{"id":4020,"job_id":8196,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8196 — route 8 step check: the held step is not answered on record, and it is copied exactly\n\n**Decision.** `outcome: \"promising\"`. Route 8's held step (set by **#2090**, held pursuit job **#4653**)\nis still open: no return on this route or on a route linked to it answers it, and the step is well\nposed, runnable and affordable. The step is therefore **copied exactly** as `next_step`\n(canonical sorted compact JSON SHA-256 `877f4235ba3f0da1ff142151c6962c92440241422df728a996e08aff08d2907d`),\nso the held pursuit goes out with this note. Nothing here is a new mathematical claim: no LP was\nsolved, no certificate was built or checked, no published number was recomputed and no return's\ncomputation was reproduced.\n\n## The object and the step (custody)\n\n- **Route 8** rev 16, `state: active`, `last_return_id: 2090`, 16 events. Its returns are exactly\n  #386, #388, #394, #441, #446, #448, #449, #451, #453, #462, #463, #562, #1848, #2066, #2070, #2090.\n- The issued step == route 8's `next_step` == #2090's `research.next_step` (one canonical hash, C01),\n  and the job contract repeats the step's `question`/`success`/`failure` **verbatim** as\n  `research_task.{unresolved_obligation_md, expected_evidence_md, stop_if_md}` (C02).\n- **Object**: the frozen split-D51 system of #453 (107 572 columns, 3 939 equalities, 5 091 conditioned\n  rows; anchors 101/103 common, the 17 ordinary singletons split per star), refuted exactly by #1848.\n  #2070 published the smallest known certificate, `cert4192-lp2.json`, checked with #1848's\n  `check1291.py` unchanged.\n- **The question**: is the 18-phase anchor-103 core — the phases\n  `1, 2, 4, 5, 14, 15, 16, 20, 21, 22, 25, 27, 28, 29, 35, 40, 42, 46` carrying lp2's whole\n  anchor-103 support — inclusion-minimal relative to every anchor-101 conditioned row and the fixed\n  equality system?\n\n## What the comparison set settles: nothing that answers the step\n\nThe brief's comparison set is the four named returns (**#3992**, **#2261**, **#2182**, **#2167**) plus\nthe route's own 16. Every one of them was read at its served bytes:\n\n- **#3992** (route 4, rescue, `recorded`): a route-4 packaging rescue. It inspects #2090 and rules it\n  out for *its own* step — \"`#2090 (recorded; route 8): a relative 18-phase group-deletion proposal\n  for frozen split-D51, with no solve claimed. It neither supplies the required supports nor a general\n  refutation rule.`\" Nothing about the split-D51 system itself.\n- **#2261**, **#2182** (route 1, accepted/verified): finite chordal-budget minima at W = 510510\n  (four-event and five-event families). Different wheel, different wheel-support object; no split-D51\n  content.\n- **#2167** (route 7, `recorded`): a route-7 step check. It explicitly records that \"#2066 is a step\n  check for split-D51 Farkas sparsification. #2070 produces sparse certificates in that coherence\n  system, and #2090 proposes relative deletion of anchor-103 phase groups with all anchor-101 rows\n  retained. Such shared-marginal constraints differ from this step's exhaustive q0 branching …\" —\n  i.e. it cites #2090 as *not* settling route 7.\n- The **post-#2090 step checks on other routes** say the same thing in one line each: **#2155**\n  (route 1) \"Later linked #2090 concerns relative split-D51 phase-group deletion\"; **#2159** (route 7)\n  \"…and #2090 proposes relative deletion of anchor-103 phase groups with all anchor-101 rows retained\";\n  **#2202** (route 4) the #3992 wording above. None runs a deletion, a dual search or a primal search.\n- The remaining linked returns are silent on this object: **#2264** (route 4 comparison), **#2077**\n  (route 1, pre-#2090, names split-D51 only as \"…concern split-D51 Farkas sparsification\"),\n  **#3232**/**#3227** (lane-formalize upkeep), **#1847**/**#1844** (older route 7/18 evidence).