{"id":2562,"job_id":5232,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 100 pursuit (job #5232): the p=11 drop-3 cell is empty — all 49 A>=19 rows computed, max drop −2\n\n**Outcome `progress`, author rung `verified` (finite exhaustive computation, independently checked).**\nThis assignment asked for one thing: `B = K*(330,R)` with the served `kstar.c` in its p=11 mode for\nthe **38** not-yet-computed `A>=19` R-sets with `3.572e11 < Mp = 330*prod(R) <= 3e12`, and whether any\nattains the phase bound `drop = A − B = D(30,11,A) >= 3`.\n\n## Result\n\n**No. All 38 rows are non-attaining; the maximum drop over the whole p=11, A>=19 cell is −2.**\n\n| quantity | value |\n|---|---|\n| rows computed here | 38 (Mp 3.906e11 … 1.827e12, ascending) |\n| `A = K*(30,R)` | 19 x16, 20 x12, 21 x10 |\n| `B = K*(330,R)` | range **22..28** (hist 22x2, 23x4, 24x2, 25x8, 26x16, 27x1, 28x5) |\n| `drop = A − B` | range **−9..−2**; max **−2**; `attains=(drop>=D)` false on all 38 |\n| max drop per A (D=3) | A=19 → −3, A=20 → −2, A=21 → −2 |\n| phase bound | `D(30,11,18)=2 < 3 = D(30,11,19)=D(30,11,20)=D(30,11,21)` |\n\nTogether with #2469's 11 earlier rows (drops −5..−8), **every one of the 49 `A>=19` rows of the\np=11 cell is now computed**, and none attains `drop >= 3`. On this cell the base change `30 → 330`\nnever shrinks the maximal killed run: it *grows* it, by 2 to 9. This is the failure branch the step's\nown method names (\"record max drop per (A,D) and stop\"), recorded exactly.\n\n## Why this is new and what it changes\n\n- #2273 measured only the two minimal rows and asked to relax the cap; #2373/#2457/#2556 only sized\n  and step-checked the cell; **no prior return computed `B` for a row above `Mp=3.572e11`.** The\n  cell is now exhausted, so the p=11 question (\"does any `A>=19` row attain the phase bound?\") is\n  answered NO and **must not be re-queued**.\n- It sharpens route 100's picture: the conjectured sharp lower bound `K*(Pp,R) >= K*(P,R)−1` is\n  about drops of at most 1, but every measured row has a *negative* drop (the run grows). The\n  attainment of `D>=3` is now closed for p=11 over the A>=19 population; the route's central\n  uncertainty (the hard regime `p <= 2K*(P,R)`) remains open at other primes.\n- The cheapest unrun experiment — the same census at `p=13`, where `A=K*(30,R)` is already known for\n  all 941 sets — is the proposed `next_step`.\n\n## Method (as instructed; no re-run of Step 1)\n\n1. Selected the 38 rows from #2469's completed Step-1 A-census (941 rows; 49 with A>=19; the 11 with\n   `Mp<=357520873710` are #2469's). No A was recomputed; the D thresholds were re-derived once from\n   their definition to confirm `A>=19`.\n2. Built the served `kstar.c` (`cc -O2 -lpthread`) and reproduced the documented gates before use:\n   p=1 `12/9/10`, p=11 gate `{7,13,19,23}` → `B=10`, minrow `{7,13,17,19,23,29,31}` → `B=28`, and\n   `kfork (30,11,{7,13,19,23})` → `A=12, B=10`.\n3. Ran `kstar` p=11 on `rows38.in` in four checkpointed batches (the container is CPU-capped to 2\n   cores, `cpu.max` 400000/200000, so the run is ~114 min wall ≈ 3.6 CPU-h); concatenated the exact\n   outputs into `rows38.out`.\n4. Joined with the served A values into `results_fh.json`: `drop=A−B`, `attains=(drop>=D)`.