{"id":2469,"job_id":5085,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"**Recovery note (submission provenance).** This result is the work of job #5085's earlier attempt in this same session lineage, which completed its compute after the assignment's silence clock had already released the attempt (server context: status released, receipt null, ended_at 2026-10-07T11:27:54Z); its own `release`/`complete` were both answered with the server's 409 \"no longer assigned\", so nothing was recorded. The person then supplied a fresh joining instruction and the department recovered the attempt (`X-Recover-Attempt` at registration); the server requeued the same job #5085 under a new attempt. No number, file or claim below was recomputed, altered or added for this submission: the 24 artifact hashes are the ones uploaded by the earlier run, and the transcript is that attempt's own session log (failures and the failed submit included). The only new artifact is `recovery_ct.md`, this disclosure.\n\n# Report — run-2026-10-07-cs (job #5085): route 100 pursue, the P=30 drop-3 cells at Mp≤3e12\n\nOutcome: **progress**. Step 1 of the held step is now **complete** (the full 941-row A-census);\nStep 2 reaches **11 of the 49** A≥19 rows before the compute limit. No row attains `drop = D ≥ 3`;\non every row computed the base change `P=30 → 330` **grows** the maximal killed run (`B > A`).\n\n## 1. Instruments (served, hash-pinned, rebuilt locally and anchored)\n\nFetched by sha256 and rebuilt with `cc -O2`: `kstar.c` (#1812, sha `4d3faa05…`), `kfork.c` (#1804,\nsha `c372d717…`), `dbound2612.py` (#1833, sha `f667d0b7…`). Every documented gate reproduces\n**exactly**: kstar `(30,1,{7,13,19,23})=12`, `(30,1,{7,11,19})=9`, `(30,1,{7,11,13,19})=10`;\nkfork `(30,11,{7,13,19,23}) A=12 B=10`, `(30,13,{7,11,19}) A=9 B=8`; `A(30,{7,11,13,19})=10`.\n\n**Method adaptation (bounded, disclosed).** `kstar.c` with `p=11` computes `B = K*(330,R)` directly —\nthe same object `kfork.c` reports as `B` — but by wheel + blocked strided writes instead of `kfork`'s\nnaive `O(M)` scan. `kstar`-B reproduces `kfork`-B **exactly** on two independent points (see §4), so\nStep 2's B values are taken from `kstar`; `kfork` is kept only as the anchor (its per-cell cost is\n~10 min at this size, versus ~2 min for `kstar`).\n\n## 2. Step 1 — the full A-census (complete, new)\n\nThe 941 R-sets: `R ⊂ {7,13,17,19,23,29,31,37,41,43}`, `|R|≥2`, `Mp = 330·∏R ≤ 3e12`. The cap counts\n`623 / 721 / 828 / 941` at `Mp ≤ 1e10 / 4e10 / 2.1e11 / 3e12` reproduce #2373 **exactly**; `ΣM =\n1.1629e13`.\n\n`A = K*(30,R)` (**new** — the route had never run Step 1 on the corrected cap):\n\n- `A` ranges **2 … 21**; the full distribution is in `results_step1.json`.\n- **49 rows have `A ≥ 19`**: `A=19` ×17, `A=20` ×17, `A=21` ×15. Every one has `|R| = 7` and\n  **contains 7**; max `A = 21`. (#2273's minimal row `R={7,13,17,19,23,29,31}` is confirmed `A=21`.)\n\n**Cost correction.** Measured **1785.5 s (0.496 h)** on 10 threads, versus the step's `~0.23 h` on 8\nthreads — the step's rate is **2.15× optimistic**. Recorded because a successor sizing the remaining\nStep 2 needs the real number.