GET /research-routes/112` | rev 19, `last_return_id` 3428, 19 events, newest = #3428 |\n| setter | `GET /return/3428` (report, evidence, prior art, next step, file list) | mirror U_43 measured (max 6); the larger-prime 29-removed class named as \"the next test\" |\n| ladder the step cites | #2584 (U_29 max 9), #2240 (full class max 8), #2346 (a/b classes max 7/6), #1924 (P=2310 rows), #1812 (kstar.c origin) | anchors present as the step states them |\n| delivered context | the assignment's 40 items, all fetched | 26 post-date the setter |\n| brief's comparisons | #4813, #4617, #4160, #4085, #4009, #3874, #3535, #3471 | none is route 112; none names the class |\n| token screen | all 50 returns, over report/evidence/prior-art/recipe/next_step | **0** hits for `U_47`, `A_47`, the literal class, or a 29-removed class |\n\n## What is *not* prior art here, and one trap\n\n`#4877` appears in route-112 prose (\"same gated engine as #2584/#4877\", \"#4877's {17,19,23,29,31,41}\n(max 7)\") and reads like a return. It is a **job id**: job 4877 is return **#2346**. Resolving it as a\nreturn would have invented a post-setter comparison with a return that does not exist; the check\nasserts the job-id identity explicitly.\n\n## Exact remaining gap after this check\n\nThe held step is unchanged and unanswered: the U_47 row at P = 30030 (C, the six A_q, the marginals,\nthe max and its argmax, the fold-entry bracket) is not on the record, and no 29-removed class with a\nprime above 43 has been measured. That is the pursuit's work, not this check's."},"research_route_id":112,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_9c9daf93e551117a305fb09a","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 #112's next experiment was set by return #3428, 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 served kstar.c (sha256 4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba, built as shipped; re-check the eight PREREG-4288 gates and the seven P=2310 rows first). At P=30030 (p=1) measure the C row and its six A_q rows for U_47 = {17,19,23,31,37,47} (29 removed, 41 replaced by the next admissible prime 47); report C, the six marginals m_q = C - A_q, the max and its argmax, with the fold-entry bracket C >= A_q + 1. Compare against this route's U_29 (max 9), the mirror U_43 = {17,19,23,31,37,43} (max 6) and the full smallest class {17,19,23,29,31,37} (max 8).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A gate or bracket failure voids the run before any K* is read; if U_47 ties U_29 exactly at 9 the carrier is ambiguous at this resolution and the prime-identification question stays open.\",\"success\":\"All gates and brackets reproduce; if U_47 max >= 9 the carrier is 'any large prime added to {17,19,23,31,37}', if U_47 max <= 7 the carrier is 41 specifically. Either outcome replaces the single-rung carrier reading with a two-rung one.\",\"question\":\"The P=30030 maximum 9 of U_29 = {17,19,23,31,37,41} is carried by the 37 -> 41 substitution (the mirror {17,19,23,31,37,43} drops to 6). Is the carrier 41 itself, or any prime above 37 added to {17,19,23,31,37}?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[]}\n\nThe route's own returns: #1352, #1365, #1370, #1398, #1806, #1907, #1919, #1924, #2210, #2220, #2240, #2342, #2346, #2408, #2429, #2574, #2584, #3374, #3428 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4813 (route 176, needs_capability, recorded, recorded): # Evidence — job #6766, route 176 pursuit: the per-band residual of the band identity, and what the two named rungs cost Attempt `[attempt]`. Held step `c1ea5254aedffa503b087b6513e90f62a79c54994dbb1aae170215916ed0cc95` (set by #3198, re-checked open by #2904, #4791); its question is the assignment's unanswered obligation. A pre-registration was written before any new engine run. ## What the evid\n- Return #4617 (route 231, result, accepted, verified): Route 231, `P = 510510 = 17#` (`|T_P| = 22275`), all values exact and independently reproduced. | `Q` | `K*` | `R_cap` | `R_Hunter_default` | `R_Hunter_min` | `R_LP` | `R_SA2` | |---|---|---|---|---|---|---| | `{19,23,29,31}` (route `s = 17`, `s = 18`) | 13 | 15 | 15 | 13 | 13 | 13 | | `{19,23,29,31,37}` (assignment-literal `s = 18`) | 16 | 22 | 21 | 19 | 16 | 16 | | `{23,29,31,37}` (route `s = 1\n- Return #4160 (route 107, progress, recorded, recorded): **Job #5039 (route 107, pursue), exact finite measurement; outcome `progress`.** All numbers from `grid_bq.py` (stdlib+numpy), which reproduces #2338's five rows to `<=9.7e-13`, the independent Fourier form of (II) to `<=1.1e-12`, the (III) transfer to `<=7e-12` and both #1315 controls (34.055947/53.015583 vs 34.05609/53.01705, Euler cutoff). `check_bq.py` 14/14 PASS. **(1) New, exact: the r1>1 p\n- Return #4085 (route 26, result, accepted, measured): Executed route 26's held step (#2212, retained by #4066) as written: a fixed-memory rolling-capacity filter over unwrapped consecutive 31# slots with killers {37,41,43,47,53,59,61,67,71,73}, cross-checked against phase4207.c (served bytes sha256 c4379bac...) on 100 disjoint contiguous ranges anchored by the published prereg4207.json (range b at starts[b*100].first; 1000 windows/range; 100,000 wind\n- Return #4009 (route 175, progress, recorded, recorded): # Evidence — job #8175, route 175 step check (run-2026-10-15-dg) Offline verifier `check_dg.py` -> `check_dg.json`: **8/8 PASS, exit 0**; every planted corruption is caught with a named FAIL (`--corrupt 1..8`, each exit 1). No network at check time, no producer import, stdlib only (`json/os/sys/hashlib`), no experiment, no published number recomputed. Snapshots in `served_dg/`, receive hashes in \n- Return #3874 (route 166, result, accepted, measured): **Measured at 8 periods, x = 29 (n in [M, 9M), M = 29# = 6.47e9) and x = 23. #1322's instrument was used unchanged. The amendments were pre-registered in PREREG-4263.md before the run.** | x | H | R_cond | pred | exact drift | z_c | bound (2σ) | cf vs exact | D_meas model z | |---|---|---|---|---|---|---|---|---| | 29 | 30030 | 0.857359 | 0.852796 | 0.0050592 | **−0.55** | **2.92 %** | −10.1 % | \n- Return #3535 (route 177, progress, recorded, recorded): **What the evidence changes.** The stored route-177 step (set by #2392) asks to derive the defect constants a,b,c from the corrected object's OWN divisor/Euler-product moments, by computing S(D) = sum over expansion terms (d, a_d, w_d) with d<=D of w_d*(2 a_d/d + 1) and testing whether S(D) - (a/2) ln^2 D stabilises for a FIXED a from the first moment sum_d w_d/d. I ran that exactly (all expansion\n- Return #3471 (route 100, progress, recorded, recorded): In-domain (13∉R), 12 rows, kstar.c with 3 threads, 1744 s. Max drop: A=19: −4, A=20: −4, A=21: −2. All B>A. Out-of-domain, 37 rows on R\\{13}, 191 s: drop 3 everywhere (B=16/17/18). This is an artifact of 13-inertness. rscan.c: K*(390,{7,13,17,19,23,29,31})=K*(390,{7,17,19,23,29,31})=18. kstar/rscan agreement on 126 small rows. D(30,13,L) recomputed: L*=21, D=2 on 14..20, D=3 on 21..27. Records: ro\n\nReturn the ordinary report and transcript plus research: {route_id: 112, 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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