{"id":1895,"job_id":4259,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4259 — step check on route 147's recorded next experiment\n\n**Verdict: `known`.** The returns on record already answer the step, and they answer the route's last\nlive ground negatively: on the 5,536-row slice the step names there is no drop at all — the new part is\n`d = A − B <= 0` throughout, the slice's served half carries the census's five drops (one of them the\nrecord's single `d = 2`), and the only `d = 2` row in the whole capped P=30 population sits in the\nalready-served window. The route stops here and the pursuit is not handed out. No experiment was run and\nno `A` or `B` value was computed in this pass.\n\n**Caveats first.**\n- No census was run and no `K*` value computed here. This check re-enumerates the step's own domain from\n  its stated predicates and checks inclusion, counts and the quoted bounds against the served record.\n- The decisive measurement is #1812 (route 117, author rung verified, review pending). Its scope is a\n  strict superset of the step's slice; it measures with its own instrument (`kstar.c`) and cross-checks\n  1,231 rows against #1804's independent `kfork.c`.\n- The served half of the slice is not rerun here; it is inside #1367's 15,747-row census.\n- One discrepancy is surfaced rather than smoothed over: the step's \"5,536 new rows\" includes 6\n  `|R| = 5` rows that are already in the served corpus (section \"Checked in this pass\", item 3).\n- Finite arithmetic only: nothing here is about `G_2`, `beta_2` or twin-prime infinitude.\n\n## The step (route 147 rev 4, set by #1621)\n\nFetch the pinned #1384 engine `8f958ae2…` and #1621's repair `207115f8…`; validate block-independence on\nsmall periods against a scalar oracle, with empty/all-true-block controls; enumerate `R ⊆ primes 7..97`,\n`|R| ∈ 3..5`, `p ∈ {7,11,13}\\R`, `2.5e7 < 30·prod(R)·p <= 3e8`; check the row count against the\npublished 5,536; then compute `A = K*(30,R)`, `B = K*(30p,R)` and report the exact `d = A − B` table,\nstratified by `(|R|,p)`, with every `d >= 2` witness. The route's case: `d >= 2` requires `p <= A`\n(#1267), which needs `A >= 7` with `p >= 7`, so only `P = 30` with `p ∈ {7,11,13}` can be\ndeficit-capable; that space is 7,736 rows and the 5,536 beyond the served census are the last live\nground for a second deficit.\n\n## The record, and what each return settles\n\n1. **#1267** (proven, accepted) — the necessary condition and the unique witness: `d <= floor(2A/p)`, so\n   `d >= 2` requires `p <= A`; its pair `(P,p,R) = (30, 11, {7,13,19,23})`, `A = 12`, `B = 10`, is a\n   `d = 2` row at `Mp = 1.31e7` — inside the served windows, hence **not** in the new slice.\n2. **#1367** (census, recorded) — the served half: 15,747 exact rows, 6 drops (five of size 1, one of\n   size 2 = #1267's pair), all with `p <= 2K*(P,R)`; the other 15,061 rows have minimum rise 0; `B <= A−3`\n   does not occur.\n3. **#1384** (measured, accepted) — closes the `|R| = 5` class at P=30: its reachable set is exactly the\n   12 rows served with #1365 (checked below). Also the return whose re-scoped step #1516 answered.\n4. **#1516** (recorded) — the step's own population and price: 7,736 rows, 2,200 inside the served\n   window, 5,536 beyond it; and its `p <= A` filter empties every re-scoped `P >= 210` cell.\n5. **#1804** (verified, accepted) — an independent instrument and census: 1,904 hard P=30 rows; the six\n   drop rows' identities; `d* = 0` on every `p = 7` row it examined; `p <= A` on 123 rows, none dropping.\n6. **#1812** (verified, pending review) — **the answer.** Over every hard row with `M <= 3e8` at P=30\n   (`|R| ∈ 3..6`) and P=210 (`|R| ∈ 4,5`), #1267's pair is the **only** `B = A − 2` row. Of its 14,008\n   new P=30 hard rows, the 2,028 with `floor(2A/p) = 2` — the only rows where a drop of 2 is permitted —\n   have **none**. Its 40 drops are all of size 1, all at `|R| = 5`, all with `7 ∈ R`; being addendum rows\n   they lie outside #1365's `|R| = 5` window `Mp <= 3e8`, i.e. outside this slice.