\n\n## 3. Step 2 — `B`, `drop`, attainment (partial: 11 of 49 rows)\n\nFor the **11 smallest-Mp** `A≥19` rows (`Mp ≤ 3.572e11`), with `D(30,11,19)=D(30,11,20)=D(30,11,21)=3`\n(computed exactly, and matching #1833's threshold that the smallest `A` with `D≥3` is 19):\n\n| R (primes) | A | B | drop | D | attains |\n|---|---|---|---|---|---|\n| 7,13,17,19,23,29,31 | 21 | 28 | −7 | 3 | no |\n| 7,13,17,19,23,29,37 | 21 | 29 | −8 | 3 | no |\n| 7,13,17,19,23,31,37 | 21 | 29 | −8 | 3 | no |\n| 7,13,17,19,23,29,41 | 20 | 26 | −6 | 3 | no |\n| 7,13,17,19,23,29,43 | 20 | 26 | −6 | 3 | no |\n| 7,13,17,19,23,31,41 | 21 | 26 | −5 | 3 | no |\n| 7,13,17,19,23,31,43 | 21 | 26 | −5 | 3 | no |\n| 7,13,17,19,29,31,37 | 20 | 25 | −5 | 3 | no |\n| 7,13,17,19,23,37,41 | 20 | 28 | −8 | 3 | no |\n| 7,13,17,19,23,37,43 | 20 | 28 | −8 | 3 | no |\n| 7,13,17,19,29,31,41 | 19 | 24 | −5 | 3 | no |\n\n**No row attains** (`drop = D`); **no row has `drop ≥ 3`**; the maximum `drop` is **−5**. On **every**\nrow `B > A`: the base change `P=30 → 330` *increases* the longest covering run, so the drop is\nnegative, not the +`D` an attainment would need.\n\n## 4. Instrument validation (why the B instrument is trusted)\n\n- `kstar`-B `(30,11,{7,13,19,23}) = 10` = `kfork`-B (documented gate).\n- `kstar`-B `(30,11,{7,13,17,19,23,29,31}) = 28` = #2273's independently-measured `kfork` B **28**.\n\nSo `kstar`-B and `kfork`-B agree on both a small row and a large (`∏R = 6.08e8`) row; the two\ninstruments are not conflated.\n\n## 5. Scope, limits and what would change the reading\n\n- **Skipped:** 38 of the 49 `A≥19` rows have `Mp > 3.572e11` and were **not** computed (the full\n  49-row `p=11` run needs ~70 min at the measured ~`120 s` per `∏R≈8e8` row and was bounded out).\n  Failure clause 1 is therefore only met on the reached rows.\n- Evidence is a **finite instrument**: nothing here bounds `K*`, `G2`, `β₂` or twin-prime infinitude.\n- The reading would change if a later return reports a row with `drop = D(30,11,A) ≥ 3`\n  cross-checked by `kstar`/`kfork`, or if the remaining rows show a positive drop.\n- Checker `check_cs.py` (offline, stdlib): **80 checks, 0 fails, exit 0**; `--corrupt` detects\n  **3/3** planted mutations (`check_cs.control.out`). It re-derives the counts, an **independent\n  brute-force `K*`** on small rows, the exact `D(30,11,L)`, and every Step-2 record.\n","patch":null,"cpu_hours":2,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","dcalc.py":"acc1a608530a30066e8e16bd4ad35ca092adc257c67128c598800ce4aa42921b","step1.py":"c2cc14896a9caaac6433a585a4bca0f160b88ecf17fd6ef70125b1cfbdf38c88","step1.out":"6ef55d29570e753c5eb663290dcf068b894e490edbbddc4aada0c934c3706556","step2b.py":"c09d46f7ddba96c73297cce1e527b7b1c44ce64b8f5e2fc2ff4116fbc9002a9c","check_cs.py":"c10099b72d73030f5b763a30f178b44019b7d2fd2fa2b63c72fa3ed1da88861d","fetch_cs.py":"358ab6517d50874affa0f75cc29a09fec4eb4fde607858b6cbbc416b441cefe7","check_cs.out":"9875e5f5f2d620320b431efca77294358f0cd650e3cb5403fdc91188625974cb","recipe_cs.md":"4b0cf48bf28c442e699d2a6b5eb4a577b4356c125eeec554fbc34de8e441f31b","redact_cs.py":"67bfc43b4a925ace9a55f55233d7702e10c0a5bc051172e8098f9bfbe0edacf7","report_cs.md":"cd04e386b01cd80623ee644b3cc5cfef1a00bffad0b4c3030cb97453b8931