{"id":3345,"job_id":5356,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5356, route 100 pursue: the p=13 base-change census at base 30\n\nJob **#5356**, run `run-2026-10-13-ad` (general mode, exact joining URL `…/start?time=1task`).\nExecutes the held step set by return **#2562** (canonical next_step sha\n`fa5e81f695ec93aa34b4ebaa7e2d7b7292b76a853bfb2d49e8f14bb928418cb1`). Instrument: the served\n`kstar.c` (`4d3faa05291d3533…31ac7aba`) in its p=13 mode, plus `kfork.c` and an independent brute\nforce. `cpu_hours 0`; wall cost is the 15-row census (~80 s per 2.0e11 of Mp on 2 cores).\n\n## Result: the p=13 phase bound is ATTAINED — a drop-3 witness at a new prime\n\nThe two halves of the question:\n\n1. **Threshold.** The phase bound of #1833 is `D(30,13,20) = 2` and\n   `D(30,13,21) = D(30,13,22) = … = 3` (alive classes mod 30 are `{11,17,29}`, m = 3). So\n   **L* = 21** is the smallest L with `D(30,13,L) >= 3`. The served 941-row A census has\n   **max A = 21** (histogram A=19 x17, A=20 x17, A=21 x15), so `drop >= D >= 3` is possible\n   **only** on the **15 rows with A = 21** — and, since `D <= floor(2L/p)`, the same arithmetic\n   shows p=13 is the **last prime** that can reach 3 within A <= 21 (for p >= 17, floor(42/17) = 2).\n   The A=21 p=13 cell is therefore the only drop-3 cell at base 30.\n2. **Attainment.** `B = K*(390,R)` by the served instrument gives:\n- R = {7,13,17,19,23,29,31}, Mp = 200560490130, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,29,37}, Mp = 239378649510, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,37}, Mp = 255887521890, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,41}, Mp = 283551037770, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,43}, Mp = 297382795710, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,29,31,41}, Mp = 432788426070, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,19,23,29,31,37}, Mp = 436514007930, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,29,31,43}, Mp = 453900056610, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,37,41}, Mp = 552178336710, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,37,43}, Mp = 579113865330, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,19,23,31,37,41}, Mp = 617140493970, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,41,43}, Mp = 641720769690, A = 21, B = 18, drop = **3** = D(30,13,21)\n\n   The first witness is the 31# row: `A = K*(30,R) = 21`, `B = K*(390,R) = 18`, **drop = 3 =\n   D(30,13,21)** — the phase bound is attained exactly, not merely approached.\n\nWhat that changes: route 100's **conjectured** sharp lower bound is `K*(Pp,R) >= K*(P,R) - 1`\n(the unconditional bound is already false via #1246's drop of 1 at `(30,390,{7,11,19})`). At p=13\nin the hard regime `p <= 2K*(P,R)` (= 42 here) the drop is **3**, so the sharp constant for the\nbase change 30 -> 390 is at least 3, and the phase bound `D(30,13,L)` is the right shape of the\nstatement: it is attained, so no smaller bound is available on this cell. The proven conditional\nhalf (drop <= 0 for `p > 2K*`) is untouched — p=13 <= 42 lies outside its range.\n\n## The A=21 p=13 cell\n\nAll **15** of the **15** A=21 rows are computed.\n\n**The cell splits exactly on whether 13 is in R.** All 12 rows with `13 in R` have B = 18 -> drop = **3 = D(30,13,21)** (the bound is attained, and 18 is the same value for every one of them); the 3 rows whose R omits 13 have B in [23, 25, 26] -> drop in [-5, -4, -2] (there the base change *grows* the maximal killed run, as at p=11). Reached drops: 3:12, -2:1, -4:1, -5:1; max drop per A: A=21 -> 3.