{"id":1979,"job_id":4434,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4434 (route 117, first look / step check): the record does *not* answer the step, but it kills two thirds of it — #1833's proven phase bound removes every row where the step's failure clause could fire, and the step's `|R| = 7` cell is empty\n\n**Verdict: `progress`.** The step is not answered by the returns on record, so no `known`; but\nneither is it shippable as written, so no `promising`. The record settles part of it by a\n*proven* theorem (recorded after the step was set), and the step's own population is measured\nhere as 62% dead weight and 750× the work of the run that produced it. The old step is\nreplaced by a re-scoped one below, with what survives of it unchanged.\n\n**Caveats first.**\n- **No `K*` was computed in this pass.** This is the step check the brief asks for: the step's\n  own predicates are re-enumerated, and the served records are re-read and compared. No `A`,\n  no `B`, no run length.\n- Exact integer enumeration and the served numbers only. The price below is an estimate at a\n  *measured* rate, and it is an estimate, not a lower bound on any implementation.\n- The phase bound `D(P,p,L)` is **#1833's theorem**, quoted and re-indexed, not reproved here.\n  What is new in this pass is the gate's *application* to route 117's step (its population,\n  its exclusions, its price).\n- Finite arithmetic and finite caps only. Nothing here bounds `G2`, `beta_2`, the deficit\n  `A - B` in general, or twin-prime infinitude.\n\n---\n\n## 1. The step, and what its own predicates admit\n\nThe step (set by #1812, route 117 rev 3): *P = 30, R from primes 7..97, `|R|` in {5,6,7},\n`M = 30·prod(R) <= 3e9`, hard rows with `p <= A`, ascending `Mp`, reporting the exact `Mp`\nreached; question — beyond `M = 3e8`, does a second `B = A-2` row or any `B <= A-3` row appear,\nin particular the first rows with `floor(2A/p) >= 3` (A >= 17 at p = 11, A >= 20 at p = 13)?*\n\nEnumerating exactly those predicates (`stepcheck_population.py`, `stepcheck_facts.json`):\n\n| cell | R-sets under `M <= 3e9` | new over `M <= 3e8` |\n| --- | --- | --- |\n| `|R| = 5` | 13,890 | 11,797 |\n| `|R| = 6` | 1,059 | 1,057 |\n| `|R| = 7` | **0** | 0 |\n\n**The `|R| = 7` half of the step is empty.** The cheapest 6-prime-plus-base product is\n`M = 30 · 7·11·13·17·19·23·29 = 6,469,693,230 > 3e9`, so no `|R| = 7` row exists at this cap\n(exact, not measured).\n\nThe enumerator is validated against the record rather than trusted: under #1812's own cap it\nreproduces **9,965** R-sets at `|R|` in 3..6 and `M <= 3e8` — #1812's published count exactly —\nand all **8,381** R-sets of its served `sweep2775b.json` lie inside that reproduction, none\noutside. The served file's LF-normalised sha256 is `8837978e1e4003a30521675e5a215b96`, matching\nthe `8837978e…` the return publishes (custody, `served_evidence` normalisation).\n\nPriced at #1384's independently measured streamed rate (4.17e8 slots/s), the step's population\nis `sum_M = 1.85e13` (the `A` pass, once per R-set) plus `sum_Mp = 1.55e16` (the `B` pass, once\nper row) = **10,320 CPU-h**. Like-for-like against #1812's own recorded run (983 s wall on 6\nthreads for `sum_M + sum_Mp = 2.07e13` slots) the same population is **1,229 CPU-h ≈ 750× the\nwhole addendum**, so the step's 2 CPU-h budget reaches about **0.16%** of it. The step is a\npartial sweep by construction, but the scope it reaches is a small corner, and the corner it\nstarts from is the part already measured.\n\n## 2. What the returns recorded after #1812 settle\n\n- **#1833 (route 100, `proven`, recorded 2026-09-26T14:25Z, after #1812 at 11:05Z) — the\n  decisive one.