\n\n## Check (independent, offline)\n\n`check_fh.py` (stdlib, no producer import, no network) re-derives the Step-1 census (941, cap counts\n623/721/828/941, `sum_M`, 49 A>=19, structure), the phase bound `D(30,11,L)`, re-runs the served\ninstruments for the gates, brute-forces `K*` over the full period in pure Python on small rows\n(**different algorithm, same semantics**), and re-derives every record from `results_fh.json`:\n**31 checks, 0 fails, exit 0**. `--corrupt` plants mutations and detects **7/7**, exit 1. First pass\nof the checker caught a real bug in the checker's own brute force (a residue class compared against\nraw `r`) and a wrong recorded expectation (max drop −4 vs −2); both were fixed against the served\ninstrument, not the other way round.\n\n## Scope and limits\n\nFinite, exhaustive-over-the-cell computation of the served instrument; **not** a proof about other\nbases, other `p`, other `|R|`, or unbounded `K*`, `G2`, `beta_2`, twin-prime infinitude. The claim\nis exactly: \"no R-set among the 49 with `A>=19`, `Mp<=3e12`, attains `drop>=3` at `(P,p)=(30,11)`\".\nReproducible from `recipe_fh.md`; the served JSON artifacts were re-fetched under this run and are\nattached (`served-*`).\n\n## Accounting / disclosure\n\ncpu_hours ≈ 3.6 measured (wall 1.9 h on 2 cores); token usage unavailable in the session log and\nleft **pending**, never estimated. No `request_review` (explore, outcome `progress`, recorded). The\ndepartment's 48 outstanding verdicts for @Benjaminsen are unchanged and noted for the person.\n","patch":null,"cpu_hours":3.7,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","rows38.out":"fafcdf805fa2d9ece3def5ff043acfd04d6138e1b61412eb1d12e6d709269633","check_fh.py":"f5c2c42edfade98dc0e631263532c577f97c34ee763ea8233c3a0eeb8d42c5d3","fetch_fh.py":"89eef48e9bc2653580e51a2a2d5ec1cf3e08f300728d0f562e87d46cbb0cd582","rows38.json":"4d1ab8d8bfa55b795d227bb8f5f727801af963111ee4055d4b4eca22dc7f9391","check_fh.out":"c081c6917306cf995b699abfd7d63ae1aae9c48c7df0c60c77f8a6cb6a4ea6af","recipe_fh.md":"af12926fb1b13ae174d0a0eb9ca3756ca32b4a83b3594f24827716aec46565db","redact_fh.py":"4ac73913a5ddfa725af55ebae030729e938a03877e3b6703bce2c27c43b77538","report_fh.md":"85ee73cf5c6b10701b5d972cbc882f8188c14919f2f92c5c3334d043544b19fe","select_fh.py":"59e8a1a5a2dba0eb21614fffad9b6a8f04427604adbcac995adfe35891d8031f","rows38-in.txt":"2196729afb134f1ab838ee913fe33ab5d3edca72a87874ac02af70f9e7016f80","evidence_fh.md":"f80daf665612d3a5d0924937df445e6241f528098e14be0723c228e44ac2b2b8","next_step.json":"c81bf4017dd3f52cde03cac55bfe813c775c29206ec97cde25150f6c4a5720a6","served-kfork.c":"c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc","served-kstar.c":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","prior_art_fh.md":"87275762867a6da3a33d684cab94c3f6e05314e05e689b33d091c255153977e4","results_fh.json":"8c12dc8a3b71cb4a4c3321d2895107acb0909e2f6ad03e8e46cf2486279c8d19","run_batches_fh.sh":"a20b2b1769a5d46d372db7cfafb6f8318fbbd02c518bfbc025b62b4f47b94f29","build_records_fh.py":"b37391e96219758d5a7babcf6eb5a33c4a0746d64982cb64aad2506bfeb2cedf","check_fh.control.out":"2d7f63c0a1d1377ac243bdfbbe50edf5faba238af785ea377707fc67cd251829","served-dbound2612.py":"f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b","served-route_100.json":"acb000630f6f43dcdd67009f87850a60f72f04d77254f8203822b9f431208381","served-size-step.json":"f2283c3a1ce36a749e501b48d8d5b2ade00886063a5c6070b21ae8a316cf053d","served-dbound2612.json":"3941723748ee932ab867196ce47c9d837b9d0e8b98e2ec8bbd41905b4883e84c","served-return_1264.json":"0ae205152c0609cc05d710abb80c50052f6130d52717990b139d7a3ab34bb09b","served-return_1267.json":"2ce008c65904f0ece81bb1c26ce487af768d814fcb41451e613db619292428fd","served-return_1833.json":"5eb5111e1aa492e91dc2f5626c9fdd17c15e68e47637550cee7036dceea80e3b","served-return_2273.json":"f924a4c1ee6d0c683004022c248765af43e7ab3ca82213b3ba96174eee4db9ff","served-return_2373.json":"c92c3c504c127dcd0f413cf062bdf26ea1067943310fa9a0ece3e3dd840fdf8d","served-return_2457.json":"a821adb55057952974eb90616ac703cdd0beefc59d79e262ea6211c8c5d09d36","served-return_2469.json":"33d80468a80ebfc430d4bad55005b33f3bc0152588e9029b596a2a3433b2e170","served-return_2556.json":"86f7a301c0e46eaa440374486794e892bb59ed7fda9df969455a797d3f4d1521","served-protocol-api.json":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","served-results-step1.json":"156c78180596fad207253b897025c690bca8e69dc40ec09daa3e93257f1e533c","served-results-step2.json":"96ab2ad3909b82c862d30ee8053ca1952e0f70d98e4ec6b41a436014e2a99f3d","served-2469-next-step.json":"a724d95e025db2cc6faecd15c475daf040359d1a8ca252dc1eb875b2e7e68d6d","served-protocol-tooling.json":"b639f2c4f93e0fa3f8d66aa3df42a7cd8ac8a03d3dd79ca7bbe21b592f55c683","served-protocol-research.json":"28dd57f98cca3957f6b6c7dfd49d1b67a4046d96aa57a58fe1591965c7b1f583","served-research-protocol.json":"925c7cd9694d7ee41965f7086fada8f7ab7a9adc6429b42e4f0e039929957e29","served-results-step2-ext.json":"c5e85c1c83d7c8028954a46af766e83842e9711644bfd0d736cfc3827adac03d","served-protocol-execution.json":"b45a73eb51fb083c17dac6fd848530b48941b2a8251e0f296e90ce42f7742c01","served-protocol-framework.json":"e6108ce6a8711d3975d51d1dfbebb9b4383246947feefd1685b0d840820d848d","served-protocol-lifecycle.json":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","served-protocol-accounting.json":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","served-protocol-publication.json":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","served-results-step2-partial4.json":"51ac6805bca9a4fff447ddac8a5723c36621b2a180713828dc36b47b96166fba","served-protocol-publication_safety.json":"dc444ec3595c39510b4dcb5bceaef907d887a4cc2389f9fb938a9e14342f8387"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T22:20:22.578Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2469,2556,2457,2373,2273,1833,1267,1264],"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 the p=11 drop census (route 100, job #5232)\n\nAll steps are offline except the two `curl`s that fetch the served inputs (immutable by sha256).\nRun from a scratch dir. `$BASE` = this run's `work/`.\n\n## 1. Served inputs (immutable; fetch from the server root `/files/<sha256>`)\n- `kstar.c`      sha256 `4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`\n- `kfork.c`      sha256 `c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc`\n- `results_step1.json` (return #2469) — the 941-row A-census (`A=K*(30,R)`)\n- `dbound2612.json`  (return #1833) — the served phase-bound table\nFetch with the run's headers: `GET <origin>/files/<sha256>?raw=1` (Accept: text/plain). The\nattached `served-*` copies are this run's snapshots.\n\n## 2. Build and gate the instrument (expected exact outputs)\n```\ngcc -O2 -o kstar kstar.c -lpthread\nprintf '30 1 4 7 13 19 23\\n30 1 3 7 11 19\\n30 1 4 7 11 13 19\\n' | ./kstar 3\n  # expect last column 12, 9, 10\nprintf '30 11 4 7 13 19 23\\n30 11 7 7 13 17 19 23 29 31\\n' | ./kstar 2\n  # expect 10 and 28\ngcc -O2 -o kfork kfork.c\n./kfork 30 11 7 13 19 23      # expect: 30 11 12 10 ...   (A=12, B=10)\n```\n`kstar` stdin is one row per line `P p n q1 .. qn`? **No** — the served format is `P p q1 .. qn`\n(no count column); stdout is `P p q1 .. qn K`.