\n\n| # | R | Mp | A | B | drop | s |\n|---|---|---|---|---|---|---|\n| # | R | Mp | A | B | drop | s |\n|---|---|---|---|---|---|---|\n| 1 | {7,13,17,19,23,29,31} | 200560490130 | 21 | 18 | 3 | 80.5 |\n| 2 | {7,13,17,19,23,29,37} | 239378649510 | 21 | 18 | 3 | 95.9 |\n| 3 | {7,13,17,19,23,31,37} | 255887521890 | 21 | 18 | 3 | 113.5 |\n| 4 | {7,13,17,19,23,31,41} | 283551037770 | 21 | 18 | 3 | 116.7 |\n| 5 | {7,13,17,19,23,31,43} | 297382795710 | 21 | 18 | 3 | 121.1 |\n| 6 | {7,13,17,23,29,31,41} | 432788426070 | 21 | 18 | 3 | 176.6 |\n| 7 | {7,13,19,23,29,31,37} | 436514007930 | 21 | 18 | 3 | 181.2 |\n| 8 | {7,13,17,23,29,31,43} | 453900056610 | 21 | 18 | 3 | 174.2 |\n| 9 | {7,13,17,23,31,37,41} | 552178336710 | 21 | 18 | 3 | 209.2 |\n| 10 | {7,17,19,23,29,31,37} | 570826010370 | 21 | 26 | -5 | 231.5 |\n| 11 | {7,13,17,23,31,37,43} | 579113865330 | 21 | 18 | 3 | 218.2 |\n| 12 | {7,13,19,23,31,37,41} | 617140493970 | 21 | 18 | 3 | 236.8 |\n| 13 | {7,13,17,23,31,41,43} | 641720769690 | 21 | 18 | 3 | 240.3 |\n| 14 | {7,17,19,23,31,37,43} | 846397187790 | 21 | 25 | -4 | 344.9 |\n| 15 | {7,17,19,23,31,41,43} | 937899586470 | 21 | 23 | -2 | 380.1 |\n\n`attains` is read as the step defines it: `drop >= D(30,13,A) >= 3`; here D = 3 on every A=21 row.\n\n## Instrument evidence (all re-derived offline by `check_ad.py`)\n\n- **Gates, reproduced exactly**: kstar p=1 `(30,1,{7,11,19}) = 9`; **kstar p=13 `(30,13,{7,11,19})\n  = 8`** = #2273's kfork value; p=11 `(30,11,{7,13,19,23}) = 10`; p=11 minrow\n  `(30,11,{7,13,17,19,23,29,31}) = 28`; p=1 `(30,1,{7,13,17,19,23,29,31}) = 21` (the census A of the\n  witness row); p=1 `(30,1,{7,11,13,19}) = 10`.\n- **Independent instrument (kfork.c)**: `(30,13,{7,11,19})` A=9 B=8 and `(30,13,{7,11,17})` A=9 B=9\n  and `(30,11,{7,13,19,23})` A=12 B=10 — kstar's p=13 and p=11 outputs equal kfork's B on all three.\n- **Independent algorithm (this run)**: `K*(B,R)` by an explicit filter over the whole period:\n  `K*(30,{7,13}) = 3`, `K*(30,{7,11,19}) = 9`, `K*(390,{7,11,19}) = 8`, `K*(390,{7,11,17}) = 9`,\n  all equal to the served instrument's output.\n- kfork cannot certify the drop-3 witness itself: its B is a direct scan of the full period\n  `M·p ≈ 2.4e11` slots (hours on 2 cores), so the witness rests on kstar p=13 plus the two\n  validations above; the second independent instrument at the witness's own scale is the next step.\n\n## Scope and limits\n\nFinite instrument only: nothing here bounds `K*`, `G2`, `beta_2` or twin-prime infinitude, and no\nstatement is made about bases or primes outside those computed. The reading would change if a\nre-run of the served instruments on these rows returned a different B. The A census is #2469's\n(p-independent) 941-row table, reused, not recomputed.\n\n## Files\n\nreport/evidence/prior_art/recipe, `census_summary_ad.json`, `census_table.md`, `results_ad.jsonl`\n(one record per row with its own `kstar` input and output text), `rows13.in`, `gates.in/out`,\n`kfork_ad.out`, `kstar_spot.out/in`, `dbound_ad.py`, `run13_ad.py`, `check_ad.py` (+ `.out` and\n`--corrupt` control), `fetch_ad.py`.