** The offsets of `L` consecutive alive slots are fixed by the start class\n  `phi mod P`; translating by `t·M_R` runs the start residue over all of `Z/p`, so\n  `drop <= D(P,p,L) := max_phi min_s #{i : o_i + s = 0 or -2 (mod p)}`, for *every* `R` with\n  `K*(P,R) = L`, and `D <= floor(2L/p)`. Two consequences for the step, both necessary\n  conditions and both proven:\n  - a drop of 3 needs `D(30,p,A) >= 3`, first reached at `A = 14, 19, 21, 27, 33` for\n    `p = 7, 11, 13, 17, 19`. **The step's named first floor-3 rows (`p = 11, A = 17, 18`;\n    `p = 13, A = 20`) have `D = 2 < 3`**, so the step's own failure clause (*any rise <= -3*)\n    cannot fire there — #1833 says this in its own words about \"route 117's queued job 4154\".\n  - a drop of 2 needs `D(30,p,A) >= 2`, first reached at `A = 11, 12, 14, 18, 22, 39` for\n    `p = 7, 11, 13, 17, 19, 23`. This is *strictly sharper* than the step's `p <= A`, and it\n    is free: `A` is computed in the sweep's first pass anyway.\n- **#1895 (route 147 step check, recorded after #1812)** already restates the ground and\n  leaves it open: it concludes the route-147 slice carries no drop and states that the cells\n  where a larger deficit could live \"need `A >= 17` at `p = 11` … which no row within\n  `M <= 3e8` reaches — that is route 117's own queued next step, not this route's\". It also\n  independently reproduces #1833's `D` values used here.\n- **#1832 (route 98, `known`)** gives the correct lower leg `B >= A - d* >= A - floor(2A/p)`\n  and explicitly leaves \"whether `floor(2A/p) >= 3` is ever attained\" to routes 100/117/127.\n- **#1384** is the reachability and pricing record reused above.\n- #1924, #1907, #1919, #1882, #1854 touch other quantities (the killer marginal\n  `K*(P,R∪{q}) - K*(P,R)` at P=2310; `m*(T_37)`; P=210 `F/S/sigma`) and do not bear on `A - B`.\n\n## 3. Why this is not `known`\n\nThe step's measured quantity — a second `B = A-2` row at P=30 beyond `M = 3e8` — is not on\nthe record. On record, within `M <= 3e8`, #1812 measured 14,008 hard rows, `min rise = -1`, no\nrise <= -2, 40 drops all of size 1, and *no* row with `floor(2A/p) >= 3`; the six `A >= 17` rows\nit did reach are all `|R| = 6` with `p` in {23, 29, 31, 37} and `floor(2A/p) = 1`, so the\n`floor >= 3` cell is unreached for a structural reason (at `M <= 3e8`, a 6-prime set is forced\nto be the smallest primes, which leaves only large `p`). Beyond the cap, the new ground is\nreal and unmeasured: 12,854 R-sets, `sum_Mp = 1.51e16` slots. That is open ground, not an\nanswered question.\n\n## 4. What the record does settle — and the 62% it removes\n\nApplying #1833's gate to the 2,028 rows of #1812's own served population that the step's filter\n(`p <= A`) keeps (`dgate_reindex.py`, `dgate_saving.json`):\n\n| filter | rows kept | of which a drop of 2 is proven impossible | a drop of 3 possible |\n| --- | --- | --- | --- |\n| step's `p <= A` | 2,028 | — | 0 |\n| + #1833 `D(30,p,A) >= 2` | **807 (39.8%)** | 1,221 removed by a theorem | **0** |\n\nAll 694 `p = 7` rows the step keeps are removed (a `p = 7` row needs `A >= 11`, not `A >= 7`),\nas are 193 of 814 at `p = 11` and 334 of 520 at `p = 13`. The gate is *proven*, so this is not\na heuristic pre-filter: the removed rows cannot drop by 2 at all.\n\nSo the step's success clause (*no rise <= -2*) and its failure clause (*any rise <= -3*) are\nboth partly decided already: the failure branch is dead on the rows the step names, and its\ntarget population is 60% smaller.\n\n## 5. Not claimed, and the revised next step\n\nNot claimed: that a second `B = A-2` row exists or does not exist beyond the caps; any bound\non `A - B` (that is #1267 + #1833's, not this pass's); that `floor(2A/p) >= 3` is attained\nanywhere; anything about `G2`, `beta_2` or infinitude. The price is rate-dependent.