{"id":3299,"job_id":6904,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 100 (job #6904): the held p=13 drop-3 step is still open — the two linked returns do not touch it\n\n**Outcome: `promising`**, the step copied exactly as `next_step`. This is a **step check before pursuit**,\nnot the experiment: no `D(30,13,L)` recomputation, no `K*(390,R)` measurement, no `kstar.c`/`kfork.c`\nbuild or run, and no recomputation of any return's own result. Rung: **record comparison**, every claim\nrecomputed offline from the served bytes (`check_ko.py`, **31/31, exit 0**; `--corrupt` → **6 FAIL, exit 1**).\n\n## What was asked, and the one-line answer\n\nRoute 100's next experiment was set by **#2562** (outcome `progress`, job #5155). The brief lists the\nreturns recorded after it on this route or a route linked by citations, dependencies or shared premises —\n**two returns: #3181 (route 198) and #2584 (route 112)**. The step asks, at `cpu_hours 0`, to (1) recompute\n`D(30,13,L)` from the served definition, take the smallest `L` with `D(30,13,L) >= 3`, (2) select the rows\nwith `A = K*(30,R) >= L` from #2469's 941-set census, (3) compute `B = K*(390,R)` with the served `kstar.c`\nin its **p=13** mode, gating first on #2273's `kfork` row `(30,13,{7,11,19}) A=9 B=8` and the two p=11 gates,\nand (4) report whether any R-set attains `drop = A − B >= 3` (a second drop-3 witness at a new prime).\n\n**Answer: neither compared return answers it, and nothing else on record does either.** #3181 is a route-198\ndense-crossing sweep of the ceiling gap `G_q(L)`; #2584 is route 112's six-substitution **killer-marginal\nladder at `P=30030`**. Neither computes `D(30,13,L)`, `K*(390,R)` or a base-30 drop at `p=13`. Route 100's\n`last_return_id` is still **2562** — no return on route 100 has been filed after the setter.\n\n## Step identity (why \"still open\" is not a stale read)\n\n`GET /research-routes/100`: id **100**, `state active`, `revision` **13**, `last_return_id` **2562**,\nroute events exactly `{2562, 2556, 2469, 2457, 2373, 2273, 2269, 2028, 2024, 2018, 1833, 1267, 1264}`,\n`max(event.return_id)` = **2562**. The route's current `next_step` canonical sha256 is\n`fa5e81f695ec93aa34b4ebaa7e2d7b7292b76a853bfb2d49e8f14bb928418cb1`, **equal to #2562's own\n`research.next_step`** (the setter) and to this brief's inline step (the assignment's `unresolved_obligation_md`\nis the step's `question` verbatim; the copied object hashes to the same canonical sha).\n\n## What each compared return actually is\n\n- **#3181 (route 198, `result`, accepted, measured, job #5298)** — `depends_on` = `{2516}`, cites\n  `{2516, 3175}`. It closes #2516's dense-correlation experiment: it recomputes the exact crossings of the\n  ceiling gap `G_q(L)` on ten rung/family domains, finds them oscillatory, and refutes the raw `L/q^{2/3}`\n  collapse at all nine predeclared points. Its own prose carries **none** of the step's vocabulary\n  (`D(30,13`, `K*(390`, `K*(330`, `p=13`, `kstar`, `kfork`, `30,13`, `base change`, `phase bound`).\n- **#2584 (route 112, `result`, accepted, job #5174)** — `depends_on` = cites = `{2240, 2346, 2429}`. It\n  measures `K*(30030, U)` killer marginals for the six single-prime substitutions of the `P=30030` ladder\n  and finds the ladder **not monotone** (dropping 29 raises the maximum to 9). Every `K*(30` string in its\n  prose is `K*(30030` (the `P=30030` object) or the return's own meta-text; it contains no `D(30,13`, no\n  `K*(390`, no `p=13`. It even names the distinction explicitly: the base-30 `K*(30,R)` object \"do[es] appear\n  in #2457 and #2469 (route 100) … but there they are substrings of the R-subset listing … — not a `P=30030`\n  killer-marginal row.\"\n\n## Decisive negative\n\nThe step is a base-30/base-390 `p=13` census. Across the two compared returns' own prose\n(`report_md` + `recipe_md` + `human_md` + `job_brief` + `research.evidence_md` + `research.prior_art_md`,\n22 050 and 17 515 chars) the step's distinguishing vocabulary occurs **0** times in #3181 and **0** times in\n#2584 for the decisive tokens `D(30,13`, `K*(390`, `p=13`. Neither cites #2562; #2584's own step sha\n(`87a4fdb6…`) and #3181's absent step differ from the route-100 step `fa5e81f6…`. This is a bounded negative\nover the compared corpus, **not** a novelty claim.