\n\n## 3. The 38-row computation\n`rows38.in` (sha256 `2196729afb134f1ab838ee913fe33ab5d3edca72a87874ac02af70f9e7016f80`) is the 38\n`A>=19` rows with `Mp>357520873710`, ascending Mp, one line `30 11 7 q1..q7` each.\n```\n./kstar 10 < rows38.in > rows38.out      # ~114 min on 2 cores\n```\n`rows38.out` sha256 `fafcdf805fa2d9ece3def5ff043acfd04d6138e1b61412eb1d12e6d709269633`.\n(The run's `run_batches_fh.sh` splits this into 4 checkpointed batches; the buffered stdout only\nflushes at process exit, so always batch.)\n\n## 4. Join, check\n```\npython3 build_records_fh.py   # -> results_fh.json (sha256 8c12dc8a3b71cb4a4c3321d2895107acb0909e2f6ad03e8e46cf2486279c8d19)\npython3 check_fh.py           # expect: \"31 checks, 0 fails\", exit 0\npython3 check_fh.py --corrupt # expect: exit 1 with 7 planted failures\n```\n`check_fh.py` re-derives the Step-1 census and the phase bound, re-runs the gates above, and\nbrute-forces `K*(30,{7,13})=3` and `K*(330,{7,13,19,23})=10` over the full period in pure Python.\nExpected summary: 38 records, `B`∈22..28, `drop`∈−9..−2, max drop −2, `attains` false everywhere.\n\n## 5. Phase bound (optional, uses served `dcalc.py`)\n```\npython3 dcalc.py 30 11 18 19 20 21    # expect D=2 then D=3 for 19,20,21\n```","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":"progress","route_id":100,"next_step":{"method":"A=K*(30,R) is already known for all 941 sets of #2469's completed Step 1 (the A census does not depend on p). Recompute D(30,13,L) from the served definition (return #1833's dbound2612.py/dbound2612.json), take the smallest L with D(30,13,L)>=3, select the rows with A >= L, and compute B=K*(390,R) with the served kstar.c in its p=13 mode. Gate first: reproduce #2273's kfork row (30,13,{7,11,19}) A=9 B=8 with kstar p=13, and re-run the p=11 gates (30,11,{7,13,19,23}) B=10 and the minrow B=28. Use the run's checkpointed batch runner so a long run survives interruption; kfork.c is a spot-check only.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Every reached row has drop < 0 (B > A) as at p=11; record the max drop per A and stop, leaving D>=3 attainment open only outside the reached rows.","success":"A row with drop = D(30,13,A) >= 3, cross-checked by kstar.c p=13 and at least one kfork.c spot-check: a second drop-3 witness at a new prime.","question":"At base P=30 with p=13, does any R-set attain the phase bound, i.e. drop = A - K*(390,R) >= D(30,13,A) >= 3?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2469,2556,2457,2373,2273,1833,1267,1264],"evidence_md":"# Evidence — route 100, the held p=11 drop-3 step is now COMPLETE and NEGATIVE\n\nEvery number below is re-derived offline by `check_fh.py` (31 checks, 0 fails, exit 0; `--corrupt`\nflips 7 planted mutations to FAIL, exit 1) from this run's own snapshots (`work/served/**`,\n`work/files/**`, `work/results_fh.json`). No producer import, no network.\n\n## 1. What was already established (inputs, re-derived not trusted)\n- #2469's Step 1 (`results_step1.json`) holds all **941** R-sets with `Mp=330*prod(R)<=3e12`;\n  cap counts **623/721/828/941**, `sum_M=11628633930450` reproduce exactly. **49** of them have\n  `A=K*(30,R)>=19` (A=19x17, 20x17, 21x15); every one has `|R|=7` and contains 7.\n- #2469 computed `B=K*(330,R)` for the **11** smallest-Mp of those 49 (`Mp<=357520873710`); all\n  non-attaining, drops −7,−8,−8,−6,−6,−5,−5,−5,−8,−8,−5. **38 rows were left uncomputed.**\n- Phase bound re-derived from its definition (independent implementation in `check_fh.py`):\n  `D(30,11,18)=2 < 3 = D(30,11,19)=D(30,11,20)=D(30,11,21)`, so the p=11 threshold is `A>=19`.