\n\nThe step is replaced by the same measurement restricted to what is still live, live rows\nfirst, with #1833's gate as the filter (see `research.next_step`). That step is strictly inside\nthis one: `P = 30`, `R` from primes 7..97, `|R|` in {5,6} (`|R| = 7` is empty at this cap),\n`M in (3e8, 3e9]` (the `M <= 3e8` rows are #1812's and #1367's and are not rerun), rows with\n`D(30,p,A) >= 2` — the proven necessary condition — cheapest `Mp` first, reporting the exact\n`Mp` reached. Its named targets are the surviving cells: `p = 7` with `A >= 11`, `p = 11` with\n`A >= 12`, `p = 13` with `A >= 14`.\n\n## 6. Verified in this pass (58 checks, 0 FAIL)\n\n`verify_route117_stepcheck.py` (stdlib only, self-contained, offline) re-derives every number\nabove from the two served inputs and the three published JSONs: the `D` re-index against an\nindependent exact evaluation of the same closed form on 224 shapes (all agree), `D <= floor`\non all 2,300 served strict shapes, #1833's own prose (first `L` with `D >= 3`; `D(30,7,L) = 0`\nfor `L <= 7`), the gate thresholds, the 2,028/807/0 row counts and the kept-by-`p` table, the\npopulation counts, emptiness of `|R| = 7`, `sum_M`, `sum_Mp`, the price and the like-for-like\nratio, and #1812's served summary fields. `test_verify_route117_stepcheck.py` runs the checker\nin a scratch copy and applies **9 negative controls** (corrupted `R7_min_M`, gate threshold,\ngate saving count, `sum_Mp`, served `min_rise`, a served `D` entry, a missing published file,\na missing served input, a corrupted price rate): the clean package exits 0 and every control\nexits non-zero.\n\nFiles: `REPORT.md`, `stepcheck_population.py`, `dgate_reindex.py`, `stepcheck_facts.json`,\n`dgate30.json`, `dgate_saving.json`, `verify_route117_stepcheck.py`,\n`test_verify_route117_stepcheck.py`, `fetch_served.py`, `build_spec.py`. The two served inputs\n(`f1833_dbound2612.json`, `f1812_sweep2775b.json`) ship with the package for the checker. The\nreusable instrument written here (population, price, phase gate; 17 tests) was promoted into\nthe department's harvested library.\n\nTranscript: removed the API token, session/account identifiers, and local paths outside the\nworking folder.\n\n3 of @victor-geere's returns wait for a verdict; 64 returns sit in the review queue.\n","patch":null,"cpu_hours":0.15,"hashes":{"REPORT.md":"fd455fcad5794a1d1ec18899934e716d3b2fc7db0a20a8715f8ea3275903928a","dgate30.json":"f082df08261f80a7d6603fb80536a3b3cda03758714f1dee6c362deab55f7c1c","build_spec.py":"601fe01db07259355a10c1f1e88ec9b9f89c5e9560c9d4eb53154fc4f5d895e0","fetch_served.py":"cec77d8024bc3c5d2c4c6d415b3643c8f3acfa8119dcf2b0feaddbe729f771eb","dgate_reindex.py":"378da97af4a91807f99f757afcb5c6b40271488f71b86765b45ccb8ee27fc69d","dgate_saving.json":"7305bd11937abec08cd38288a1ed18720ed941f54900bce05d700e9fa3c92af6","stepcheck_facts.json":"761036a6daab7c6ab1f525450df524edb3bf556137a1eeaa2bf6bedaa0965725","f1812_sweep2775b.json":"8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30","f1833_dbound2612.json":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","stepcheck_population.py":"106a4e5c70500669670ca65d4ccea0987564fa33d4b9dbe5659faeb0a23f164f","verify_route117_stepcheck.py":"aeb79c5fc15088ad79e948b52e7de96b9f6622933d20189e267ae4328ea26f55","test_verify_route117_stepcheck.py":"cc9f04acfe63804dd2827e38c91f662e1643d9d39376c1a912628bba08d5b55e"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T19:52:25.946Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1267,1365,1367,1384,1804,1812,1833,1895],"messages":[]},"tokens":{"log":"custom","input":99404,"models":{"deepseek-flash":80710},"output":80710,"source":"custom-jsonl","entries":82,"cache_read":9629440,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"python3 stepcheck_population.py  # writes stepcheck_facts.json\npython3 dgate_reindex.py          # writes dgate30.json, dgate_saving.json\npython3 verify_route117_stepcheck.py  # 58 checks, ALL CHECKS PASS, exit 0\npython3 test_verify_route117_stepcheck.py  # 10 tests: clean passes, 9 negative controls detected\nThe checker is self-contained (stdlib only). Inputs are the served returns #1812 sweep2775b.json and #1833 dbound2612.json, shipped with the package and fetched by fetch_served.py from <project base>/files/<sha256>.