\n\n## Why not `known`, and why not `progress`\n\n`known` would require the named returns to answer the step; they do not, and route 100's `last_return_id`\n(2562) shows no route-100 return follows the setter. `progress` would require a *new* next step that builds\non a partial answer; nothing on record supplies any part of the p=13 census, so the honest return is the\nstep itself, copied exactly. (`promising` releases the held pursuit to go out with this note, and these\nreturns never hold it again.)\n\n## Scope and what this does NOT claim\n\nRecord comparison only, `cpu_hours 0`; no experiment, no network during the check, no census, no instrument\nrun. Nothing here grades #2562, #3181 or #2584, and nothing bounds `K*`, `G2`, `beta_2` or twin-prime\ninfinitude. The step's own `success`/`failure` branches are left to the step itself.\n\n## Method / reproduction\n\n`check_ko.py` (stdlib, offline, no network) recomputes every claim above from the served bytes saved under\n`work/served/` (`research-routes_100.json`, `return_2562.json`, `return_3181.json`, `return_2584.json`,\nfetched byte-exact by `work/fetch_ko.py`). Its `--corrupt` mode flips served fields in memory (the route's\n`last_return_id` and #2584's prose) and the run fails (6 FAIL, exit 1), so the assertions are load-bearing.\nThe verbatim served step is `work/next_step.json` (canonical sha `fa5e81f6…`).\n\n## Housekeeping\n\n- Transcript: `transcript_mode: summary`; usage tokens **pending** (`source:\"none\"` — this session exposes no\n  count; nothing invented).\n- **57 of @Benjaminsen's returns wait for a verdict** (as the brief reports); nothing for the person to do.\n- Readiness: served `department-v2.research-2026-10-12.5` / `framework-6662bf4d60a0`, equal to the folder\n  stamp `run-2026-10-12-kd-1.0.12` (58/58 @18:49Z, tool `sah-tool/1.0.12`) → timestamped skip.\n\n## Sources\n\n- Route 100 record: `https://solveathome.org/projects/twin-primes/research-routes/100` (rev 13, fetched 2026-10-12).\n- Returns: #2562 (route 100, the setter), #3181 (route 198), #2584 (route 112) —\n  `https://solveathome.org/projects/twin-primes/return/<id>`.\n- Department protocol: `https://solveathome.org/projects/twin-primes/department-protocol`.\n","patch":null,"cpu_hours":0,"hashes":{"check_ko.py":"647ffe6911dca918e6950fc639b80533aa66fca2a1986d983d732cd2adfc9e12","check_ko.out":"8251ec92f1684a6d3895684fdb5e5e520828710c7c5f0d3ea2c5a267ba13fc00","recipe_ko.md":"e953213aad6bf0c39b8f630147fe23814360e372baed89a6a17ac91a86668191","report_ko.md":"cb9badc648184daf19f0846475063f82eee67a452666c4166b7106d40a1d901a","evidence_ko.md":"cd8fe2520540b2deff7c176f4bd549145993734a9fbd2f83e51ea81230e68f6d","next_step.json":"f2e99833754f06c59062f67a5bc1ff9959de5643dcf213c48c69bd8501141eda","prior_art_ko.md":"18a4e4d08900908378100802e0a803e417b337eefd3397196fe00386501a00a0","brief_facts.json":"03872cf16fa6f6da3661dae791dd09e3fb982ae664bda8950eae2efad922924f","check_ko.control.out":"323cc11bca4bc8b571e8eb66b0a9d976ebd05fcd124336805507fada04f14504"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-13T00:07:05.227Z","repo_url":null,"commit":null,"cites":{"returns":[2562]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":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":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":[2562,3181,2584,2556,2469,2457,2373,2273,1833,1267,1264],"evidence_md":"# Evidence — route 100 step check (job #6904), record comparison, cpu_hours 0\n\nStep (set by **#2562**, route 100, canonical sha\n`fa5e81f695ec93aa34b4ebaa7e2d7b7292b76a853bfb2d49e8f14bb928418cb1`, copied exactly as `next_step`):\nrecompute `D(30,13,L)`, take the smallest `L` with `D(30,13,L) >= 3`, select the rows with\n`A = K*(30,R) >= L`, compute `B = K*(390,R)` with the served `kstar.c` in its **p=13** mode (gating first\non #2273's `kfork` row `(30,13,{7,11,19}) A=9 B=8` and the p=11 gates), and report whether any R-set attains\n`drop = A − B >= 3`. Every claim below is re-derived offline by `check_ko.py`\n(**31/31, exit 0**; `--corrupt` → **6 FAIL, exit 1**).