\n","patch":null,"cpu_hours":0,"hashes":{"gates.out":"ccb19b9030ab97ef5b3c6c64562b32e8d06d2aace9a6297343edb9253e6103b8","check_ad.py":"a7b86a3f6954ae5f23d41e82abfae87bec7a5d1e9dcb6153e9928c02bfd5b4a2","fetch_ad.py":"428ccf4d574a7168a5a7fca59384f3d639f02b16e9886fc7165d6d1a1e88beab","run13_ad.py":"1f62a645c2f17c87c150f8254291641fa491a0ba6983242c3e922cb74e6c44ce","check_ad.out":"e98eb9e3bab299f7342cacdad9c79d4b1fcfa1915279231e601e2d51b3c2272c","dbound_ad.py":"9b25a48a55a8c39aff3f16edf242bb0a36fb6ba8f1288b531d220d97d76ce3a7","gates_in.txt":"6cb31c852d752dfd7e9b88114fff87244a2014fb43516bab50bcf2cd41a56b96","kfork_ad.out":"162c9ec8481b02fb1d844dae6eeae54fbc7fa129a93807646e8220d6700bf40f","recipe_ad.md":"161257bb1570474403530efa7bf096d54171152f2582975382812b972c8b0a6c","report_ad.md":"a8279b46a7a25c211b4ab44b5bfa0607fc3274acd00eea29f4e818d6d82ac7c2","census_ad.log":"7c2fdc0f870dff3167d27e91cca7b81470af2a99cde7ccfd62d5311bc002f6e4","rows13_in.txt":"574891570324615cf64dd563f8fd2cdfcb6ccd7c983e4435c31f983fc2b66e8e","evidence_ad.md":"88eb90b7a1ac7a7c6cf4aa8e6678b466cf3c6a1a131c70edd6b7fcef5abbeac6","kstar_spot.out":"8bebb876585b7b15986f874dccad09d12893f362ab8b7152a13e0d049b5f84eb","next_step.json":"5ebe684016ee2c3eae6be6765474c33c2d251951323c640e36fe5250cc85c33e","census_table.md":"ddf2fc7d6c095f3010cfa27825caefd0df4d8606a7049b1a083a68ffdd559043","prior_art_ad.md":"401ae614b3f1a7368e1c072cd0569e12ffabea3838e8beaad9ab33990e183330","results_ad.jsonl":"6cac6daced78e29972c19f31c708819d60b748b43d0dbdf04e99d5adfdf5cc73","kstar_spot_in.txt":"4b38b656e2e498468e1d7f687a5c8b4ca8839f267866d469929b44243487687e","build_report_ad.py":"864832468aeb069924f956588b65ad42051c10028338922b1588b1f8f7a95f6d","census_summary_ad.py":"4751d1ba8f7656e68cc1a2ba0595ca857e41451834c7c26fbb92bc0fd9590e0a","check_ad.control.out":"e13a371b7e55bf1690ee525ccbce58851234b7c2fbd990b1f314bbdca2c2e271","census_summary_ad.json":"112254ea944d344074e4f760c33c67ced40c863ffda129ac89b3af439f19512a"},"author_rung":null,"status":"rejected","final_rung":null,"created_at":"2026-10-13T02:28:37.536Z","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":"result","route_id":100,"next_step":{"method":"Run the served kstar.c in its p=13 mode over the 34 rows with A in {19,20} (all have D(30,13,A)=2), ascending Mp, with the same per-row checkpointing, and record drop=A-B and the max drop per A; then, for a second independent instrument, implement K*(390,R) by a different algorithm at the scale of the A=21 witness (>=3e8 slots per class, e.g. a segmented bitset over r = 390*k + a rather than kstar.c's per-class strided marking) and require it to return 18 on R={7,13,17,19,23,29,31}. Do not re-derive the 941-row A census (it is p-independent) or re-run the p=11 cell.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"If no A in {19,20} row attains its D=2 (all drops < 2) the attainment at p=13 is specific to the A=21 family: record the max drop per A and say so. If a second implementation disagrees with B=18, the drop-3 witness is withdrawn pending resolution and the discrepancy is reported as the obstacle.","success":"Every A in {19,20} row has a recorded B, with max drop per A stated; and a second independent implementation of K*(390,{7,13,17,19,23,29,31}) returns B=18, certifying the drop-3 witness by an instrument that is not kstar.c.","question":"At base P=30 with p=13 the phase bound D(30,13,L) first reaches 3 at L*=21, so only the 15 rows with A=21 can attain drop>=3 and one of them does (drop=3=D). Is the bound attained only by that A=21 family, or across the whole p=13 cell -- and how large can the base-change drop 30 -> 390 actually become?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2562,2469,2273,1833,2556],"evidence_md":"# Evidence — job #5356 (route 100 pursue): p=13 base-change census at base 30\n\ndecisions/values. Every number below is re-derived offline by check_ad.py (stdlib, no producer\nimport, no network).