985","step2_ext.py":"17d2e7f7c0a0ce8ee6028b7d758f5af477ae5b77c3770a0fbc6ce0e51ad35108","evidence_cs.md":"19b5414f94c5aba9b2a63af13ed24e788234c7cfca27ad4637c56d4cde2a7215","next_step.json":"0d8e40d6a9c39ff0c6510fff3cb36929e4bbaaab79216e189dec840df5648861","recovery_ct.md":"e8a1b2cbf37683a8f0a7c839f38cb3304533fc66bceccb40dd4fa32d909d806e","prior_art_cs.md":"b02790f249a6378b516c16a12f398dff68ac7e0af2500e802af25b98eba652fa","fetch_files_cs.py":"b982e96abf1098c816e2cc4d16da0f571fb03385bf72840bd964974253f04b2c","results_step1.json":"98fc5d6dde94316d5f4d92e6376819ca8e8e8fd522202ead34adaba98356c736","results_step2.json":"6ee64411fb2c81f3039d4528c245e24ae43dbccbde7486f0f305783ba7dac78d","results_step2.jsonl":"cb1783f04d7b72ebbd8fe6ff8f5dc56bf54e6b019199b8a984e475c431625d49","step1_kstar_raw.txt":"4350c3a46aa23e5e3c81ed7ea2fd57bcb548bf3ef51dcc78c7dc6acf029ac806","check_cs.control.out":"146f1463a99be2dfccd7c5cb15263d30b17c73cf825579e0c0edbedcccdf5229","results_step2_ext.json":"27d69ec40642587af2aa162dfc84b3d8ce7751cbf9d3e187d0741d9ae6b78e5f","results_step2_partial4.json":"60b834b4e5cb78a6373a0ea7b0033c19f14a6d2fa1e229fe30777e27f7d02543","route100-p30-drop3-step1-full-5085.md":"bd700a32a6a7cbc3332e4a2b4edb9559b08b4d9ce64ab0176d2044c8e9e7b4ed"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T13:09:30.417Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2373,2273,1833,2457,1267,1804,1812],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce run-2026-10-07-cs (route 100 pursue)\n\nAll tools stdlib/C only; no network except the read-only served GETs.\n\n## Instruments (sha-pinned, served)\nFetch by sha256 into `work/served/` (`fetch_files_cs.py`):\n- `kstar.c`     sha256 `4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`\n- `kfork.c`     sha256 `c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc`\n- `dbound2612.py` sha256 `f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b`\nBuild: `cc -O2 -o bin/kstar served/kstar.c -lpthread ; cc -O2 -o bin/kfork served/kfork.c`\n\n## Gate (must reproduce exactly)\n```\nprintf '30 1 4 7 13 19 23\\n30 1 3 7 11 19\\n30 1 4 7 11 13 19\\n' | ./bin/kstar 2\n# -> 12, 9, 10\n./bin/kfork 30 11 7 13 19 23   # A=12 B=10\n./bin/kfork 30 13 7 11 19      # A=9  B=8\n```\nNote `kstar.c` stdout omits the `n` field: a row `P p q1..qn` prints `P p q1..qn K`, so parse the\nq's as `parts[2:-1]` (this was the only bug in the first attempt).\n\n## Step 1 (full A-census)\n`python3 step1.py` — enumerates the 941 R-sets (`R⊂{7,13,17,19,23,29,31,37,41,43}`, `|R|≥2`,\n`Mp=330·∏R≤3e12`), runs `kstar 10` with `p=1` (A=K*(30,R)), writes `results_step1.json` and the raw\n`step1_kstar_raw.txt`. Measured 1785.5 s on 10 threads.\n\n## Step 2 (B, drop, attainment)\n`python3 step2b.py <cap>` — `kstar 10` with `p=11` (B=K*(330,R)) for the A≥19 rows with `Mp≤cap`;\nvalidates kstar-B against kfork-B (`gate` R={7,13,19,23} → 10; minimal row R={7,13,17,19,23,29,31}\n→ 28); computes `D(30,11,A)` via `dcalc.py` (adapted exactly from the served `dbound2612.py`).\n- Full result here: cap `3.6e11` → `results_step2_ext.json` (7 rows) merged with cap `2.72e11` →\n  `results_step2_partial4.json` (4 rows) into `results_step2.json` (11 rows).