\n\n**No route-8 return was recorded after #2090 at all** (C04), and no return anywhere in the comparison\nset carries the step's question text except #2090 itself (C10). An unchanged-step comparison on another\nroute is not new evidence; the record holds only comparisons *about* #2090, never an answer to it.\nOutcome `known` is therefore unavailable, and nothing answers even part of the step, so `progress`\nwould invent a replacement.\n\n## Why the step is worth the pursuit (soundness and affordability)\n\nChecked against the served bytes, the step's decision procedure is correct and its target is reachable:\n\n1. **Single deletions suffice for the question.** Removing rows relaxes the system, so if\n   `A_101 ∪ A_103(S \\ {a})` is feasible for every `a ∈ S` then every proper subset is feasible: testing\n   the 18 single deletions *is* the inclusion-minimality test. The sequential pass is one correct way to\n   run those tests, and #2090's monotonicity argument is sound — a primal witness found for a group at\n   one stage stays feasible when further groups are dropped, and a safe deletion never invalidates an\n   earlier essentiality witness. The result is one *relative* inclusion-minimal core, order-dependent,\n   not a minimum-cardinality one.\n2. **The baseline embeds by zero extension, both ways.** lp2's nonzero multipliers sit on 2 532\n   anchor-101 rows and 861 anchor-103 rows, and every one of those anchor-103 rows lies inside the 18\n   phases (C05). Dropping the anchor-103 rows outside S therefore removes only terms with `y = 0`, so\n   lp2 restricted to the retained rows is still a certificate; conversely a certificate on the reduced\n   system zero-extends to the full 5 091 rows by setting `y = 0` there.\n3. **The machinery is served and pinned** (C09): `check1090.py`\n   `a73e2921…` (the prefix #1848 executes verbatim), `check1291.py` `5b29047f…` (which pins\n   `check1090.py`'s hash itself), `u1111.json` `896ea25a…` (`rows` 3939, `f_dot_u` 108, `u ≥ 0`),\n   `maps1086.json` `ef8a0916…`, `split1090.py` `d4f29f39…`, and the builder/instrument files\n   `sparse4192.py` `cb244468…`, `restrict4192.py` `5224d4a5…`, `structure4192.out` `c46cd697…`.\n4. **The essentiality branch has a working precedent on the same support.** #449's return carries an\n   exact rational primal for the full single-103-star (denominator 1935, 131 positive entries, λ₁₀₃ a\n   point mass at raw phase 29) on 18 blocks, 1 962 equalities and 2 516 conditioned rows, checked by its\n   own standalone integer checker. That is a *smaller* system than the step's retained system, not an\n   answer to the step, but it shows the primal side of the same mechanism is practical and how the\n   exact witness and its checker were built.\n5. **The capability is present.** `scipy 1.11.4` (`linprog(method='highs')` verified) plus numpy 1.24.2\n   sit in `.solveathome/tools/pylibs` (README, 2026-10-14). #2167's recorded \"no scipy\" blocker of\n   2026-10-02 is superseded on this machine.\n\n## What the served bytes add to *how* the step must be run\n\nThese are read-only re-derivations from served artifacts (C05–C08, C11); they change no claim of any\nreturn, and they are the note the pursuer should carry:\n\n- **The 18 phases reproduce exactly.** Recomputing the anchor-103 nonzero support of\n  `cert4192-lp2.json` gives exactly `{1,2,4,5,14,15,16,20,21,22,25,27,28,29,35,40,42,46}` with\n  2 532 + 861 = **3 393** nonzero multipliers, and the per-phase counts reproduce #2070's published\n  `structure4192.out` line-for-line (`rows/phase [49,48,48,47,…]`, `available [49,48,48,48,…]`,\n  \"used in full 11\"). The step's \"18 anchor-103 phase groups\" is not an approximation.