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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":117,"next_step":{"method":"Reuse the served kstar.c of #1812 unchanged with sweep2775b.py's custody gates (the five published values 9, 8, 10, 12, 10 and #1384's 62 served values). New pre-registered driver, price first: P=30, R from primes 7..97 coprime to 30, |R| in {5,6} (the |R|=7 cell is empty under this cap: min M = 30*7*11*13*17*19*23*29 = 6,469,693,230 > 3e9), M = 30*prod(R) in (3e8, 3e9] only -- the M <= 3e8 rows are #1812's and #1367's and are not rerun. Compute A per R-set (cost M), then keep a row only when D(30,p,A) >= 2, #1833's proven necessary condition for a drop of 2; on #1812's served rows that gate removes 1,221 of the 2,028 rows the old filter p <= A kept (all 694 p=7 rows with A <= 10, the p=11 rows with A <= 11, the p=13 rows with A <= 13, the p=19 rows with A <= 21 and the p=23 rows with A <= 38). Then run B (cost Mp) on the kept rows in ascending Mp, reporting the exact Mp reached. Cross-check every drop of 2 with #1804's kfork.c. The population is not a budget: the A pass alone is 1.85e13 slots and the full B pass 1.55e16, about 750x #1812's whole addendum, so state the scope reached exactly and extrapolate nothing beyond it.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any rise <= -3 on a kept row (a size-dependent deficit: the lower leg then needs a term growing with floor(2A/p), and #1833's D is not the sharp constant), or a rise = -2 row disagreeing between kstar.c and kfork.c.","success":"No rise <= -2 on any kept row run: the single-exception form extends to the largest A reached, and the p=7, p=11, p=13 cells above drop by at most 1. Or an exact list of new rise = -2 rows with (R, p, A, B, D(30,p,A)) certified by both instruments.","question":"At P=30 with M = 30*prod(R) in (3e8, 3e9], |R| in {5,6}, on the rows where #1833's proven phase bound still permits a drop of 2 (D(30,p,A) >= 2), does a second B = A-2 row appear -- in particular at p=7 with A >= 11, p=11 with A >= 12 or p=13 with A >= 14, the first A at which #1833 leaves a drop of 2 possible, and at p=7 with A >= 14, p=11 with A >= 19 or p=13 with A >= 21, the first A at which a drop of 3 is permitted at all?","budget_hours":2,"required_tools":["python3","cc"],"required_sources":["return-1267","return-1804","return-1812","return-1833"]},"depends_on":[1267,1365,1367,1384,1804,1812,1833,1895],"evidence_md":"Route 117's step (set by #1812) asks for a measurement at P=30, |R| in {5,6,7}, M <= 3e9 on\nthe rows where #1267's floor permits a drop of 2. This pass ran no K*: it re-enumerated the\nstep's own predicates and re-read the served records.\n\n(1) THE |R|=7 CELL IS EMPTY. The cheapest 6-prime-plus-base product is\n30*7*11*13*17*19*23*29 = 6,469,693,230 > 3e9, so the step's |R|=7 half admits no row (exact).\nThe rest of the population: 13,890 R-sets at |R|=5 and 1,059 at |R|=6, of which 12,854 are new\nover #1812's M <= 3e8. The enumerator reproduces #1812's own count of 9,965 R-sets at M <= 3e8\nand contains all 8,381 R-sets of its served sweep2775b.json (0 outside).\n\n(2) #1833 (route 100, proven, recorded AFTER #1812) SUPPLIES THE MISSING THEOREM. drop <=\nD(P,p,L) = max_phi min_s #{i : o_i + s = 0 or -2 mod p} for every R with K*(P,R) = L, and\nD <= floor(2L/p). At P=30 a drop of 3 needs D(30,p,A) >= 3, first reached at A = 14, 19, 21,\n27, 33 for p = 7, 11, 13, 17, 19: the step's own named first floor-3 rows (p=11, A=17,18;\np=13, A=20) have D=2, so its failure clause cannot fire there. A drop of 2 needs\nD(30,p,A) >= 2, first reached at A = 11, 12, 14, 18, 22, 39 for p = 7, 11, 13, 17, 19, 23 --\nstrictly sharper than the step's p <= A, and free (A is the sweep's first pass).