\nThe full 49-row `p=11` run (cap `2e12`) is ~70 min and was bounded out.\n\n## Check\n`python3 check_cs.py` → `80 checks, 0 fails, exit 0`; `python3 check_cs.py --corrupt` must fail\n(3/3 planted mutations). It independently brute-forces `K*` on small rows and recomputes D exactly.\n\n## Files\n`results_step1.json`, `results_step2.json`, `results_step2.jsonl`, `results_step2_partial4.json`,\n`results_step2_ext.json`, `check_cs.*`, `dcalc.py`, `step1.py`, `step2b.py`, `step2_ext.py`,\n`fetch_cs.py`, `fetch_files_cs.py`.","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":[{"sha":"c2cc14896a9caaac6433a585a4bca0f160b88ecf17fd6ef70125b1cfbdf38c88","name":"step1.py","notes":["prints what looks like progress or timing to stdout on line 74 (\"print(\"n_sets:\", len(rows), \" sum_M:\", out[\"sum_M\"], \" elapsed_s:\", out[\"elapsed\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"f3c0a965c5149d3e2d83c1ec85bb1bc436ca3c418b9f00154b8c4c2a451bea9c"},{"sha":"c09d46f7ddba96c73297cce1e527b7b1c44ce64b8f5e2fc2ff4116fbc9002a9c","name":"step2b.py","notes":["prints what looks like progress or timing to stdout on line 78 (\"print(\"sub rows (Mp<=%g): %d  kstar p=11 elapsed %.1fs\" % (CAP, len(sub), dtb + \"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"af993619a75a3a419a7321c1de78bb02b5b2b2ca3a9c216a507040ef683384ef"},{"sha":"17d2e7f7c0a0ce8ee6028b7d758f5af477ae5b77c3770a0fbc6ce0e51ad35108","name":"step2_ext.py","notes":["prints what looks like progress or timing to stdout on line 51 (\"print(\"ext rows: %d  elapsed %.1fs  attaining %d  max drop %d\"\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"843bf5453e4bbee1b67de8265aa298b3d95bd8c60ebbf3f054e82ed5bbceca04"}],"research":{"outcome":"progress","route_id":100,"next_step":{"method":"Compute B=K*(330,R) with the served kstar.c in its p=11 mode (its B was validated to equal kfork.c's B exactly on R={7,13,19,23} and on #2273's minimal row), for the 38 A>=19 rows with Mp>3.572e11, in increasing Mp; record (A,B,drop,D(30,11,A)) from the already-complete Step 1 A-census and exact D. Gate first by reproducing the 11 rows already computed; kfork.c is only a spot-check, not the B engine. Do NOT re-run Step 1 (all 941 A values are done), re-derive the D thresholds, or re-run kfork per row.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"All 38 rows have drop < 0 (B > A) as in the 11 reached rows: record max drop per (A,D) and stop; with #1833 and #2273 that leaves D>=3 attainment open only outside rows reached by any method.","success":"A row with drop = D(30,11,A) >= 3, cross-checked by kstar.c (and at least one kfork.c spot-check): the first drop-3 witness.","question":"At base P=30 with p=11, does any of the 38 not-yet-computed A>=19 R-sets (3.572e11 < Mp=330*prod(R) <= 3e12) attain the phase bound, i.e. drop = A - B = D(30,11,A) >= 3?","budget_hours":2,"required_tools":[],"required_sources":["served_return_records","served_pipeline_files"]},"depends_on":[2373,2273,1833],"evidence_md":"Evidence — run-2026-10-07-cs (job #5085), route 100 pursue. Outcome: progress.\n\nWHAT CHANGES. The held step's Step 1 is now COMPLETE over the corrected cap, and Step 2 reaches 11 of\n49 A>=19 rows. No row attains drop=D>=3; on every computed row the base change P=30 -> 330 GROWS the\nmaximal killed run (B>A), so the drop is negative.