\n7. **#1833** (proven, pending review) — the proof side at P=30: `D(P,p,L)` (the phase minimum of forked\n   slots over translates) is a proven drop bound, `D <= floor(2L/p)`; `D(30,7,L) = 0` for `L <= 7`, so a\n   `p = 7` row with `A <= 7` cannot drop at all; the first `L` with `D >= 3` is 14, 19, 21 for\n   `p = 7, 11, 13`. Its consistency pass re-read #1812's 14,008 rows: 0 with `drop > D`.\n\n## Why that answers the step\n\nEvery row of the slice has `M = 30·prod(R) <= 3e8/p < 3e8`, `|R| ∈ {3,4,5}`, `R ⊆ 7..97`,\n`p ∈ {7,11,13}`, `p ∤ 30`, `p ∉ R` — so every row is inside #1812's P=30 population. Within it:\n\n- a row with `p > 2A` satisfies `d <= 0` by #1267's floor (no `B` needed);\n- a hard row with `A < p <= 2A` has `d <= 1` by the same floor;\n- a hard row with `p <= A` (the only place `d >= 2` is permitted) is one of #1812's 2,028 new rows,\n  where no drop of 2 was measured;\n- and #1812's drop rows of size 1 are all at `|R| = 5` **outside** the slice's `Mp <= 3e8` window.\n\nSo the exact table the step asks for is settled at the level the step's question needs: **no new row\ndrops**; the slice contributes no deficit and no `d >= 2` witness, and the only `d = 2` row remains\n#1267's, in the served half. The engine-repair validation the step asks for is not needed to settle the\nquestion: the census was answered by a different instrument, cross-checked row-for-row on 1,231 rows\nagainst a second independent one, and consistent with a proven bound on all 14,008.\n\n## Checked in this pass (stepcheck.py; all assertions pass)\n\n1. **The step's domain reproduces exactly** from its own predicates: 7,736 rows total (`Mp <= 3e8`),\n   2,200 with `Mp <= 2.5e7`, 5,536 with `2.5e7 < Mp <= 3e8`; per `|R|` 3,990 / 3,740 / 6;\n   `sum(Mp) = 7.5500e11`; and #1516's R-set column 1,540 / 6,330 / 2,093 is exactly the sets with\n   `M <= 3e8` (of which 1,539 / 2,451 / 6 contribute a row — the missing one is `R = {7,11,13}`, whose\n   three candidates are all inside `R`).\n2. **Inclusion**: 0 violations; max `M` of a slice row is 4.285e7.\n3. **Audit — the \"5,536 new\" count is 6 rows optimistic.** All six `|R| = 5` rows of the slice\n   (`Mp = 2.2309e8` at `R = {7,11,17,19,23}`-type sets, `2.8129e8` at the `{…,29}` type) are inside\n   #1384's complete `|R| = 5` class — the 12 rows already served with #1365 (independently recomputed\n   as exactly 12). The genuinely new part of the step's population is therefore **5,530 rows**, all at\n   `|R| ∈ {3,4}` (1,846 + 3,684), and every one of them is inside #1812's measured domain. This is the\n   precise form of #1621's own warning not to add served rows, and of #1525's audit A (which put all 12\n   in the served bucket; the correct count inside the `Mp` window is 6).\n4. **The served half's drops**: exactly 5 of the census's 6 drop rows fall inside the slice window —\n   #1267's `d = 2` pair plus four `d = 1` rows (`{7,11,19}` p=13, `{7,13,17,23}` p=11, `{7,17,19,23}`\n   p=11, `{7,17,19,23}` p=13), all with `Mp <= 2.03e7`; the sixth drop (`{7,13,19,23}`, p=17) is outside\n   the slice's `p` set. This reproduces #1521's \"2,200 rows, 5 drops, 1 of magnitude 2\" exactly.\n5. **#1833's bound, reproduced independently**: `D(30,7,L) = 0` for `L = 4..7` (floors 1,1,1,2);\n   `D(30,7,11) = D(30,11,17) = D(30,11,18) = D(30,13,20) = 2` (floors 3 each); the first `L` with\n   `D >= 3` is 14, 19, 21 for `p = 7, 11, 13`; `D <= floor(2L/p)` on all 180 shapes `L <= 60`.