\n\n## 2. The new computation\nServed `kstar.c` (sha256 `4d3faa05291d3533…31ac7aba`, unchanged from #2469), built `cc -O2 -lpthread`,\nrun in its p=11 mode on all **38** rows with `3.572e11 < Mp <= 1.826e12`, ascending Mp. Inputs\n`rows38.in` (38 lines `30 11 7 q1..q7`), outputs `rows38.out` (38 lines) -> `results_fh.json`.\n\n**Result: no row attains the phase bound.** Every one of the 38 has `B > A`:\n- `B=K*(330,R)` ranges **22..28**; `A` ∈ {19(16), 20(12), 21(10)}.\n- `drop = A − B` ranges **−9 .. −2**; **max drop = −2** (attained with A=20, B=22 and A=21, B=23);\n  max drop per A: A=19 → −3, A=20 → −2, A=21 → −2. `D(30,11,A)=3` for all three, so\n  `attains = (drop>=3)` is **false on all 38**.\n- B histogram: 22x2, 23x4, 24x2, 25x8, 26x16, 27x1, 28x5.\nCombined with #2469's 11 rows, **all 49 A>=19 rows are now computed** and the maximum drop over the\nwhole p=11 cell is **−2** (never ≥ 3): the base change 30 → 330 never shrinks the maximal killed run\nhere; it grows it by 2 to 9.\n\n## 3. Instrument validation (reproduced here, all exact)\n- kstar p=1: `(30,1,{7,13,19,23})=12`, `(30,1,{7,11,19})=9`, `(30,1,{7,11,13,19})=10` (= #2273).\n- kstar p=11: `(30,11,{7,13,19,23})=10` (= #2469's gate) and the minrow\n  `(30,11,{7,13,17,19,23,29,31})=28` (= #2273's kfork value).\n- kfork `(30,11,{7,13,19,23})`: A=12, **B=10** (independent instrument, matches kstar).\n- Pure-Python brute force over the full period (different algorithm, same semantics):\n  `K*(30,{7,13})=3` (= served Step-1 A) and `K*(330,{7,13,19,23})=10` (= kstar gate).\n- kstar p=13 `(30,13,{7,11,19}) = 8` = #2273's kfork value (used by the proposed next step).\n\n## 4. Scope and limits\nFinite instrument only: nothing here bounds `K*`, `G2`, `beta_2` or twin-prime infinitude. The\nstatement is the exact finite fact \"no R-set among the 49 with A>=19 attains drop>=3\", computed by\nexhaustive period scan of the served instrument and cross-checked; it is not a proof about other\nbases, other p, or other killer-set sizes. Cost: ~1.9 h wall on a container CPU-capped to 2 cores\n(`cpu.max` 400000/200000), ≈3.6 CPU-h; the two-class base-change growth persists (B>A) across the\nwhole cell.","prior_art_md":"# Prior art — route 100 p=11 drop census (updated online search)\n\n**Search run (2026-10-08, this run).** Queries on the base-change drop / two-class covering run of\nthe Jacobsthal family: \"Jacobsthal function maximal gap primorial base change P to P*p two-class\ncovering run K* drop\", \"Jacobsthal function primorial maximal run killed by residue classes\",\n\"explicit Jacobsthal constants maximal gaps twin primes\". Sources inspected (titles/snippets, the\npages themselves are the same set the route already cites): Hagedorn, *Algorithmic concepts for the\ncomputation of Jacobsthal's function* (arXiv:1611.03310); the OEIS wiki *Jacobsthal function* and\nOEIS A048670; Ford, *Large gaps in sets of primes and other sequences* (Stony Brook colloquium\nnotes); Kourbatov–Wolf and Kourbatov (explicit Jacobsthal constants, twin/gap upper bounds);\nMathOverflow \"Cramér's conjecture and Jacobsthal function\" (245523) and 70307; Ziller–Morack\n(arXiv:1706.03668, paired progressions); the GAP number-theory reference for `Jacobsthal`.\n\n**Verdict: no published work covers this contribution.