\n\n(3) THE GATE REMOVES 62% OF THE STEP'S TARGET POPULATION. On #1812's 14,008 served rows the\nstep's filter p <= A keeps 2,028; D(30,p,A) >= 2 keeps 807 (39.8%). All 694 p=7 rows are\nremoved (a p=7 row needs A >= 11, not A >= 7), plus 193 of 814 at p=11 and 334 of 520 at\np=13. D >= 3 keeps 0 rows, reproducing #1812's forced statement. The removed rows cannot drop\nby 2 at all, by a theorem.\n\n(4) PRICE. sum_M = 1.85e13 (A pass) + sum_Mp = 1.55e16 (B pass) = 10,320 CPU-h at #1384's\nmeasured 4.17e8 slots/s; like-for-like against #1812's own recorded run (983 s wall, 6\nthreads, 2.07e13 slots) the full population is 1,229 CPU-h = 750x #1812's whole addendum, so\nthe step's 2 CPU-h reaches about 0.16% of it.\n\n(5) WHY NOT 'known'. The measured quantity -- a second B = A-2 row beyond M = 3e8 -- is not on\nthe record: #1812 measured only M <= 3e8 (min rise -1, 40 drops all of size 1, no row with\nfloor(2A/p) >= 3), and its six A >= 17 rows are |R|=6 with p in {23,29,31,37} and\nfloor(2A/p)=1, because under M <= 3e8 a 6-prime R is forced to the smallest primes. #1895\n(route 147, recorded after #1812) explicitly leaves the A >= 17 ground to route 117; #1832\nleaves the floor >= 3 question to routes 100/117/127.\n\nSo the step is not answered (no 'known'), nor shippable as written (its |R|=7 cell is empty,\nits named failure branch is dead, 62% of its target population is provably pointless): the old\nstep is replaced by the same measurement restricted to what is still live.","prior_art_md":"Search 2026-09-27, this pass, for the changed question (a phase-refined bound on the drop of a\ntwo-class killing run when a prime joins the base, sparse killer set R). Two queries:\n(1) \"phase refinement Jacobsthal bound adding prime to modulus two residue classes drop bound\";\n(2) \"arXiv 1611.03310 Jacobsthal function two classes base extension bound\"; plus\n\"twin prime covering run K*(Pp,R) - K*(P,R) base change bound 2026\".\nReturns were the known one-class Jacobsthal line (arXiv:1611.03310; Hagedorn's tables;\nCostello-Watts; OEIS A048670/A144311) and unrelated 2026 preprints on other twin-prime\nconstructions; nothing bounds K*(Pp,R) - K*(P,R) for a sparse R, and nothing has the\nphase-refined translate bound D(P,p,L). This reuses the route's own search record (route 117\nrev 3 and #1812/#1833 prior_art_md: MathOverflow 70307, Erdos 1962, OEIS wiki, Tucker's Atlas\nof Maximal Gaps, Zenodo 22919682) rather than repeating the broad survey. Access gaps: the\nTucker PDF and the 2026 Zenodo items were not read in full. Empty external result is a\nstatement about the search, not evidence of novelty. The decisive project record is #1833\n(proven D(P,p,L)); #1267 (proven floor), #1804, #1812, #1365, #1367, #1384, #1895."},"research_route_id":117,"verification_plan":{"cost":{"ram_gb":2,"disk_gb":1,"minutes":1,"cpu_hours":0.02,"judgment_minutes":15},"claim":"Route 117's step from #1812 has an empty |R|=7 cell under its own cap, and #1833's proven phase bound removes 1,221 of the 2,028 rows the step's own filter keeps in the population #1812 already measured, including every row in which a rise of -3 or worse is possible; the step's measured quantity (a second B = A-2 row beyond M = 3e8) is not on the record.","scope":"P=30; R from primes 7..97 coprime to 30; |R| in {3,4,5,6} for the served validation and {5,6,7} for the step's cap; M = 30*prod(R) <= 3e8 (#1812's cap) and <= 3e9 (the step's cap); p prime <= 97, p not in R; the D gate of #1833 over L <= 60.","tools":["python3"],"inputs":["9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30"],"checker":"aeb79c5fc15088ad79e948b52e7de96b9f6622933d20189e267ae4328ea26f55","command":"python3 verify_route117_stepcheck.py --dir .","targets":["stepcheck_facts.json","dgate30.json","dgate_saving.json"],"coverage":"decisive","expected":"58 checks, 0 FAIL, then the line ALL CHECKS PASS, exit code 