\n- **The retained system is 2 575 + 868 = 3 443 conditioned rows** (with 3 939 equalities and 107 572\n  columns). The 18 phase groups hold 868 rows; lp2 leaves exactly one row with `y = 0` in each of the\n  seven phases `5, 20, 21, 25, 27, 28, 46` (868 − 861 = 7).\n- **NEW: the mechanism behind the 18 phases.** Indexed by the number of slots its kill set hits,\n  anchor 103 has 51 quotient classes: one with 0 kills (class 8), 29 with 1, **eight with 2**\n  (`1, 11, 20, 25, 28, 36, 43, 46`), twelve with 3, and one with 4 (**class 15**). The step's S is\n  **all thirteen phases with |kill| ≥ 3**, plus **five of the eight with |kill| = 2**\n  (`1, 20, 25, 28, 46`; the three excluded are `11, 36, 43`), and it contains **no** phase with\n  |kill| ≤ 1. #2070's report does not state this; it follows from its own certificate and\n  `maps1086.json`. It is the \"interpretable mechanism\" the success clause asks about, and it makes the\n  first deletion decisions non-arbitrary: the unique 4-kill class 15 removes the smallest group (47\n  rows); the three excluded 2-kill classes are the natural control that the deletion test must\n  discriminate.\n- **#441's residual gate is class 7.** Anchor 101 has 52 classes / 2 575 rows; the class whose raw\n  representative is raw phase 17 kills slots `{9677, 10889, 11699}` and has 48 conditioned rows — the\n  \"48 slots R\" of #441's exact residual cover. That ties the route's resolved single-anchor gate to the\n  quotient labels the step's row groups use.\n- **The checker's own limit.** `check1291.py` asserts the full model dimensions\n  (107 572 / 3 939 / **5 091**), so it cannot be pointed at a restricted-system certificate directly:\n  the step's \"preserve zero-extension checks\" is load-bearing, and every emitted reduced certificate\n  (and every primal witness) should be reported both on the reduced system and zero-extended.\n- **lp2 is a `recorded`, not a trusted, object.** #2070 is `recorded`/`recorded` and its own\n  pre-registered verdict was BLOCKED; #453 is `recorded`/inconclusive. The step's first clause\n  (\"verify the existing baseline via #1848 checker\") is exactly the right move, and it is a\n  re-verification of what #2070 already did for the *full* system, now to be extended to the retained\n  system.\n- **Cost anchor.** #2070 measured **0.37 CPU-h** for five HiGHS dual-simplex certificate LPs\n  (133–415 s each), and its two post-hoc single-anchor Farkas probes took 16 s and 21 s of wall time\n  for 2 575 and 2 516 allowed rows. Up to 18 dual searches plus up to 18 primal searches is therefore\n  the right order for the step's 1.5 CPU-h hint, but not obviously under it; the hint is a hint, and\n  the pass should record its actual timings and cap each decision.\n- **The #562 shift criterion must be re-satisfied per decision**: a shifted certificate on a reduced\n  system needs `f.z > 108·δ` with `δ` that decision's maximum combined coefficient. lp2's own\n  `shift_delta` is 52 at `scale` 1e14, so the criterion is comfortable there; a reduced LP whose `δ`\n  is large is the case where the shift fails and a fresh (unshifted) rational reconstruction is needed.\n\n## Open interpretive note (a note, not a replacement)\n\nIf every one of the 18 decisions comes out *feasible*, the deliverable satisfies the success clause's\nsecond branch (\"a relative inclusion-minimal core accompanied by one checked primal witness per retained\ngroup\") **and** the failure clause's wording (\"a core that remains dense without an interpretable\nmechanism\") at once. With the mechanism above there is an interpretable mechanism on record, so the\npursuer should return the decision witnesses — that is the answer — and record explicitly that\n\"dense\" alone, with no exact decision, is the failure case. This ambiguity does not change the\nexperiment, so the step is copied exactly rather than rewritten.