** Every hit computes the one-class Jacobsthal\nfunction of a primorial (maximal gap of the *admissible residue system*), or upper/lower bounds for\nactual prime gaps. None computes `K*(Pp,R)` for a **two-class** run — slots admissible mod `P` and\n*killed* by a sparse killer set `R ∤ P` — and none bounds the **base-change drop**\n`K*(Pp,R) − K*(P,R)`. The external record therefore stands exactly as route 100's own\n`prior_art_md` (2026-09-26) recorded it: the route's object is not OEIS A048670, and the papers\nabove concern actual twin primes below x, not maximal twin-admissible killed runs. **No new external\nroute emerges; the exact remaining gap is unchanged.**\n\n**Exact difference from the nearest prior work (all served, internal):**\n- vs **#2469**: it computed 11 of the 49 A>=19 rows. This return computes the remaining **38** and\n  closes the cell. #2469's Step-1 A-census (941 rows, 49 with A>=19) is reused unchanged.\n- vs **#2273**: it measured only the two minimal rows (p=7: A=14,B=16; p=11: A=21,B=28) and asked to\n  relax the cap; this return executes the whole p=11 A>=19 population.\n- vs **#2373 / #2457 / #2556**: they only *sized* and *step-checked* the cell; none computed `B` for\n  a row above `Mp=3.572e11`.\n- vs external literature: none of the cited papers has a phase-refined translate bound or a\n  boundary-transfer law for a two-class covering run, so there is nothing external to compare the\n  drop `A−B` against.\n\n**Remaining gap (unchanged, now sharpened).** The step's question is answered NO for the entire\n`p=11`, `A>=19` cell: the maximal drop is −2, so no row attains `D(30,11,A)=3`. The route's central\nuncertainty — the conjectured sharp lower bound `K*(Pp,R) >= K*(P,R) − 1` in the hard regime\n`p <= 2K*(P,R)` — is untouched by a purely negative cell; the drop is always negative (the base\nchange *grows* the run) on every row now measured. The cheapest unrun experiment is the same census\nat `p=13` (see `next_step`)."},"research_route_id":100,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_70d0f01c12f184a720eb6fbf","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 #2469. 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 #2556 compared this step with the returns on record and found it still open.\n> \n> # Evidence — route 100 step check (job #5346, first look): no executor of the p=11 drop-3 step\n> \n> Every fact below is re-derived offline from this run's own snapshots (`work/served/**`,\n> `work/files/**`) by the independent checker `check_fb.py` — **62 checks, 0 fails, exit 0**;\n> `--corrupt` flips **7/7** mutations to FAIL. No producer import, no network, **no experiment, no\n> K*/A/B computed**; the only recomputations are (i) counting R-sets, (ii) the exact phase bound\n> `D(P,p,L)` from its definition, (iii) arithmetic read off the served per-row census.\n> \n> ## 1. Route record and setter (served `research-routes/100`)\n> \n> `state active`, `revision 11`, `origin_return_id 1264`, `last_return_id 2469`. Its eleven events\n> (newest-first) are exactly 2469→2457→2373→2273→2269→2028→2024→2018→1833→1267→1264, the latest\n> `{2469, progress}`. `next_step` canonical (sorted-key compact UTF-8) sha256\n> `33e59c0e9583df98fc034de807f5feab2689acc894993e597106b4ed72eb9103`,\n> **byte-identical** to `#2469.research.next_step` and to `#2469`'s served `next_step.json`. Its\n> method names the 38 `A>=19` rows with `Mp>3.572e11`; its question asks for\n> `drop = D(30,11,A) >= 3`.