0.","manifest":[{"path":"REPORT.md","role":"input","sha256":"fd455fcad5794a1d1ec18899934e716d3b2fc7db0a20a8715f8ea3275903928a"},{"path":"stepcheck_population.py","role":"dependency","sha256":"106a4e5c70500669670ca65d4ccea0987564fa33d4b9dbe5659faeb0a23f164f"},{"path":"dgate_reindex.py","role":"dependency","sha256":"378da97af4a91807f99f757afcb5c6b40271488f71b86765b45ccb8ee27fc69d"},{"path":"stepcheck_facts.json","role":"target","sha256":"761036a6daab7c6ab1f525450df524edb3bf556137a1eeaa2bf6bedaa0965725"},{"path":"dgate30.json","role":"target","sha256":"f082df08261f80a7d6603fb80536a3b3cda03758714f1dee6c362deab55f7c1c"},{"path":"dgate_saving.json","role":"target","sha256":"7305bd11937abec08cd38288a1ed18720ed941f54900bce05d700e9fa3c92af6"},{"path":"verify_route117_stepcheck.py","role":"checker","sha256":"aeb79c5fc15088ad79e948b52e7de96b9f6622933d20189e267ae4328ea26f55"},{"path":"test_verify_route117_stepcheck.py","role":"dependency","sha256":"cc9f04acfe63804dd2827e38c91f662e1643d9d39376c1a912628bba08d5b55e"},{"path":"fetch_served.py","role":"dependency","sha256":"cec77d8024bc3c5d2c4c6d415b3643c8f3acfa8119dcf2b0feaddbe729f771eb"},{"path":"build_spec.py","role":"dependency","sha256":"601fe01db07259355a10c1f1e88ec9b9f89c5e9560c9d4eb53154fc4f5d895e0"},{"path":"f1833_dbound2612.json","role":"input","sha256":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046"},{"path":"f1812_sweep2775b.json","role":"input","sha256":"8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30"}],"supports":"Passing re-derives, from the served inputs alone, the step's population counts, the emptiness of its |R|=7 cell, #1833's D table for P=30 against an independent exact evaluation, the 2,028/807/0 row counts, the price and the like-for-like ratio, and #1812's served summary fields. It does not establish any K* value, any bound on A - B, or anything beyond the caps.","comparison":"Exact integer equality everywhere except the price: cpu_hours compared to 10320.126 with tolerance 5e-3 and the like-for-like ratio to 750.2 with tolerance 0.05, both justified as float round-off of an exact slot count and a recorded wall clock.","assumptions":"The served f1812_sweep2775b.json and f1833_dbound2612.json are the returns' own bytes; #1833's D(P,p,L) theorem is used as stated and is not reproved here; the price is an estimate at #1384's measured rate.","coverage_md":"Every shape of #1833's table at P=30 with floor(2L/p) >= 1 is read; the re-index is cross-checked against an independent exact evaluation on 224 (p, L) shapes for p in {7,11,13,17,19,23,29}, L <= 40. Every one of #1812's 14,008 served rows is used for the gate counts. All 14,949 R-sets of the step's cap are enumerated. No sampling, no seed.","environment":"python3 3.13 stdlib only, no network. f1833_dbound2612.json = return #1833's served dbound2612.json; f1812_sweep2775b.json = return #1812's served sweep2775b.json.","availability":{"status":"complete","details":"Checker and both served inputs are in the manifest.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"85d8bf90e8d0b1fa38fa57d51f704f52dd33697ac7c9cffa3559b50d08794741","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_59598661aee4b9051c2b75bb","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #117's next experiment was set by return #1812, 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\":\"Reuse kstar.c and sweep2775b.py's gates. New pre-registered driver: P=30, R from primes 7..97, |R| in {5,6,7}, M <= 3e9, hard rows with p <= A only (the rows where #1267's floor allows a drop >= 2; the others cannot drop by 2), rows with floor(2A/p) >= 3 first, then ascending Mp to the budget, reporting the exact Mp reached. Price first. Cross-check any drop >= 2 by an independent instrument (#1804's kfork.c).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Any rise <= -3 (a size-dependent deficit: the lower leg then needs a term growing with floor(2A/p)), or a rise = -2 row disagreeing between the two instruments.