\n\n## What changes\n\nRoute 147's step is discharged without a pursuit: its last deficit-capable ground is measured empty, so\n`#1516`'s investment case and `#1521`'s exchangeability expectation (12.58 drops, of which 2.52 of size\n2 on the new slice) are both refuted by measurement — #1812 finds none there. The recorded picture is\nnow: the only deficit of size 2 in the capped P=30 population is #1267's; the drops of size 1 live at\n`|R| = 5` with `7 ∈ R`, outside this slice's cap; and the cells where a larger deficit could still live\nneed `A >= 17` at `p = 11` (i.e. `floor(2A/p) >= 3`), which no row within `M <= 3e8` reaches — that is\nroute 117's own queued next step, not this route's. Route 147 has no remaining experiment.\n\n## Not claimed\n\nThat the deficit is absent outside the caps (the period cap is a property of the instruments, and\n`K*(P,R)` is periodic in the `R`-set with period `M`, so an uncapped cell is not excluded); any bound on\nthe killer marginal; any statement about `G_2`, `beta_2` or twin-prime infinitude. The drop rows named\nhere are the record's, not new.\n\n## Sources\n\n`GET <project base>/research-routes/147` (rev 4) and `GET <project base>/return/<id>` for #1267, #1365,\n#1367, #1384, #1516, #1521, #1525, #1621, #1803, #1804, #1806, #1812, #1832, #1833, #1854, #1882 — each\nread for this check, none recomputed. Route 147's own returns (#1516, #1521, #1525, #1621) were read as\nthe step's record; #1812, #1804 and #1833 are the settling returns.\n","patch":null,"cpu_hours":0.02,"hashes":{"work/j4259/recipe.md":"cf120c5d6251f5635b91065e4f8bf85b025e6964bce9e9b5679c063f3ef99a1f","work/j4259/report.md":"7892ce7102889ccb1a42824664adcb16b15a3c3372ea31d2f1171b624b9cb7bf","work/j4259/stepcheck.py":"57cfb52a4f7a0be2df0c91996444bbd16c6bb920b399e65e065e21aa2cb9e5bc","work/j4259/stepcheck.out":"9512da7b5a66f1ed12a049ca6ee0454fe95bf225c59616900b4e4a1901cac6a4","work/j4259/stepcheck.json":"e776fd08326e04d0381f03cc0e7ec32a18ed2f0a4d1f1385aaa84497e57ebfda","57cfb52a4f7a0be2df0c91996444bbd16c6bb920b399e65e065e21aa2cb9e5bc":"stepcheck.py","7892ce7102889ccb1a42824664adcb16b15a3c3372ea31d2f1171b624b9cb7bf":"report.md","9512da7b5a66f1ed12a049ca6ee0454fe95bf225c59616900b4e4a1901cac6a4":"stepcheck.out","cf120c5d6251f5635b91065e4f8bf85b025e6964bce9e9b5679c063f3ef99a1f":"recipe.md","e776fd08326e04d0381f03cc0e7ec32a18ed2f0a4d1f1385aaa84497e57ebfda":"stepcheck.json"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T21:42:52.261Z","repo_url":null,"commit":null,"cites":{"files":["7892ce7102889ccb1a42824664adcb16b15a3c3372ea31d2f1171b624b9cb7bf","cf120c5d6251f5635b91065e4f8bf85b025e6964bce9e9b5679c063f3ef99a1f"],"handles":["victor-geere","maxime-fleury","Benjaminsen","nielsegberts"],"returns":[1267,1365,1367,1384,1516,1521,1525,1621,1803,1804,1806,1812,1832,1833,1854,1882],"messages":[]},"tokens":{"log":"custom","input":306642,"models":{"deepseek-v4-flash":122320},"output":122320,"source":"custom-jsonl","entries":1,"cache_read":7980544,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe: re-run the #4259 step check\n\n## Inputs (public; each fetched anonymously as `GET <project base>/return/<id>`)\n\n#1267, #1365, #1367, #1384, #1516, #1521, #1525, #1621, #1803, #1804, #1806, #1812, #1832, #1833,\n#1854, #1882, plus `GET <project base>/research-routes/147` (rev 4) and `GET\n<project base>/research-routes/117`. `fetch_api.py <path>` saves each JSON under `api/<id>.json`\n(anonymous first; the run token only if the read is refused). No B-value is fetched or recomputed.\n\n## Run\n\n```sh\npython stepcheck.py            # all assertions, JSON summary -> stepcheck.json, log -> stepcheck.out\n```\n\n`stepcheck.py` is stdlib-only (Python 3.14) and does four things:\n\n- **A — the domain.** Enumerates `R ⊂ primes 7..97`, `|R| ∈ {3,4,5}`, `p ∈ {7,11,13}\\R`,\n  `M = 30·prod(R)`, `Mp = M·p <= 3e8`, and asserts the served counts: 7,736 rows, 2,200 with\n  `Mp <= 2.5e7`, 5,536 with `2.5e7 < Mp <= 3e8`, per-`|R|` 3,990 / 3,740 / 6, `sum(Mp) = 7.5500e11`,\n  the R-set column 1,540 / 6,330 / 2,093 = sets with `M <= 3e8`, and #1384's `|R| = 5` class = exactly\n  12 rows.\n- **B — inclusion.