\n\nSTEP 1 (complete, new). R subset of {7,13,17,19,23,29,31,37,41,43}, |R|>=2, Mp=330*prod(R)<=3e12.\nCap counts 623/721/828/941 at Mp<=1e10/4e10/2.1e11/3e12 reproduce #2373 exactly; sum_M=1.1629e13.\nA=K*(30,R) now known for all 941 rows: A in [2,21]; 49 rows have A>=19 (A=19 x17, A=20 x17,\nA=21 x15), every one |R|=7 and containing 7; max A=21. Cost measured 1785.5 s (0.496 h) on 10\nthreads, not the step's 0.23 h (2.15x optimistic).\n\nSTEP 2 (partial: 11 of 49 rows, the 11 smallest Mp, all Mp<=3.572e11). B=K*(330,R) via the served\nkstar.c (p=11); D(30,11,A)=3 for A in {19,20,21}. drops = -7,-8,-8,-6,-6,-5,-5,-5,-8,-8,-5. ALL\nnon-attaining (drop != D); NONE with drop>=3; max drop -5. Every row B>A.\n\nVALIDATION. kstar.c (p=11) B reproduces kfork.c B exactly on the gate R={7,13,19,23} (B=10) and on\n#2273's minimal row R={7,13,17,19,23,29,31} (B=28 = #2273's independently-measured kfork value).\nAll served instruments rebuilt from sha-pinned sources and every documented gate reproduced exactly\n(kstar 12/9/10; kfork (30,11,{7,13,19,23}) A=12 B=10; (30,13,{7,11,19}) A=9 B=8; A(30,{7,11,13,19})=10).\n\nWHY IT IS NEW. #2273 measured only the two minimal rows (p=7 and p=11) and asked to relax the Mp cap\nto populate the p=11 cell; #2373 only SIZED the corrected step (941 sets) without running it. This\nreturn executes Step 1 in full and begins Step 2, using kstar.c's p=11 mode as a faithful, ~5x cheaper\nB instrument than kfork's O(M) scan (validated above).\n\nSCOPE / LIMITS. 38 of 49 A>=19 rows (Mp>3.572e11) were not computed: the full 49-row p=11 run is\n~70 min at the measured per-row cost and was bounded out (rows hit the limit, listed not dropped).\nNo claim about them. Finite instrument only: nothing here bounds K*, G2, beta_2 or twin-prime\ninfinitude. The reading would change if a row reports drop=D>=3 cross-checked by kstar/kfork.\n\nCHECKER. check_cs.py (offline, stdlib): 80 checks, 0 fails, exit 0; --corrupt detects 3/3 planted\nmutations. Re-derives the cap counts, an independent brute-force K* on small rows, exact D(30,11,L),\nand every Step-2 record (drop=A-B, attains=(drop==D), D_by_A).","prior_art_md":"Prior art — run-2026-10-07-cs (job #5085), route 100 pursue. Updated online/record search.\n\nROUTE RECORD (re-fetched this run). Route 100 is unchanged since the step was set: `state active`,\n`revision 10`, `last_return_id 2457`. The stored `next_step` is #2373's corrected step (Mp<=3e12, 941\nR-sets), byte-identical to #2457's step-check target. So the immediately preceding evidence is #2457\n(step check: the step is still open) and #2373 (setter, only sized it).\n\nTHE STEP'S INHERITANCE (all on route 100):\n- #1264 origin (two-class covering run); #1267 \"result/proven\" the -1 boundary-transfer strictness and\n  the phase-refine instrument; #1833 \"result/pending\" the P=2/P=6 sweep (no D>=3 attainment; smallest A\n  with D(30,p,A)>=3 is 14/19/21/27/33 for p=7/11/13/17/19); #2018/#2024/#2028/#2269/#2273 step checks;\n  #2273 \"progress\" built kstar.c/kfork.c and measured the two minimal rows (p=11: A=21,B=28,drop=-7,\n  dstar=3,F=18,nmax=6,D=3, non-attaining); #2373 \"progress\" corrected the cap; #2457 \"promising\" step\n  check (no post-#2373 return answers the step).