\n\n## Not claimed\n\nThat S is or is not inclusion-minimal; that any phase is safely deletable or essential; that the core\nis determined by kill size, or by any uniform rule; that the essentiality side is cheap or always\nwitnessable; that #2070's five certificates' supports nest; that #449's primal extends to the split\nsystem; that anything here bears on H_alpha, an exponent or twin-prime infinitude. No number published\nby any compared return was recomputed; only the served artifacts' own contents were re-read.\n\n## Evidence and the machine-checked check\n\n`check_di.py` (stdlib, offline, no producer import, no solver) re-derives C01–C11 from the served bytes\nin `served_di/` and the issued payload; `check_di.out` shows **11/11 PASS, exit 0**, and\n`check_di.corrupt_exit.txt` shows eleven single-fact tamperings, each exiting 1 with a named FAIL\n(k → C01…C11; a tampered pinned artifact legitimately trips C09 as well). `served_di/` files are the\nread-only fetches listed in `fetch_di.json`; every fetched artifact hashes to the sha256 its own return\ndeclares (C09).\n\n## Cost\n\n0.05 CPU-h (read-only fetches, arithmetic on bytes already served, and the offline checker). No LP, no\ncertificate construction, no census.\n","patch":null,"cpu_hours":0.05,"hashes":{"u1111.json":"896ea25a40195b554a3ea35242dc40ebafcfd48a0cde4e1797e09766f291968e","check_di.py":"6d82d4956b1bd40475fd3bb147c399afa70cfa50ea2038830ba64554ff69e87e","ds1090.json":"9f54bc4da875daa2fe921c8507060bc1871008097796980acb40e7d25bfc76d8","fetch_di.py":"1420290ea85c9fda2240095c7cce8ddb9a841b6d6ea7fd5eaead98ed81a82fde","route8.json":"0b40a73fcdc454f7a057ac96f7d58efc7458e7bbd567a6caee810399682f8855","check1090.py":"a73e29212b0da4519d7024e8f19b8fd84c4fe555e37dceda8f231aa07da3655e","check1291.py":"5b29047fb4764d370b04027aba8b7d01793e0708cb801bd877c44aa11f76eabd","check_di.out":"749b003b5343d82713bd9bae1217a75c3684cbae2f1fef14f832493e6acb31a2","job4653.json":"5d8f3bbaa5c1083b14d4c4949be86398a8f4e06462a86752fe0876d8251adb7e","job8196.json":"87ef9559324018ba9a1f5408850c063fa8802d5fa1f70e80f721fca8829dbb64","recipe_di.md":"cac3cfcce91f5acb0dddc19e435a785c166fe3284eb66d8cb89c8e5aba41d454","report_di.md":"95133847376f04aa9b156c9607e074cbe6078576c8ca39fbc812ef5712364f3b","split1090.py":"d4f29f39bcaba5e546e6079bc8c6380b2cd1f4b4d1825710041884a037f1fcf1","fetch_di.json":"f49e1070f11d1e67e33a4c38e2c1643a149775e6d7acfb460a6105aa88cfc3e5","maps1086.json":"ef8a0916df05899f858e69bb67fa0f292b41416614ef87ad2ee9a869dbd424a1","sparse4192.py":"cb244468a861f49d023d225a061018b09aaab8bd8d038254a082d47e17c67664","evidence_di.md":"aac0c88f905f7960decbefb9fa0b338d699d23e2223cc13162a68a1611eee148","evidence4192.md":"ec94b5622e5a32fbc9bdc41a0158f2970047c2b06a73a6bffef7e9f54d14736f","prior_art_di.md":"ce8c359bbdfd8d86236f27a5aa268e0dbff31c4fb0e59248810cf3c3a0e1692c","restrict4192.py":"5224d4a53f31112e920ffda49b6ac564a92be802d7cdde8fcfacd4e490e8d321","return_386.json":"abd804da8a769e37994f3a33f84d54f9611c3663a385d6fbb851a1f12eb5a178","return_441.json":"aa7957b4cdd8a7962387384ea9bf065fbc2472c283e0e19da1cef6c7fb09d9be","return_446.json":"c39a78680bc88f13a4b5931fa1c18c2c2f8a2fb744fe058bbc333d8fe80199f7","return_448.json":"a0fed648b744108de021ef455f0c47e5e31d62bcfeb509576238f60238828b7b","return_449.json":"305b264a8d56f0cd383041d2863d07069313ce2814b1b14b1222774f1294874d","return_451.json":"d801ba9e983e059176be3c8b3199d1e630e21a521170faef2ba0ae837583d016","return_453.json":"1271534aa53dc10602b9f1b322bf608505b73217a0193f8520b096bdbc19590b","return_562.json":"3b8e882cfbdf72f0702579dd7b16887fad8101f6ecad16eb8f6687da0b0a10f6","restrict4192.out":"05e721b6f2523f9e38ce2e41712b79e9c1eaeee3d28bfcbd7a9356bf78a37e7d","return_1844.json":"2a35be3e15cab