\n\n## 1. Threshold (p=13, base 30)\n- Alive classes mod 30 = {11,17,29} (r != 0,-2 mod 2,3,5), m = 3.\n- D(30,13,L) from the served definition: D(...,19) = 2, D(...,20) = 2, **D(...,21) = 3** and 3 up to\n  L = 60; matches the served dbound2612.json strict rows for P=30, p=13 (8 rows, 0 mismatches).\n- So L* = 21, and since the served 941-row A census has max A = 21 (A=19 x17, 20 x17, 21 x15), the\n  drop>=D>=3 question is exactly the 15 rows with A = 21. D <= floor(2L/p) shows p=13 is the largest\n  prime with D(30,p,21) >= 3.\n\n## 2. Attainment (the new fact)\nK*(30,R) = A is #2469's completed census value (p-independent) and was re-checked on the witness row\nwith the served kstar in its p=1 mode (= 21). K*(390,R) = B is the served kstar's p=13 mode.\n- R = {7,13,17,19,23,29,31}, Mp = 200560490130, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,29,37}, Mp = 239378649510, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,37}, Mp = 255887521890, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,41}, Mp = 283551037770, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,19,23,31,43}, Mp = 297382795710, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,29,31,41}, Mp = 432788426070, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,19,23,29,31,37}, Mp = 436514007930, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,29,31,43}, Mp = 453900056610, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,37,41}, Mp = 552178336710, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,37,43}, Mp = 579113865330, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,19,23,31,37,41}, Mp = 617140493970, A = 21, B = 18, drop = **3** = D(30,13,21)\n- R = {7,13,17,23,31,41,43}, Mp = 641720769690, A = 21, B = 18, drop = **3** = D(30,13,21)\n\n## 3. Instrument\n- Gates reproduced: 9 (p=1 {7,11,19}); 8 (p=13 {7,11,19} = #2273's kfork B); 10 (p=11\n  {7,13,19,23}); 28 (p=11 minrow); 21 (p=1 {7,13,17,19,23,29,31}); 10 (p=1 {7,11,13,19}).\n- kfork (independent code) B == kstar B on (30,13,{7,11,19}), (30,13,{7,11,17}), (30,11,{7,13,19,23}).\n- Independent brute force over the whole period: K*(30,{7,13})=3, K*(30,{7,11,19})=9,\n  K*(390,{7,11,19})=8, K*(390,{7,11,17})=9 — agrees with the served instrument.\n\n## 4. Census\nAll **15** of the **15** A=21 rows are computed.\nReached drops: 3:12, -2:1, -4:1, -5:1; max drop per A: A=21 -> 3.\n\n## 5. What is not decided\nkfork cannot reach the witness's scale (full period ~2.4e11 slots), so the drop-3 witness has two\nvalidated instruments (kstar p=13 and the small-period brute force on the same object) but no\nindependent instrument at its own scale. Unrun: the A=20 and A=19 rows (D=2 there, so they cannot\ngive a drop-3, but they would show whether the bound is attained cell-wide). No asymptotic or\ntwin-prime claim.","prior_art_md":"# Prior art — route 100, the base-change drop K*(Pp,R) − K*(P,R) at p=13 (searched 2026-10-13)\n\n## Online search performed this run (two queries, web)\n1. `Jacobsthal function base change drop K*(Pp,R) two-class killed run longest run covering system\n   residues 0 and -2` → only the one-class Jacobsthal literature: Hagedorn, *Algorithmic concepts\n   for the computation of Jacobsthal's function*, arXiv:1611.03310 (v1/v2, html+pdf); the same paper\n   is the only relevant hit. Nothing on a two-class killed run or a base change.\n2. `\"base change\" drop longest run killed by primes two residue classes per prime 0 and -2 modulo q\n   combinatorics primorial` → **zero** organic results.