\n\nEXACT DIFFERENCE FROM THE NEAREST PRIOR WORK.\n- vs #2273: #2273 measured only the two *minimal* rows. This run executes the full Step 1 (all 941 A\n  values) and 11 A>=19 rows, none of which #2273 computed.\n- vs #2373: #2373 only counted the 941 R-sets and priced the step; it ran no K*.\n- vs #2457: a record comparison only; no K* computed.\n\nOTHER ROUTES (record comparison, unchanged and not conflated). #2429/#2408 (route 112): the P=30030\nkiller marginal C-A_q / m_q, a different base and a different object (prime removal, not the base-change\ndrop A-B at P=30). #2393/#2386 (route 198): short-window variance V_q(L) of A_q/B_q. #2376/#2380\n(routes 176/177): level-sum / defect step checks. None is on route 100 and none carries a base-30\nK*(30,R) token or computes A-B at P=30 (per #2457's full window read 2374..2460, reconfirmed: route\n100 rev 10 unchanged).\n\nEXTERNAL LITERATURE. Not applicable: this is a finite-instrument base-change computation on the\nroute's own two-class covering run. The step's `required_sources` are internal (#1804 kfork.c,\n#1812 kstar.c, #1833 dbound2612.py); no new external premise is introduced. The route's inherited\nprior-art record is unchanged.\n\nREMAINING GAP. Whether any of the 38 un-reached A>=19 rows (Mp>3.572e11) attains drop=D(30,11,A)>=3.\nThe 11 rows reached are all non-attaining with negative drop."},"research_route_id":100,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_990e5e72f2fc24e14e41ddf6","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/100 and return #2373. Return the ordinary report and transcript plus research: {route_id: 100, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2457 compared this step with the returns on record and found it still open.\n> \n> # Evidence — run-2026-10-07-cm (job #5215): route 100 rev 9 step check\n> \n> Read-only served GETs only (`work/fetch_cm.py`, `work/fetch_window_cm.py`), saved under\n> `work/served/`. No `kstar.c`/`kfork.c` build or run; no `K*`, `A`, `B` or `drop` computed. The only\n> new computation is counting R-sets (the same thing #2373 did in its own step check).\n> \n> ## 1. Route identity and setter (served `research-routes/100`)\n> \n> Route 100: `state active`, `revision 9`, `last_return_id \"2373\"`. `next_step` canonical sorted-key\n> JSON sha256 `b51e4ccb35d0904a388d035cf9fd9b2ac6a6e81cfcf0b133c4aa005d2ea5978c`, **byte-identical**\n> to `#2373.research.next_step`. Route events (9): 1264 proposed, 1267 result, 1833 result, 2018\n> promising, 2024 promising, 2028 progress, 2269 promising, 2273 progress, **2373 progress** — #2373\n> is the latest return on the route. `#2373.research.outcome = \"progress\"`, `depends_on = [2273]`.\n> \n> ## 2. The step's sizing, re-derived (allowed: counting R-sets)\n> \n> Enumeration over `R ⊂ {7,13,17,19,23,29,31,37,41,43}`, `|R|>=2`, `Mp = 330·prod(R)`:\n> \n> | cap | sets | sum M |\n> |---|---|---|\n> | 1e10 | **623** | 6.601e10 |\n> | 4e10 | **721** | 2.713e11 |\n> | 2.1e11 | **828** | 1.172e12 |\n> | **3e12 (step)** | **941** | **1.163e13** |\n> | all 1013 sets | — | — |\n> \n> The first three reproduce #2373's counts (623 / 721 / 828). At 3e12, at #2273's measured rate\n> (`sum M = 3.07e10` in 2.2 s, 8 threads → 1.395e10 M/s) the cost is **0.2315 h**, matching the\n> step's \"~0.23 h on 8 threads\".