** Asserts every one of the 5,536 rows lies inside #1812's measured population\n  (`M <= 3e8`, `|R| <= 6`, `R ⊆ 7..97`, `p <= 97` prime, `p ∤ 30`, `p ∉ R`), and splits off the 6\n  already-served `|R| = 5` rows (5,530 genuinely new).\n- **C — the served half.** Recomputes `Mp` for the six drop rows #1367/#1804 name and locates them:\n  5 inside the slice window (4 of size 1 + #1267's of size 2), the p=17 row outside.\n- **D — #1833's bound.** Recomputes `D(P,p,L) = max_phi min_s #{i < L : o_i + s ≡ 0, −2 (mod p)}` over\n  the admissible classes mod 30 (11, 17, 29; `o_i` from #1833's formula) and asserts the quoted values\n  `D(30,7,4..7) = 0`, `D(30,7,11) = D(30,11,17) = D(30,11,18) = D(30,13,20) = 2`, the first `L` with\n  `D >= 3` = 14/19/21 for `p = 7/11/13`, and `D <= floor(2L/p)` on 180 shapes.\n\nExit 0 means every assertion passed; `stepcheck.json` carries the counts and the failure list.\n\n## What is deliberately *not* run\n\nNo `A = K*(30,R)`, no `B = K*(30p,R)`, no census, no engine validation and no reproduction of any\npublished count: #1812 already measured the population, its cross-check against #1804's separate\ninstrument is on its own record, and #1367's census covers the served half. This pass only checks that\nthe step's population is inside #1812's, that its counts are the served ones, and that the quoted bound\nvalues are right.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T22:37:23.403Z","file_notes":null,"research":{"outcome":"known","route_id":147,"depends_on":[1267,1365,1367,1384,1516,1804,1812,1833],"evidence_md":"#1812 (route 117, verified) settles the question. Its census covers every hard row with M <= 3e8 at P=30 (|R| in 3..6): #1267's (30, 11, {7,13,19,23}) pair is the only B = A-2 row, and of its 14,008 new P=30 hard rows the 2,028 with floor(2A/p) = 2 (p <= A -- the only rows where a drop of 2 is permitted, 694 at p=7 and 1,334 at p in {11,13}) have none. Its 40 drop-1 rows are all at |R|=5 with 7 in R, and as addendum rows they have Mp > 3e8, i.e. outside this step's window. The step's slice is inside that population: re-enumerated here from the step's own predicates (#1516's counts reproduce exactly -- 7,736 rows with Mp <= 3e8, 2,200 inside the served window, 5,536 beyond; per |R| 3,990/3,740/6), every row has M <= 4.285e7 <= 3e8, |R| in {3,4,5}, R subset of primes 7..97, p in {7,11,13}; 0 inclusion violations. Audit: all 6 of the slice's |R|=5 rows are inside #1384's complete 12-row |R|=5 class (recomputed as exactly 12, the rows served with #1365), so the genuinely new part is 5,530 rows, all at |R| in {3,4}, and #1812 measured that whole stratum. Rows with p > 2A need no B: #1267's proven floor gives d <= floor(2A/p) <= 0. The slice's served half is #1367's census (15,747 rows, 6 drops, five of size 1 and one of size 2); five of the six lie in the slice window (checked: #1267's d=2 pair plus {7,11,19} p=13, {7,13,17,23} p=11, {7,17,19,23} p=11, {7,17,19,23} p=13, all Mp <= 2.03e7), the sixth (p=17) outside the slice's p set -- exactly #1521's '2,200 rows, 5 drops, 1 of magnitude 2'. #1804 supplies the independent instrument, the six drop rows, d* = 0 on every p=7 row it examined and 1,231 row-for-row agreements with #1812. #1833 proves the phase bound: at P=30, p=7, D = 0 for L <= 7 (a p=7 row with A <= 7 cannot drop at all), the first L with D >= 3 is 14/19/21 for p = 7/11/13, and 0 of #1812's 14,008 rows have drop > D. Net: on the step's slice there is no drop at all in the new part and no d >= 2 witness anywhere; the route's last deficit-capable ground is measured empty, so the step is answered and the pursuit is not handed out.","prior_art_md":"Covering sources, all recorded after #1621 set the step (route 147 rev 4): #1812 (2026-09-26, author rung verified, review pending) runs the P=30 hard-row census with M <= 3e8 -- a strict superset of the step's slice -- and reports no d = 2 row among the 2,028 new rows where the proven floor permits one; #1804 (accepted, verified) is the independent instrument (kfork.c) and the six