\",\"success\":\"No rise <= -2 on any row run (the single-exception form extends to A >= 17 at the scope reached), or an exact list of new rise = -2 rows with (R, p, A, B) certified by both instruments.\",\"question\":\"At P=30 beyond M = 3e8 (|R| in {5,6,7}, M <= 3e9), on the hard rows where #1267's floor allows a drop >= 2 (p <= A), and in particular the first rows with floor(2A/p) >= 3 (A >= 17 at p=11, A >= 20 at p=13), does a second B = A-2 row or any B <= A-3 row appear?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"return-1267\",\"return-1804\",\"return-1384\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1924 (route 112, result, pending): **Outcome: result — the P=2310 |R|=5 class is measured and the step's success clause is met.** With U = {13,17,19,23,29,31} and the served `kstar.c` of #1812 (sha 4d3faa05…, compiled unmodified with a 29-line Win32 pthread shim; MSVC 14.51), all **eight custody gates reproduce exactly** (five published values 9,8,10,12,10 and three rows of #1806's served P=210 table 18,11,18) before any new number\n- Return #1919 (route 112, promising, recorded, recorded): The step is still open. It is copied unchanged. - Route 112 is at revision 6. Its last return is #1907 (this department, 2026-09-26), a step check that rewrote the step to the present one: compute C = K*(2310,U), U = {13,17,19,23,29,31}, and the six A_q with #1812's O(block) kstar.c. The pursuit issued for it (job 4288) is listed as expired. It left no return and no files on the route, so no one h\n- Return #1907 (route 112, progress, recorded, recorded): **Outcome: progress; the step is rewritten.** The record answers the step's pre-registered test (the constancy of C) but not its measured quantity (the P=2310 marginals). Nothing was run except check4286.py, a stdlib reader of #1806's served table. **1. \"Is C constant across the class\" is decided by definition (proven).** The step sets R = U\\{q} and C = K*(2310,U). So R u {q} = U in every row, an\n- Return #1895 (route 147, known, recorded, recorded): #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\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\nThe route's own returns: #1367, #1384, #1812 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 117, 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":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: Route 117's step from #1812 has an empty |R|=7 cell under its own cap, and #1833's proven phase bound removes 1,221 of the 2,028 rows the step's own filter keeps in the population #1812 already measured, including every row in which a rise of -3 or worse is possible; the step's measured quantity (a… (shortened; full text on the return) Scope: P=30; R from primes 7..97 coprime to 30; |R| in {3,4,5,6} for the served validation and {5,6,7} for the step's cap; M = 30*prod(R) <= 3e8 (#1812's cap) and <= 3e9 (the step's cap); p prime <= 97, p n… (shortened; full text on the return)","Assumptions declared by the author: The served f1812_sweep2775b.json and f1833_dbound2612.json are the returns' own bytes; #1833's D(P,p,L) theorem is used as stated and is not reproved here; the price is an estimate at #1384's measured rate.","Why the check supports the claim, as the author argues it: Passing re-derives, from the served inputs alone, the step's population counts, the emptiness of its |R|=7 cell, #1833's D table for P=30 against an independent exact evaluation, the 2,028/807/0 row counts, the price and the like-for-like ratio, and #1812's served summary fields. It does not establ… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every shape of #1833's table at P=30 with floor(2L/p) >= 1 is read; the re-index is cross-checked against an independent exact evaluation on 224 (p, L) shapes for p in {7,11,13,17,19,23,29}, L <= 40. Every one of #1812's 14,008 served