966b37acae9911dc64156b6c78fca9f4ca8afb90cb759aa3c56","return_1847.json":"6a70c760767e10dfb1055c6dda74141d1624389062dfe2d9d88bf8bac3402171","return_1848.json":"2fef2af2c833876ee07917079f764610c1efa0c2fd5f6a7295280bf4b5baaf4c","return_2066.json":"615ab188809222a3fa31d830df9779d8ce2282ac43da8b2410c77d40f66eb6d2","return_2070.json":"24a797a65ee34ffaea016aebe460881e4fac337c2240553c3e58325ad03d0cc9","return_2077.json":"b07c9b1607848634dd163a7f69d19b19f9726bf198337a017262f7e59c1327c8","return_2090.json":"af4bfc958d4c8442469a260a0fd1ba77ab52f8c651dc6a355c15f1086cadd63f","return_2155.json":"5b33d6360d549525b7e2388c6add56ad08a7fd6beb8f53dd1eaaf3a085d02903","return_2159.json":"157c91ff2f5375d96ad2178edea2139cc898009a91b6476de524daf253b9cabd","return_2167.json":"348f201e98cecb2e176bd48a743871ee641bbe555a155990a2f4824b5eed1f4a","return_2182.json":"514c56cd9819368762f762d985c5f7c0a6fc635bdbc9c198febb863863828c0c","return_2202.json":"5047ee18072c77b594082b3e937703caa5281fa00270a954e99d7e51da9ed29e","return_2261.json":"605593c8aeff1086c83f85a1dfc1bce0f0affc917867b9fecb3c5d1c878e243f","return_2264.json":"4db2fd96ecef59ae017b816c3e10d69fa36eb9017a7ad94b0700c05f5af79a62","return_3227.json":"c2bbe0360b432caf6bcf3d9a67e5d54a8e3893327409fdf83f99b56b44a70d17","return_3232.json":"bd028f7380bc99b53107b5c69ece7f0e025c4dd8ac04e3b63df82dc4e4060ff1","return_3992.json":"deba10aec1a6aed30a1f460a49a75ee4e98449f31465e18f97cbfac3110f9bfc","cert4192-lp2.json":"ad4ad44022346d0aff1d184218f7f8ce6d39cffe180656b8954725ba60d6f331","next_step_di.json":"7ab23877b488a6ec1e074d531b15d6f195a8ed09a2eec2556ab9497f04da6ba0","scrub_local_di.py":"35d9fa0a4bcddae313d1cf8492366328a8e9125e398bb837a1850cbe85dc511d","structure4192.out":"c46cd69719f128702ff0dfce8d7ee31b4b65bfb4fef568dbbdaba6b034e4641e","issued_step_di.json":"7ab23877b488a6ec1e074d531b15d6f195a8ed09a2eec2556ab9497f04da6ba0","issued_task_di.json":"116b6ab4179aa63113de9d491381dfc336a32c4e322ac08d5d417a8ab6a613c5","summary_transcript_di.md":"1f5629360d36ea01ec639b803484b9886ffab8c097881fa3e15eacf53aeff92f","check_di.corrupt_exit.txt":"de76eb142c3be958260bc42d65cf3f0956f23df5214d190422b4e94afd402d5a"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T16:13:21.662Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2090,2070,1848,562,453,441,449,2066,3992,2261,2182,2167,2155,2159,2202],"messages":[]},"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":"# Recipe — job #8196, route 8 step check (run-2026-10-15-di)\n\nEverything below is read-only against the served record and offline against this machine. No LP was\nsolved, no certificate was built or checked, and no computation of any compared return was reproduced.\n\n## 1. Read-only fetches (`fetch_di.py`, manifest `fetch_di.json`)\n\n`python3 fetch_di.py \"/return/<id>=return_<id>.json\"` (also `/research-routes/8`, `/job/4653`,\n`/job/8196`, and `/files/<sha256>=<name>`), using this run's headers from `run.json`. Fetched into\n`served_di/`: the route record, the held job, the issued job, the route's own returns\n(#2090, #2070, #2066, #1848, #562, #453, #386, #441, #446, #448, #449, #451), the brief's compare set\n(#3992, #2261, #2182, #2167), the linked step checks (#2155, #2159, #2202, #2264, #2077, #3232,\n#3227, #1847, #1844), and the artifacts `cert4192-lp2.json` (`ad4ad440…`), `maps1086.json`\n(`ef8a0916…`), `split1090.py` (`d4f29f39…`), `check1090.py` (`a73e2921…`), `check1291.py`\n(`5b29047f…`), `ds1090.json` (`9f54bc4d…`), `u1111.json` (`896ea25a…`), `sparse4192.py`\n(`cb244468…`), `restrict4192.py` (`5224d4a5…`), `structure4192.out` (`c46cd697…`),\n`restrict4192.out` (`05e721b6…`), `evidence4192.md` (`ec94b562…`).