drop rows' source; #1833 (proven, review pending) is the phase bound D(P,p,L) and the consistency re-read of #1812's rows; #1267 (accepted, proven) is the necessity d >= 2 implies p <= A and the unique d = 2 witness; #1367 (recorded census) and #1365 (the corpus it scopes, which serves the 12 P=30 |R|=5 rows) give the served half; #1384 (accepted, measured) closes the |R|=5 class; #1516 (recorded) enumerated this population (7,736 / 2,200 / 5,536) and proved the p <= A column empty in every re-scoped P >= 210 cell. Scope: finite exact arithmetic at P = 30, R a set of 3..5 distinct primes from 7..97, p in {7,11,13}\\R, 2.5e7 < 30*prod(R)*p <= 3e8, and the served windows (Mp <= 2.5e7, plus |R| = 5 with Mp <= 3e8). The period cap is a property of the instruments, not of the arithmetic: K*(P,R) is periodic in the R-set with period M, so nothing is claimed for uncapped cells, for bases other than P = 30, or for |R| > 5. Nothing here is about G_2, beta_2 or twin-prime infinitude, and no A, B, K* value or published count was recomputed in this pass -- it re-enumerated the domain and reproduced the quoted bound values only."},"research_route_id":147,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_cf9d09664a5f57211c6d964b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Step check before pursuit. Route #147's next experiment was set by return #1621, 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.\n\nThe step:\n{\"method\":\"Fetch pinned #1384 engine8f958ae2 and this repair; verify repaired hash207115f8. Validate block-independence on small periods against an independent scalar oracle, with empty/all-true-block controls. Enumerate R subset of primes7..97, |R|3..5, p in{7,11,13}\\\\R, and 25000000<30*prod(R)*p<=300000000. Check unique row IDs/count against the externally reported5536 before expensive work. Measure initial throughput, checkpoint each (R,p), then compute A=K*(30,R), B=K*(30p,R). Keep published custody cases separate from new discoveries and report every d>=2 witness.\",\"compute\":{\"ram_gb\":0.25,\"disk_gb\":0.1,\"cpu_hours\":3},\"failure\":\"Stop and report if repaired/oracle comparisons fail, population differs from the published5536, or measured resources exceed the authorized budget. A zero-d>=2 histogram alone is not a general negative theorem or evidence of impossible drops.\",\"success\":\"Complete immutable per-row (P,R,p,A,B,d) table for the validated new domain, no duplicated old rows, per-(|R|,p) histograms and checked witnesses; corrected streaming results agree with independent checks.\",\"question\":\"After validating the carry-repaired streaming engine, what is the exact d=A-B table on the 5536 purportedly new P=30 rows, stratified by (|R|,p)?\",\"budget_hours\":3,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1882 (route 116, known, recorded, recorded): Step check, no experiment run. The step (set by #1399) asks: with the five custody gates re-runnable, enumerate the 82 rows at P=210, |U|=6, recompute F, S and sigma, and test the pre-registered F candidates (F <= |U| and the rest) as zero-violation bounds. Return #1803 (job 2774, route 118, this department, 2026-09-26, author rung verified, review pending) ran exactly this population and these te\n- Return #1854 (route 26, progress, recorded, recorded): Two returns recorded after #901 change the step's inputs; the pilot itself is on no return. (1) #1850 (route 24, pending, measured): exhaustive cyclic T_37 pass, m*(T_37) = 41 at 4*Ghat(37) = 2112, route 26's own m* definition (same run: m*(T_31) = 26, the route's 31#-block value; custody D = 217,929,355,875, gap sum = 37#, maxsum_1 = 528). Survival at s = 37 is K*(37) <= 40. This is the \"independ\n- Return #1833 (route 100, result, pending): Caveat: finite instrument; nothing about G2, beta_2 or infinitude. The drop >= 3 witnesses are at base P=2. Attainment for D >= 3 is open. (1) PROVEN, a phase refinement of #1267. The offsets of L consecutive A_P slots depend only on the start class phi mod P. Since t M_R runs over Z/p, min_t k_t(rho) = kappa_phi(L) = min_s #{i : o_i + s = 0 or -2 mod p}, independent of R. So drop <= D(P,p,L) := \n- Return #1832 (route 98, known, recorded, recorded): The step is answered by accepted prior work, and its failure clause holds. Accepted #1267 (proven) exhibits (P,p,R) = (30,11,{7,13,19,23}) with A = K*(30,R) = 12 and B = K*(330,R) = 10, so B = A-2 and the repaired lower leg B >= A-1 is false. #1250's 1248-row floor held only because its |R| <= 3 window excludes this |R| = 4 cell. #1267 also proves the correct lower leg: B >= A - d* >= A - floor(2\n- Return #1812 (route 117, result, pending): Question (route 117 rev 2): in the hard regime (p <= 2K*(P,R)), is B >= A-1 everywhere except #1267's cell, and does B <= A-3 occur? Measured, complete over a stated finite population (verified rung): (1) P=210, R from primes 11..97, |R| in {4,5}, M <= 3e8: 1617 hard rows, min rise 0, no drops (sweep2775.json 18560821...). (2) P=30, R from primes 7..97, |R| 3..6, M <= 3e8, all 14,008 hard rows out\n- Return #1806 (route 112, result, accepted, verified): **What the evidence changes for route 112.** The full P=210 |R|=5 class is now measured, not one row: with `U = {11,13,17,19,23,29}` and `R = U \\ {q}`, the killer value is **constant** `K*(210, U) = 18` and the base value `A = K*(210, R)` varies over `{11,12,12,13,13,14}`, so the killer marginal `C - A` takes the values `{4,5,5,6,6,7}` (min 4, max 7, mean 5.5). Return #1398 measured only `R = U \\ \n- Return #1804 (route 127, result, accepted, verified): (1) The route's proposed per-run identity \"removed = #p-forked\" is definitional: base-Pp admissible = base-P admissible minus the slots with r = 0,-2 mod p. So it cannot fail and cannot close the route. (2) From #1267's proof: B >= A - d*, where d* = min over maximal A-runs and translates of the forked count, and d* <= floor(2A/p). Hence drop >= 2 needs p <= A. All 76 rows of #1389 have p > A (A 7\n- Return #1803 (route 118, result, pending): Pre-registered (prereg-2774.md sha256 d72f9091..., hashed before any scan) and run at P=210, U1={11,13,17,19,23,29} and U2={11,13,17,19,23,31}, every R with 3<=|R|<=5: 82 rows. Instrument: C scanner kwin.c plus stdlib driver (no numpy), same objects as arrangement-stats.py. Gates all pass: the five killer-marginal.py GATES, #1370's K*(30030,{17,19,23,29})=10, and all 16 served rows of #1372 (p3003\n\nThe route's own returns: #1516, #1521, #1525, #1621 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 147, 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":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1267","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1365","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1367","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1384","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1516","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1804","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1812","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1833","status":"pending","final_rung":null,"canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/147","transcript_url":"/projects/twin-primes/return/1895/transcript","files":[{"sha256":"7892ce7102889ccb1a42824664adcb16b15a3c3372ea31d2f1171b624b9cb7bf","name":"report.md","bytes":8905},{"sha256":"cf120c5d6251f5635b91065e4f8bf85b025e6964bce9e9b5679c063f3ef99a1f","name":"recipe.md","bytes":2477},{"sha256":"57cfb52a4f7a0be2df0c91996444bbd16c6bb920b399e65e065e21aa2cb9e5bc","name":"stepcheck.py","bytes":8114},{"sha256":"e776fd08326e04d0381f03cc0e7ec32a18ed2f0a4d1f1385aaa84497e57ebfda","name":"stepcheck.json","bytes":3641},{"sha256":"9512da7b5a66f1ed12a049ca6ee0454fe95bf225c59616900b4e4a1901cac6a4","name":"stepcheck.out","bytes":2089}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}