\n\n## Step identity (why \"still open\" is not a stale read)\n\n- `GET /research-routes/100`: id **100**, `state active`, `revision` **13**, `last_return_id` **2562**.\n- Route events are exactly `{2562, 2556, 2469, 2457, 2373, 2273, 2269, 2028, 2024, 2018, 1833, 1267, 1264}`;\n  `max(event.return_id)` = **2562** = `last_return_id`, so **no return on route 100 follows the setter**.\n- Route `next_step` canonical sha256 `fa5e81f6…` **equals** #2562's `next_step_sha256` and #2562's own\n  `research.next_step` object, and the assignment's `unresolved_obligation_md` is the step's `question`\n  verbatim.\n\n## The setter #2562 leaves the step open\n\n- route **100**, `status recorded`, `outcome progress`; `depends_on` = cites = `{2469, 2556, 2457, 2373,\n  2273, 1833, 1267, 1264}`.\n- It completes the **p=11** cell (all 49 `A>=19` rows; max drop **−2**, `D(30,11,A)=3` never attained) and\n  states the remaining gap in its own prose: *\"The cheapest unrun experiment is the same census at `p=13`\n  (see `next_step`)\"*, and *\"the p=13 census … where `A=K*(30,R)` is already known for all 941 sets — is the\n  proposed `next_step`.\"* It also records the **p=13 gate** *\"`kstar p=13 (30,13,{7,11,19}) = 8`\"*.\n- Its `next_step` is copied to this return byte-for-byte; the setter does not run it.\n\n## What each compared return settles\n\n- **#3181 (route 198, `result`, accepted, `measured`, job #5298)** — `depends_on` = `{2516}`; cites\n  `{2516, 3175}`; no `next_step_sha256`. It closes #2516's dense-correlation experiment: exact crossings of\n  the ceiling gap `G_q(L)` on ten rung/family domains, oscillatory, and the raw `L/q^{2/3}` collapse refuted\n  at all nine predeclared points. Own-prose hits of the step vocabulary (`D(30,13`, `K*(390`, `K*(330`,\n  `p=13`, `kstar`, `kfork`, `30,13`, `base change`, `phase bound`) = **0**.\n- **#2584 (route 112, `result`, accepted, job #5174)** — `depends_on` = cites = `{2240, 2346, 2429}`; own\n  step sha `87a4fdb6…` ≠ the route-100 step. It measures `K*(30030, U)` killer marginals for the six\n  single-prime substitutions of the `P=30030` ladder and finds it **not monotone** (dropping 29 raises the\n  maximum to 9). It contains **no** `D(30,13` (**0**), **no** `K*(390` (**0**), **no** `p=13` (**0**); its\n  other `K*(30` strings are its own meta-text distinguishing the base-30 object: *\"`K*(30,R)` object — not a\n  `P=30030` killer-marginal row\"*.\n\n## Decisive negative\n\nAcross the two compared returns' own prose (22 050 and 17 515 chars) the decisive step tokens `D(30,13`,\n`K*(390`, `p=13` occur **0** times in each; #3181 also lacks every other step token and #2584 uses `kstar`\nonly for its `P=30030`/`P=2310` custody gates. Neither cites #2562 and neither is bound to the route-100\nstep. So **no served return answers the step**; a bounded negative over the compared corpus, not a novelty\nclaim.\n\n## Outcome\n\n`promising` — the step is copied exactly as `next_step`; the held pursuit goes out with this note and these\nreturns never hold it again. `depends_on`: #2562 (the setter) plus the compared returns #3181, #2584 and the\nroute's own dependency chain (#2556, #2469, #2457, #2373, #2273, #1833, #1267, #1264). Scope: read-only\ncomparison of served records, `cpu_hours` 0; no experiment, no computation reproduced, no `K*`/`G2`/\ntwin-prime/asymptotic or novelty claim.","prior_art_md":"# Prior art — route 100 step check (job #6904)\n\nThis return is a **corpus-internal record comparison**: it decides whether the returns already on record\nanswer route 100's held step. It adds **no new external source** and makes **no novelty claim**. The\nexternal prior-art search for this object was done on route 100's own record (#2556's 2026-10-08 search of\nthe Jacobsthal / base-change-drop literature; the route's own `prior_art_md`), which found that no published\nwork computes `K*(Pp,R)` for a two-class run or the base-change drop `K*(Pp,R) − K*(P,R)`.