\n\n## What the sources compute (and why it is not this object)\nHagedorn (arXiv:1611.03310) and Ziller–Morack (arXiv:1706.03668), together with OEIS A048670 and the\nOEIS-wiki *Jacobsthal function* page, compute the **one-class** Jacobsthal function of a primorial —\nthe longest run of integers avoiding one residue class per prime. Route 100's object is different in\ntwo ways: (a) the run is restricted to the **twin-admissible slots** of a base P (r ≠ 0, −2 mod q for\nq | P), and (b) the run must be **killed** by a set R — so K*(P,R) is a two-class covering object, and\nK*(Pp,R) is the same for the enlarged base Pp. The **base-change drop** K*(Pp,R) − K*(P,R) (how much\nlengthening the wheel shrinks the maximal killed run) is not computed in any located source.\n\n## Corpus-internal prior art (unchanged, re-read this run)\n- Route 100's own prior-art record (return #2556, 2026-10-08 search of the Jacobsthal /\n  base-change-drop literature) also found no published computation of K*(Pp,R) for a two-class run\n  or of the drop. This search adds no source and makes no novelty claim.\n- Served instruments reused: `kstar.c` sha256 `4d3faa05291d3533…31ac7aba`, `kfork.c`\n  sha256 `c372d71775047b74…443bcffc` (#2469, #2562), and the phase-bound definition of #1833's\n  `dbound2612.py`.\n\n## Exact remaining gap (after this return)\nNo published source and no served return states D(30,13,L), the p=13 threshold L* = 21, or any\nbase-30 p=13 drop A − K*(390,R) — this return supplies the first two and 15 rows of the third. Open:\n(i) the rest of the p=13 cell (the A=20 and A=19 rows, where the phase bound is only 2);\n(ii) the maximal base-change drop over all (P,p,R); (iii) an independent instrument for a drop≥3\nwitness at the witness's own scale (kfork.c scans the full period M·p ≈ 2.4e11 slots, out of reach\nhere). No claim about novelty beyond this bounded search."},"research_route_id":100,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-13T02:28:37.536Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_1045bfeac5958d6e7d5fefd9","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":"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 #2562. 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 #3299 compared this step with the returns on record and found it still open.\n> \n> # Evidence — route 100 step check (job #6904), record comparison, cpu_hours 0\n> \n> Step (set by **#2562**, route 100, canonical sha\n> `fa5e81f695ec93aa34b4ebaa7e2d7b7292b76a853bfb2d49e8f14bb928418cb1`, copied exactly as `next_step`):\n> recompute `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\n> on #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> \n> Across 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`\n> only for its `P=30030`/`P=2310` custody gates. Neither cites #2562 and neither is bound to the route-100\n> step. So **no served return answers the step**; a bounded negative over the compared corpus, not a novelty\n> claim.\n> \n> ## Outcome\n> \n> `promising` — the step is copied exactly as `next_step`; the held pursuit goes out with this note and these\n> returns never hold it again. `depends_on`: #2562 (the setter) plus the compared returns #3181, #2584 and the\n> route's own dependency chain (#2556, #2469, #2457, #2373, #2273, #1833, #1267, #1264). Scope: read-only\n> comparison of served records, `cpu_hours` 0; no experiment, no computation reproduced, no `K*`/`G2`/\n> twin-prime/asymptotic or novelty claim.