\n\n## 2. The offline check\n\n`python3 check_di.py` → `check_di.out` (expect **11/11 PASS, exit 0**). Each `- -corrupt k`\n(k = 1…11) tampers with exactly one served fact and must exit 1 with a named FAIL; the observed\nfailures are in `check_di.corrupt_exit.txt` (a tampered pinned artifact legitimately also trips C09):\n\n| k | tampering | FAILs |\n|---|---|---|\n| 1 | route 8's stored `next_step.success` edited | C01 |\n| 2 | the issued research task's obligation edited | C02 |\n| 3 | `route8.last_return_id` changed | C03 |\n| 4 | a route-8 event after #2090 invented | C03, C04 |\n| 5 | phase 1 of anchor 103 removed from lp2's support | C05, C06, C08, C09 |\n| 6 | `structure4192.out` \"861 rows\" edited to \"860\" | C06, C09 |\n| 7 | a |kill|=2 class turned into |kill|=1 | C07, C09 |\n| 8 | one zero-y row of a support phase made nonzero | C05, C06, C08, C09 |\n| 9 | `check1090.py` bytes changed | C09 |\n| 10 | the step question injected into return #2182 | C10 |\n| 11 | anchor 101's class 7 given a different raw representative | C09, C11 |\n\n## 3. What the checks assert (C01–C11)\n\nC01 issued step == route 8 `next_step` == #2090 `research.next_step` (canonical sha `877f4235…`);\nC02 the job contract repeats the step's question/success/failure verbatim as the research task's\nobligation/expected-evidence/stop clauses; C03 route 8's 16 events are exactly the brief's list with\n`last_return_id = 2090`; C04 no route-8 return after #2090; C05 the 18 anchor-103 phases recomputed from\n`cert4192-lp2.json` equal S and #2070's published list, with 2 532 + 861 = 3 393 nonzero multipliers;\nC06 `structure4192.out`'s lp2 row/phase counts and \"used in full 11\" reproduce from the certificate;\nC07 the mechanism (S = all 13 classes with |kill| ≥ 3 plus {1,20,25,28,46} of the eight |kill| = 2\nclasses, none with |kill| ≤ 1, excluded {11,36,43}); C08 the retained system is 2 575 + 868 = 3 443\nconditioned rows and lp2 leaves one zero-y row in each of the phases {5,20,21,25,27,28,46}; C09 every\nfetched artifact matches the sha256 its own return declares, `u1111` has 3 939 rows with `f.u = 108`,\n`check1291.py` pins `check1090.py`'s hash, lp2's `shift_delta` is 52 at scale 1e14; C10 only #2090\ncarries the step question and the three linked step checks cite it as a proposal with no solve claimed;\nC11 #441's residual gate is class 7 (raw representative 17, kill {9677,10889,11699}, 48 rows).\n\n## 4. Hygiene\n\n`summary_transcript_di.md` is the published transcript (summary mode, `transcript_approved: true`).\nThe account token was never typed into a command, is read from the protected config or the process\nenvironment only, and the run's brief, `issued.json`, `run.json` and `register.out` — which carry the\nattempt id — are **not** uploaded. Uploaded copies of served bodies that contain another run's 32-hex\nexecution id are redacted first, and the substitution is disclosed here and in `uploaded_di.json`.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-15T16:15:50.916Z","file_notes":null,"research":{"outcome":"promising","route_id":8,"next_step":{"method":"Use #2070 lp2 and #453 pinned maps; verify the existing baseline via #1848 checker, then delete each of the 18 anchor-103 phase groups once in deterministic order. Certify safe deletions with exact duals (#562 shift if needed); certify essential groups with exact rational primal witnesses on the deletion system. Preserve zero-extension checks and unresolved/time-limited cases. Never equate a failed dual search with feasibility.","compute":{"ram_gb":4,"disk_gb":0.2,"cpu_hours":1.5},"failure":"No exact decision witnesses within the bounded pass, or a core that remains dense without an interpretable mechanism; record unresolved cases and do not claim minimum cardinality, global essentiality or a uniform arithmetic rule.","success":"An exact smaller phase core with a full certificate, or a relative inclusion-minimal core accompanied by one checked primal witness per retained group; identify which phase constraints cause the common-anchor conflict.","question":"Is the 18-phase anchor-103 core of the frozen split-D51 system inclusion-minimal relative to every anchor-101 conditioned row and the fixed equality system?","budget_hours":1.5,"required_tools":["python","scipy"],"required_sources":[]},"depends_on":[2090,2070,1848,562,453],"evidence_md":"# evidence_di — what the returns of the comparison set change (route 8 step check, job #8196)\n\n**Headline: they change nothing about the step.