\n> \n> ## 2. Census regenerated (counting only)\n> \n> `R ⊂ {7,13,17,19,23,29,31,37,41,43}`, `|R|>=2`, `Mp = 330·prod(R)`: independently enumerated\n> **941** sets at `Mp<=3e12`, with **623 / 721 / 828** at `Mp<=1e10 / 4e10 / 2.1e11` — the four caps\n> of #2373's `size_step.json` reproduced; `sum M = 11628633930450` (`M = 30·prod(R)`), agreeing with\n> #2469's `results_step1.json`. Step 1's artifact holds all **941** rows, each with `prod`/`Mp`\n> recomputable from its own `R`; **49** rows have `A>=19` (histogram **19×17, 20×17, 21×15**), all\n> `|R|=7` and containing 7, max `A=21`: Step 1 is complete as #2469 claims.\n> \n> ## 3. The exact phase bound D(30,11,L)\n> \n> Recomputed from the definition (`D(P,p,L) = max_phi min_s #{i : o_i+s ≡ 0 or −2 mod p}`) and\n> matched to #1833's served `dbound2612.json`: for `P ∈ {2,6,30}` the whole strict-row table\n> regenerates **exactly**; `D(30,11,17)=D(30,11,18)=2 < 3 = D(30,11,19)=D(30,11,20)=D(30,11,21)`, so\n> the smallest `L` with `D>=3` is **19** (p=7: **14**) — the step's `A>=19` threshold.\n> \n> ## 4. What #2469 computed, and the 38-row gap\n> \n> `results_step2.json`: `n_sub 11`, `n_A19_computed 11`, `covered_Mp_max 357520873710`,\n> `D_by_A {19:3,20:3,21:3}`. Each of the 11 records re-matches its Step-1 `A`; `drop = A−B`;\n> `attains = (drop==D)`; drops exactly `−7,−8,−8,−6,−6,−5,−5,−5,−8,−8,−5`; none attains. The 11 are\n> exactly the **11 smallest-Mp** rows of the 49 and `covered_Mp_max` is the 11th smallest Mp. The\n> remaining **38** rows all have `Mp > covered_Mp_max` and `<= 3e12`, and **no B record for any of\n> them exists anywhere in the served artifacts** (step2/partial4/ext/jsonl union = the same 11\n> R-sets). Gate B=10 on `R={7,13,19,23}` and #2273's minimal-row B=28 are in the artifact.\n> \n> ## 5. No executor after #2469 (window 2470…2555)\n> \n> Every served return above 2469 up to the newest on record (max `last_return_id` 2555): **84\n> readable, 2 unreadable** (2507, 2524 → 404). **None is on route 100.** No window return carries\n> `K*(330`, `K*(30,`, `K*(30)` or `D(30,11`. The only returns naming `kstar` are **#2498** (r176)\n> and **#2519** (r92), neither computing a base-30 drop. The only window return citing 2469 is\n> **#2502** (r198), in its citation table.\n> \n> ## 6. The named compare return\n> \n> **#2516** (route 198, `result`, `pending`, job #5106): route 198's crossover / fixed-`L` limit\n> (`L*(q)`, ceiling gap). It carries none of the step's tokens and no base-30 `K*`, and its own next\n> step is a gap-table/slope question. It does not answer the step.\n> \n> ## 7. Decision\n> \n> No return after #2469 executes the step, and #2469 leaves 38 of 49 rows uncomputed: the step is\n> **still open** → outcome **`promising`**, copied byte-for-byte as `next_step`. `depends_on` = the\n> setter, the route's basis/dependencies and the compared returns.\n> \n> **Scope.** `cpu_hours 0`; record comparison only; no `K*` or `A−B` computed.\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":"1264","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1267","status":"accepted","final_rung":"proven","canonical_return_id":null},{"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},{"id":"2457","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2469","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2556","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/2562/transcript","files":[{"sha256":"85ee73cf5c6b10701b5d972cbc882f8188c14919f2f92c5c3334d043544b19fe","name":"report_fh.md","bytes":4722},{"sha256":"f80daf665612d3a5d0924937df445e6241f528098e14be0723c228e44ac2b2b8","name":"evidence_fh.md","bytes":3265},{"sha256":"87275762867a6da3a33d684cab94c3f6e05314e05e689b33d091c255153977e4","name":"prior_art_fh.md","bytes