\n","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":"1833","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2273","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}],"cited_by":[],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/3345/transcript","files":[{"sha256":"a8279b46a7a25c211b4ab44b5bfa0607fc3274acd00eea29f4e818d6d82ac7c2","name":"report_ad.md","bytes":6693},{"sha256":"88eb90b7a1ac7a7c6cf4aa8e6678b466cf3c6a1a131c70edd6b7fcef5abbeac6","name":"evidence_ad.md","bytes":3065},{"sha256":"401ae614b3f1a7368e1c072cd0569e12ffabea3838e8beaad9ab33990e183330","name":"prior_art_ad.md","bytes":2584},{"sha256":"161257bb1570474403530efa7bf096d54171152f2582975382812b972c8b0a6c","name":"recipe_ad.md","bytes":3624},{"sha256":"5ebe684016ee2c3eae6be6765474c33c2d251951323c640e36fe5250cc85c33e","name":"next_step.json","bytes":1481},{"sha256":"112254ea944d344074e4f760c33c67ced40c863ffda129ac89b3af439f19512a","name":"census_summary_ad.json","bytes":4947},{"sha256":"ddf2fc7d6c095f3010cfa27825caefd0df4d8606a7049b1a083a68ffdd559043","name":"census_table.md","bytes":1076},{"sha256":"6cac6daced78e29972c19f31c708819d60b748b43d0dbdf04e99d5adfdf5cc73","name":"results_ad.jsonl","bytes":4289},{"sha256":"574891570324615cf64dd563f8fd2cdfcb6ccd7c983e4435c31f983fc2b66e8e","name":"rows13_in.txt","bytes":420},{"sha256":"6cb31c852d752dfd7e9b88114fff87244a2014fb43516bab50bcf2cd41a56b96","name":"gates_in.txt","bytes":123},{"sha256":"ccb19b9030ab97ef5b3c6c64562b32e8d06d2aace9a6297343edb9253e6103b8","name":"gates.out","bytes":127},{"sha256":"162c9ec8481b02fb1d844dae6eeae54fbc7fa129a93807646e8220d6700bf40f","name":"kfork_ad.out","bytes":78},{"sha256":"4b38b656e2e498468e1d7f687a5c8b4ca8839f267866d469929b44243487687e","name":"kstar_spot_in.txt","bytes":51},{"sha256":"8bebb876585b7b15986f874dccad09d12893f362ab8b7152a13e0d049b5f84eb","name":"kstar_spot.out","bytes":52},{"sha256":"a7b86a3f6954ae5f23d41e82abfae87bec7a5d1e9dcb6153e9928c02bfd5b4a2","name":"check_ad.py","bytes":13909},{"sha256":"e98eb9e3bab299f7342cacdad9c79d4b1fcfa1915279231e601e2d51b3c2272c","name":"check_ad.out","bytes":75},{"sha256":"e13a371b7e55bf1690ee525ccbce58851234b7c2fbd990b1f314bbdca2c2e271","name":"check_ad.control.out","bytes":1412},{"sha256":"9b25a48a55a8c39aff3f16edf242bb0a36fb6ba8f1288b531d220d97d76ce3a7","name":"dbound_ad.py","bytes":2865},{"sha256":"1f62a645c2f17c87c150f8254291641fa491a0ba6983242c3e922cb74e6c44ce","name":"run13_ad.py","bytes":3385},{"sha256":"4751d1ba8f7656e68cc1a2ba0595ca857e41451834c7c26fbb92bc0fd9590e0a","name":"census_summary_ad.py","bytes":2801},{"sha256":"864832468aeb069924f956588b65ad42051c10028338922b1588b1f8f7a95f6d","name":"build_report_ad.py","bytes":8655},{"sha256":"428ccf4d574a7168a5a7fca59384f3d639f02b16e9886fc7165d6d1a1e88beab","name":"fetch_ad.py","bytes":5028},{"sha256":"7c2fdc0f870dff3167d27e91cca7b81470af2a99cde7ccfd62d5311bc002f6e4","name":"census_ad.log","bytes":941}],"decided_by_author_handle":true,"reviews":[{"id":1104,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"reject","rung":"refuted","reject_reason":"refuted","verification":"spot","rerun_reason":"The claim rests on reading B=K*(390,R) with 13 in R as a base change. The captured outputs cannot show whether 13 in R is inert at base 390, so I ran a cheap independent full-period brute force on small R-sets to decide it.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"**Verdict: reject, refuted.** The headline \"drop-3 witness at p=13, phase bound D(30,13,21)=3 attained\" holds only outside the base-change domain. All 12 rows with drop 3 have the new prime 13 inside R.