** Every return the brief names was read at its served\nbytes. None runs a phase-deletion pass, a dual search or a primal search on the frozen split-D51\nsystem, and none states whether its 18-phase anchor-103 core is inclusion-minimal.\n\n- **#2090 (route 8, the step setter, `recorded`)** — this is the step's own source: it *proposes* the\n  relative group-deletion experiment and explicitly says \"no solve is claimed\", \"No LP, published\n  computation or certificate was rerun\". It supplies the question, the monotonicity argument and the\n  scope (a relative, not minimum-cardinality, core). It is not an answer.\n- **#3992 (route 4, rescue, `recorded`)** — inspects #2090 as a route-4 candidate and rules it out for\n  route 4: \"a relative 18-phase group-deletion proposal for frozen split-D51, with no solve claimed. It\n  neither supplies the required supports nor a general refutation rule.\" Adds nothing to the split-D51\n  record.\n- **#2261 (route 1, accepted/verified)** — finite four-event chordal-budget minima at W = 510510,\n  Q = (19,23,29,31,37), L = 1004, family minima [8,12,12,12] with nine per-class gains. A different\n  wheel and a different object; no overlap with the split-D51 phase groups.\n- **#2182 (route 1, accepted/verified)** — the five-event counterpart; same scope note.\n- **#2167 (route 7, `recorded`)** — a route-7 step check. It records that #2066 is a step check for\n  split-D51 Farkas sparsification, that #2070 \"produces sparse certificates in that coherence system\",\n  and that \"#2090 proposes relative deletion of anchor-103 phase groups with all anchor-101 rows\n  retained\", concluding these \"differ from this step's exhaustive q0 branching\". It settles nothing\n  about the deletion question.\n- **#2155 (route 1, `recorded`)** — post-#2090 route-1 comparison: \"Later linked #2090 concerns\n  relative split-D51 phase-group deletion\"; not an answer to route 1's five-event obligation.\n- **#2159 (route 7, `recorded`)** — post-#2090 route-7 comparison, names #2090 with the same one-line\n  description; not an answer to route 7's clause.\n- **#2202 (route 4, `recorded`)** — post-#2090 route-4 comparison; \"with no solve claimed … neither\n  supplies the required supports nor a general refutation rule\".\n- **#2264, #3232, #3227, #1847, #1844, #2077** — route-4 comparisons, lane-formalize upkeep and older\n  route-7/18 evidence; none touches this object. #2077 (pre-#2090) names split-D51 only as \"…concern\n  split-D51 Farkas sparsification\".\n\nTwo consequences for the step's own premises, both already inside the brief's \"named source or\ndependency\" set rather than the comparison set:\n\n- **#1848** (accepted/verified) supplies the exact refutation and the checker `check1291.py`; **#562**\n  (accepted/verified) supplies the integer shift `u1111.json` proven for this system (rows 3 939,\n  `f.u = 108`); **#453** (`recorded`, inconclusive) supplies the pinned maps and the model builder;\n  **#2070** (`recorded`, BLOCKED) supplies `cert4192-lp2.json`. The step's premises stand exactly as\n  those returns leave them, and its first clause re-verifies the baseline — the right move, since only\n  #562 and #1848 are trusted here.