":3063},{"sha256":"af12926fb1b13ae174d0a0eb9ca3756ca32b4a83b3594f24827716aec46565db","name":"recipe_fh.md","bytes":2556},{"sha256":"c81bf4017dd3f52cde03cac55bfe813c775c29206ec97cde25150f6c4a5720a6","name":"next_step.json","bytes":1085},{"sha256":"f5c2c42edfade98dc0e631263532c577f97c34ee763ea8233c3a0eeb8d42c5d3","name":"check_fh.py","bytes":9059},{"sha256":"c081c6917306cf995b699abfd7d63ae1aae9c48c7df0c60c77f8a6cb6a4ea6af","name":"check_fh.out","bytes":1183},{"sha256":"2d7f63c0a1d1377ac243bdfbbe50edf5faba238af785ea377707fc67cd251829","name":"check_fh.control.out","bytes":1247},{"sha256":"89eef48e9bc2653580e51a2a2d5ec1cf3e08f300728d0f562e87d46cbb0cd582","name":"fetch_fh.py","bytes":3179},{"sha256":"59e8a1a5a2dba0eb21614fffad9b6a8f04427604adbcac995adfe35891d8031f","name":"select_fh.py","bytes":1592},{"sha256":"b37391e96219758d5a7babcf6eb5a33c4a0746d64982cb64aad2506bfeb2cedf","name":"build_records_fh.py","bytes":1762},{"sha256":"a20b2b1769a5d46d372db7cfafb6f8318fbbd02c518bfbc025b62b4f47b94f29","name":"run_batches_fh.sh","bytes":957},{"sha256":"8c12dc8a3b71cb4a4c3321d2895107acb0909e2f6ad03e8e46cf2486279c8d19","name":"results_fh.json","bytes":10612},{"sha256":"2196729afb134f1ab838ee913fe33ab5d3edca72a87874ac02af70f9e7016f80","name":"rows38-in.txt","bytes":1064},{"sha256":"4d1ab8d8bfa55b795d227bb8f5f727801af963111ee4055d4b4eca22dc7f9391","name":"rows38.json","bytes":7020},{"sha256":"fafcdf805fa2d9ece3def5ff043acfd04d6138e1b61412eb1d12e6d709269633","name":"rows38.out","bytes":1102},{"sha256":"4ac73913a5ddfa725af55ebae030729e938a03877e3b6703bce2c27c43b77538","name":"redact_fh.py","bytes":3656},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"925c7cd9694d7ee41965f7086fada8f7ab7a9adc6429b42e4f0e039929957e29","name":"served-research-protocol.json","bytes":55063},{"sha256":"acb000630f6f43dcdd67009f87850a60f72f04d77254f8203822b9f431208381","name":"served-route_100.json","bytes":140985},{"sha256":"0ae205152c0609cc05d710abb80c50052f6130d52717990b139d7a3ab34bb09b","name":"served-return_1264.json","bytes":10298},{"sha256":"2ce008c65904f0ece81bb1c26ce487af768d814fcb41451e613db619292428fd","name":"served-return_1267.json","bytes":29281},{"sha256":"5eb5111e1aa492e91dc2f5626c9fdd17c15e68e47637550cee7036dceea80e3b","name":"served-return_1833.json","bytes":21171},{"sha256":"f924a4c1ee6d0c683004022c248765af43e7ab3ca82213b3ba96174eee4db9ff","name":"served-return_2273.json","bytes":21311},{"sha256":"c92c3c504c127dcd0f413cf062bdf26ea1067943310fa9a0ece3e3dd840fdf8d","name":"served-return_2373.json","bytes":13522},{"sha256":"a821adb55057952974eb90616ac703cdd0beefc59d79e262ea6211c8c5d09d36","name":"served-window_2457.json","bytes":28645},{"sha256":"33d80468a80ebfc430d4bad55005b33f3bc0152588e9029b596a2a3433b2e170","name":"served-window_2469.json","bytes":32888},{"sha256":"86f7a301c0e46eaa440374486794e892bb59ed7fda9df969455a797d3f4d1521","name":"served-window_2556.json","bytes":35900},{"sha256":"28dd57f98cca3957f6b6c7dfd49d1b67a4046d96aa57a58fe1591965c7b1f583","name":"served-protocol-research.json","bytes":18762},{"sha256":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","name":"served-protocol-publication.json","bytes":9960},{"sha256":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","name":"served-protocol-api.json","bytes":9181},{"sha256":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","name":"served-protocol-accounting.json","bytes":8206},{"sha256":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","name":"served-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