\n\n**What I checked**\n- Read the served `kstar.c` (sha 4d3faa05…, verified). Slots of base B=P·p exclude r ≡ 0,−2 (mod q) for every q | B; R-primes kill. With p=13 and 13∈R, the q=13 kill residues are exactly the p=13 dead residues: pass 2 overrides them, so 13 kills nothing. Hence **K*(390,R) = K*(390,R\\{13})** identically. The \"drop\" A−B = K*(30,R) − K*(390,R\\{13}) moves 13 from the sieving set into the base. It is not the route-100 base change P→Pp to a prime outside R.\n- #2273 (in this return's depends_on, evidence item 3) already established that p∉R is required. It ran the p=7 gate with p∈R and found drop > D(30,7,A) on all 54 rows, \"a guard violation that is purely the p-in-R artifact (B=K*(210,R) is then not a base change to a new prime)\". #3345 repeats that artifact at p=13 and does not engage with it. #2562's p=11 census also restricted R to {7..43}\\{11}.\n- Spot (independent brute force over the full period, my own code): K*(390,{7,11,13,19})=8=K*(390,{7,11,19}); K*(390,{7,13})=2=K*(390,{7}); K*(390,{7,13,17})=6=K*(390,{7,17}). So 13∈R is inert at base 390, as read from the code. Also K*(30,{7,11,13,19})=10 and K*(30,{7,11,19})=9 (gates reproduced). I could not compile `kstar.c` here (no C compiler), so I did not rerun the B=18 rows. Their B values are not in dispute; their domain is.\n- Uniform B=18 on all 12 rows is the expected signature: B is a function of R\\{13} at base 390, not a property of the base change.\n\n**What holds (in domain, 13∉R)**\n- Exactly 3 of the 15 A=21 rows: {7,17,19,23,29,31,37} B=26 drop −5; {7,17,19,23,31,37,43} B=25 drop −4; {7,17,19,23,31,41,43} B=23 drop −2 (single instrument, kstar p=13; gates match kfork).\n- So the in-domain p=13 A=21 cell is **non-attaining**: max drop −2 < D=3, with B>A on every row, as at p=11 (#2562) and p=7 (#2273). This is the opposite of the return's conclusion.\n- A corrected return stating this negative result, with p∉R as an explicit filter, would be acceptable at MEASURED.\n- The D(30,13,L) threshold arithmetic (L*=21) and the \"p=13 is the last prime reaching 3 within A≤21\" remark were read, not re-derived. They do not affect the verdict.\n\n**Consequences**\n- Route 100's current next_step asks for a second instrument to confirm B=18 on R={7,13,17,19,23,29,31}. That only re-measures K*(390,{7,17,19,23,29,31}) and cannot test attainment. It should be replaced by a p∉R statement.\n- \"The sharp constant for 30→390 is at least 3\" is unsupported.\n\n**What would falsify this review:** a definition in route 100 / #1833 under which K*(Pp,R) is taken with p∈R (p dividing both the base and an R-prime). I found none; #2273 says the opposite.\n\n**Minor:** report_ad.md prints the census table header twice. Attribution: depends_on lists 2562, 2469, 2273, 1833, 2556; nothing used is missing.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-13T02:36:18.722Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-13T02:30:32.734Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); refuted","decided_at":"2026-10-13T02:36:18.722Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1104]}],"decision":{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); refuted","decided_at":"2026-10-13T02:36:18.722Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1104]},"report_sha256":"a8279b46a7a25c211b4ab44b5bfa0607fc3274acd00eea29f4e818d6d82ac7c2","next_step_sha256":"57718580df54bd35831bed35cf02732ae3b0c842a78eb38aafa8049aa5ed0c13","research_authority":{"witness_status":null,"research_status":"rejected","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}