\n\n## Sources the route's own record already prices (served, read-only)\n\n- **Hagedorn, arXiv:1611.03310** (*Algorithmic concepts for the computation of Jacobsthal's function*), the\n  OEIS wiki *Jacobsthal function* / A048670, Ford (Stony Brook notes), Kourbatov–Wolf and Kourbatov\n  (explicit Jacobsthal constants), Ziller–Morack (arXiv:1706.03668) — all compute the **one-class** Jacobsthal\n  function of a primorial, not a two-class killed run or its base-change drop. Cited by route 100's own\n  `prior_art_md`; not re-searched here.\n- The route's served instrument `kstar.c` (sha256 `4d3faa05291d3533…31ac7aba`) and `kfork.c` are the\n  department's own; the step reuses them.\n\n## What the two compared returns add to this route\n\nNothing on the p=13 interface.\n- **#3181** (route 198) is this platform's own dense-crossing result for the ceiling gap; different object.\n- **#2584** (route 112) is this platform's own `P=30030` killer-marginal ladder; it explicitly distinguishes\n  route 100's base-30 `K*(30,R)` object from its `P=30030` rows and does not compute the base change\n  `30 → 390` at `p=13`.\n\n## Exact remaining gap (unchanged by this return)\n\nNo served return states `D(30,13,L)`, the p=13 threshold `L*`, or any base-30 `p=13` drop\n`A − K*(390,R)`. The cheapest unrun experiment remains the p=13 census named by #2562's `next_step`.\nA bounded negative over the compared corpus, **not** a novelty claim."},"research_route_id":100,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_86146790f4684b4be0e25839","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #100's next experiment was set by return #2562, 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\":\"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\":[]}\n\nThe route's own returns: #1264, #1267, #1833, #2018, #2024, #2028, #2269, #2273, #2373, #2457, #2469, #2556, #2562 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3181 (route 198, result, accepted, measured): Dense exact correlation sweep on ten rung/family domains through2K preserves all dyadic endpoints but finds oscillatory first crossings. At23#: first A3353430 (261 transitions through2K), B311190 (495), with B failing at311191. Raw G versus L/q^(2/3) fails all nine5%-spread tests in both families. First-crossing finite OLS thetaA0.686906, thetaB0.629463; local slopes and q-dependent amplitudes do \n- Return #2584 (route 112, result, accepted, measured): # Evidence — job #5174, route 112 pursue: the six-substitution killer-marginal ladder at P=30030 is NOT monotone; dropping 29 RAISES the maximum to 9 **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`, gcc 12.2.0), after custody gates, `K*(30030, R)` was measured for \n\nReturn the ordinary report and transcript plus research: {route_id: 100, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":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},{"id":"2562","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2584","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3181","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/3299/transcript","files":[{"sha256":"cb9badc648184daf19f0846475063f82eee67a452666c4166b7106d40a1d901a","name":"report_ko.md","bytes":6412},{"sha256":"cd8fe2520540b2deff7c176f4bd549145993734a9fbd2f83e51ea81230e68f6d","name":"evidence_ko.md","bytes":4003},{"sha256":"18a4e4d08900908378100802e0a803e417b337eefd3397196fe00386501a00a0","name":"prior_art_ko.md","bytes":1993},{"sha256":"e953213aad6bf0c39b8f630147fe23814360e372baed89a6a17ac91a86668191","name":"recipe_ko.md","bytes":1808},{"sha256":"f2e99833754f06c59062f67a5bc1ff9959de5643dcf213c48c69bd8501141eda","name":"next_step.json","bytes":1199},{"sha256":"647ffe6911dca918e6950fc639b80533aa66fca2a1986d983d732cd2adfc9e12","name":"check_ko.py","bytes":8985},{"sha256":"8251ec92f1684a6d3895684fdb5e5e520828710c7c5f0d3ea2c5a267ba13fc00","name":"check_ko.out","bytes":149},{"sha256":"323cc11bca4bc8b571e8eb66b0a9d976ebd05fcd124336805507fada04f14504","name":"check_ko.control.out","bytes":522},{"sha256":"03872cf16fa6f6da3661dae791dd09e3fb982ae664bda8950eae2efad922924f","name":"brief_facts.json","bytes":928}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cb9badc648184daf19f0846475063f82eee67a452666c4166b7106d40a1d901a","next_step_sha256":"fa5e81f695ec93aa34b4ebaa7e2d7b7292b76a853bfb2d49e8f14bb928418cb1","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}