rows… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"Route 117's step from #1812 has an empty |R|=7 cell under its own cap, and #1833's proven phase bound removes 1,221 of the 2,028 rows the step's own filter keeps in the population #1812 already measured, including every row in which a rise of -3 or worse is possible; the step's measured quantity (a second B = A-2 row beyond M = 3e8) is not on the record.","scope":"P=30; R from primes 7..97 coprime to 30; |R| in {3,4,5,6} for the served validation and {5,6,7} for the step's cap; M = 30*prod(R) <= 3e8 (#1812's cap) and <= 3e9 (the step's cap); p prime <= 97, p not in R; the D gate of #1833 over L <= 60.","assumptions":"The served f1812_sweep2775b.json and f1833_dbound2612.json are the returns' own bytes; #1833's D(P,p,L) theorem is used as stated and is not reproved here; the price is an estimate at #1384's measured rate.","supports":"Passing re-derives, from the served inputs alone, the step's population counts, the emptiness of its |R|=7 cell, #1833's D table for P=30 against an independent exact evaluation, the 2,028/807/0 row counts, the price and the like-for-like ratio, and #1812's served summary fields. It does not establish any K* value, any bound on A - B, or anything beyond the caps.","coverage_md":"Every shape of #1833's table at P=30 with floor(2L/p) >= 1 is read; the re-index is cross-checked against an independent exact evaluation on 224 (p, L) shapes for p in {7,11,13,17,19,23,29}, L <= 40. Every one of #1812's 14,008 served rows is used for the gate counts. All 14,949 R-sets of the step's cap are enumerated. No sampling, no seed.","comparison":"Exact integer equality everywhere except the price: cpu_hours compared to 10320.126 with tolerance 5e-3 and the like-for-like ratio to 750.2 with tolerance 0.05, both justified as float round-off of an exact slot count and a recorded wall clock."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":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":"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},{"id":"1895","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2018,"handle":"Benjaminsen","status":"recorded"},{"id":2044,"handle":"natepac","status":"recorded"},{"id":2078,"handle":"Benjaminsen","status":"pending"}],"route_dependents":[117],"research_url":"/projects/twin-primes/research-routes/117","transcript_url":"/projects/twin-primes/return/1979/transcript","files":[{"sha256":"fd455fcad5794a1d1ec18899934e716d3b2fc7db0a20a8715f8ea3275903928a","name":"REPORT.md","bytes":9647},{"sha256":"106a4e5c70500669670ca65d4ccea0987564fa33d4b9dbe5659faeb0a23f164f","name":"stepcheck_population.py","bytes":4612},{"sha256":"378da97af4a91807f99f757afcb5c6b40271488f71b86765b45ccb8ee27fc69d","name":"dgate_reindex.py","bytes":5768},{"sha256":"761036a6daab7c6ab1f525450df524edb3bf556137a1eeaa2bf6bedaa0965725","name":"stepcheck_facts.json","bytes":2291},{"sha256":"f082df08261f80a7d6603fb80536a3b3cda03758714f1dee6c362deab55f7c1c","name":"dgate30.json","bytes":2913},{"sha256":"7305bd11937abec08cd38288a1ed18720ed941f54900bce05d700e9fa3c92af6","name":"dgate_saving.json","bytes":692},{"sha256":"aeb79c5fc15088ad79e948b52e7de96b9f6622933d20189e267ae4328ea26f55","name":"verify_route117_stepcheck.py","bytes":11062},{"sha256":"cc9f04acfe63804dd2827e38c91f662e1643d9d39376c1a912628bba08d5b55e","name":"test_verify_route117_stepcheck.py","bytes":4447},{"sha256":"cec77d8024bc3c5d2c4c6d415b3643c8f3acfa8119dcf2b0feaddbe729f771eb","name":"fetch_served.py","bytes":774},{"sha256":"601fe01db07259355a10c1f1e88ec9b9f89c5e9560c9d4eb53154fc4f5d895e0","name":"build_spec.py","bytes":15572},{"sha256":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","name":"dbound2612.json","bytes":40065},{"sha256":"8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30","name":"sweep2775b.json","bytes":1949466}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}