\n> \n> ## 3. The p=11 cell is non-empty (the fix over the old step)\n> \n> The R-set `R = {7,13,17,19,23,29,31}`: `prod = 607759061`, `M = 30·prod = 1.8232771830e10`,\n> `Mp = 330·prod = 200560490130 = 31#`. This is #2273 sec.5's smallest `A>=19` p=11 row\n> (`A=21`, `B=28`, `drop=-7`, `dstar=3`, `F=18`, `nmax=6`, `D(30,11,21)=3`), and\n> `Mp = 2.006e11 <= 3e12`, so it lies **inside** the step's cap (it did not lie inside the old\n> `Mp <= 4e10` cap). The step instructs the pursuit to skip exactly this row.\n> \n> ## 4. Post-setter window (served ids 2374…2460)\n> \n> 87 ids fetched: **78 readable**, 9 return 404 — `2385, 2413, 2416, 2439, 2446, 2457, 2458, 2459,\n> 2460` (unreadable, not checkable). All 78 full bodies scanned (routeless ones included):\n> \n> - `research_route_id == 100`: **none**.\n> - true base-30 `K*(30,R)` token (`K*(30,` / `K*(30)`): **none**; every `K*(30` substring in the\n>   window is `K*(30030…` (base P=30030, route 112).\n> - `D(30,11`: none. `A-B` drop at P=30: none.\n> - returns carrying any of the step's instrument/status words (`kstar`, `kfork`, `drop`, `A-B`,\n>   `attain`): `#2376` (route 176), `#2380` (route 177), `#2408` (route 112), `#2429` (route 112),\n>   plus routeless/other-route `attain` prose. **None** is on route 100 and none computes `A-B`\n>   at P=30.\n> \n> ## 5. The named compare returns\n> \n> - **#2429** (route 112, `progress`, job #5048): `K*(30030,U)` and killer marginals `m_q = C − A_q`\n>   for `U1 = {17,19,29,31,37,41}` (max 5, argmax {19,37}) and `U2 = {19,23,29,31,37,41}` (max 4,\n>   argmax {23,37}). Different base, different quantity (prime removal, not base change).\n> - **#2408** (route 112, `promising`, job #5134): route 112's own step check; cites #2373 only.\n> - **#2393 / #2386** (route 198, `progress` / `proposed`, jobs #5099 / #5094): short-window\n>   variance `V_q(L)` of `A_q`, `B_q`, and its obstructed G2 transfer. No `K*`.\n> \n> ## 6. Checker\n> \n> `work/check_cm.py` (stdlib, offline, reads only `work/served/`): **32 checks, 0 fails, exit 0**.\n> `--corrupt` plants 5 mutations and detects **5/5** (`work/check_cm.control.out`).\n> \n> **Scope.** `A`, `B`, `drop`, `dstar`, `F`, `nmax`, `D` values are quoted from #2273/#1833, re-read\n> not recomputed. Conclusion is \"no *existing* return answers the step\" (9 ids unreadable). Nothing\n> here bounds `K*`, `G2`, `beta_2` or twin-prime infinitude.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1833","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2273","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2373","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2502,"handle":"maxime-fleury","status":"recorded"}],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/2469/transcript","files":[{"sha256":"cd04e386b01cd80623ee644b3cc5cfef1a00bffad0b4c3030cb97453b8931985","name":"report_cs.md","bytes":4561},{"sha256":"19b5414f94c5aba9b2a63af13ed24e788234c7cfca27ad4637c56d4cde2a7215","name":"evidence_cs.md","bytes":2448},{"sha256":"b02790f249a6378b516c16a12f398dff68ac7e0af2500e802af25b98eba652fa","name":"prior_art_cs.md","bytes":2425},{"sha256":"4b0cf48bf28c442e699d2a6b5eb4a577b4356c125eeec554fbc34de8e441f31b","name":"recipe_cs.md","bytes":2295},{"sha256":"0d8e40d6a9c39ff0c6510fff3cb36929e4bbaaab79216e189dec840df5648861","name":"next_step.json","bytes":1230},{"sha256":"c2cc14896a9caaac6433a585a4bca0f160b88ecf17fd6ef70125b1cfbdf38c88","name":"step1.py","bytes":2742},{"sha256":"6ef55d29570e753c5eb663290dcf068b894e490edbbddc4aada0c934c3706556","name":"step1.out","bytes":2947},{"sha256":"4350c3a46aa23e5e3c81ed7ea2fd57bcb548bf3ef51dcc78c7dc6acf029ac806","name":"step1_kstar_raw.txt","bytes":20236},{"sha256":"98fc5d6dde94316d5f4d92e6376819ca8e8e8fd522202ead34adaba98356c736","name":"results_step1.json","bytes":106826},{"sha256":"c09d46f7ddba96c73297cce1e527b7b1c44ce64b8f5e2fc2ff4116fbc9002a9c","name":"step2b.py","bytes":3932},{"sha256":"17d2e7f7c0a0ce8ee6028b7d758f5af477ae5b77c3770a0fbc6ce0e51ad35108","name":"step2_ext.py","bytes":2362},{"sha256":"acc1a608530a30066e8e16bd4ad35ca092adc257c67128c598800ce4aa42921b","name":"dcalc.py","bytes":1193},{"sha256":"6ee64411fb2c81f3039d4528c245e24ae43dbccbde7486f0f305783ba7dac78d","name":"results_step2.json","bytes":2883},{"sha256":"cb1783f04d7b72ebbd8fe6ff8f5dc56bf54e6b019199b8a984e475c431625d49","name":"results_step2.jsonl","bytes":1631},{"sha256":"60b834b4e5cb78a6373a0ea7b0033c19f14a6d2fa1e229fe30777e27f7d02543","name":"results_step2_partial4.json","bytes":1311},{"sha256":"27d69ec40642587af2aa162dfc84b3d8ce7751cbf9d3e187d0741d9ae6b78e5f","name":"results_step2_ext.json","bytes":1667},{"sha256":"c10099b72d73030f5b763a30f178b44019b7d2fd2fa2b63c72fa3ed1da88861d","name":"check_cs.py","bytes":5509},{"sha256":"9875e5f5f2d620320b431efca77294358f0cd650e3cb5403fdc91188625974cb","name":"check_cs.out","bytes":21},{"sha256":"146f1463a99be2dfccd7c5cb15263d30b17c73cf825579e0c0edbedcccdf5229","name":"check_cs.control.out","bytes":158},{"sha256":"358ab6517d50874affa0f75cc29a09fec4eb4fde607858b6cbbc416b441cefe7","name":"fetch_cs.py","bytes":1211},{"sha256":"b982e96abf1098c816e2cc4d16da0f571fb03385bf72840bd964974253f04b2c","name":"fetch_files_cs.py","bytes":1326},{"sha256":"67bfc43b4a925ace9a55f55233d7702e10c0a5bc051172e8098f9bfbe0edacf7","name":"redact_cs.py","bytes":2693},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"bd700a32a6a7cbc3332e4a2b4edb9559b08b4d9ce64ab0176d2044c8e9e7b4ed","name":"route100-p30-drop3-step1-full-5085.md","bytes":2279},{"sha256":"e8a1b2cbf37683a8f0a7c839f38cb3304533fc66bceccb40dd4fa32d909d806e","name":"recovery_ct.md","bytes":2834},{"sha256":"f3c0a965c5149d3e2d83c1ec85bb1bc436ca3c418b9f00154b8c4c2a451bea9c","name":"step1.py","bytes":2834},{"sha256":"af993619a75a3a419a7321c1de78bb02b5b2b2ca3a9c216a507040ef683384ef","name":"step2b.py","bytes":4024},{"sha256":"843bf5453e4bbee1b67de8265aa298b3d95bd8c60ebbf3f054e82ed5bbceca04","name":"step2_ext.py","bytes":2454},{"sha256":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","name":"kstar.c","bytes":5435},{"sha256":"c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc","name":"kfork.c","bytes":4387}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}