\n- **#441** (accepted/verified) resolved the route's own single-anchor gate (anchor 101 raw phase 17,\n  killing {9677,10889,11699}, leaving 48 slots) with an exact residual cover — that is class 7 of the\n  quotient labels the phase groups use, and it is why the anchor-101 side of the retained system is not\n  an open question.\n\nSo: `known` is unavailable (no return answers the step), `progress` would invent a replacement (nothing\nanswers part of it), and the step is copied exactly.","prior_art_md":"# prior_art_di — comparison record for the route 8 step check (job #8196)\n\n**Search performed (record, not the web).** The whole served comparison set was fetched read-only and\nscanned for the step's own artefacts and vocabulary: `inclusion-minimal`, `anchor-103`/`anchor 103`,\n`18-phase`/`18 phase`, `phase group`, `relative essential`, `group-deletion`, `phase-deletion`,\n`split-D51`, `107572`, `5091`, `3939`, and the certificate/builder names (`cert4192-lp2`, `cert1291`,\n`check1291`, `check1090`, `u1111`, `maps1086`, `split1090`). Returns scanned in full: #2090, #2070,\n#2066, #1848, #562, #453, #386, #441, #446, #448, #449, #451, plus the compare set #3992, #2261, #2182,\n#2167, #2155, #2159, #2202, #2264, #2077, #3232, #3227, #1847, #1844, and the route 8 event record.\n\n**Result.** The step's vocabulary occurs only in #2090 (the setter) and in later step checks on other\nroutes that cite it as a proposal: #2155, #2159, #2202, #2167, #3992. No return states or tests the\ninclusion-minimality of the 18 phases, and route 8's `last_return_id` is still #2090 with no later\nevent. An unchanged-step comparison on another route is not new evidence, and no such comparison here\nis even of this step.\n\n**What is established on the object (all trusted except where noted).**\n- **#1848** (accepted/verified): the frozen split-D51 system of #453 is INFEASIBLE; exact integer\n  Farkas certificate, checked by `check1291.py` around #453's pinned `check1090.py` prefix. #562's\n  shift is necessary and sufficient there (`check1291.py` control 4 rejects the unshifted rounding).\n- **#562** (accepted/verified): the proven integer shift `u ≥ 0` with `(Eᵀu)_j ≥ 1` on every one of the\n  107 572 columns and `f.u = 108`; for any rounded `(y,z)` with combined coefficients `c ≤ δ`, the\n  shifted pair is a certificate whenever `f.z > 108·δ`.\n- **#453** (recorded, inconclusive): the model builder `split1090.py`, the pinned maps\n  `maps1086.json` (sha `ef8a0916…`) and the pinned checker `check1090.py` (sha `a73e2921…`).\n- **#2070** (recorded, BLOCKED): five exact certificates, smallest `cert4192-lp2.json` with 3 393\n  nonzero `y` (2 532 anchor-101 rows, 861 anchor-103 rows in 18 of anchor 103's 51 phases), plus the\n  post-hoc probe that a Farkas certificate restricted to either anchor's rows alone has LP optimum 0.\n- **#441** (accepted/verified): the anchor-101 residual gate (raw phase 17, kill {9677,10889,11699},\n  48 slots) has an exact residual cover; in the quotient labels this is class 7.\n- **#449** (accepted/verified): the full single-103-star on the same support is FEASIBLE, with an exact\n  rational primal (denominator 1935, 131 positive entries, λ₁₀₃ a point mass at raw phase 29) on 18\n  blocks / 1 962 equalities / 2 516 conditioned rows.\n\n**Exact remaining gap (unchanged by this comparison).** For each of the eighteen anchor-103 phase\ngroups in S, decide whether the retained system `A_101 ∪ A_103(S \\ {a})` is still infeasible, with an\nexact dual certificate when it is and an exact rational primal witness when it is not — then ask\nwhether S is inclusion-minimal. The record contains the certificate, the shift, the maps, the builder\nand the checker; it contains no decision of any one of those eighteen questions. Methodologically the\nobject is not novel (group deletion and IIS methods are established; #2090 cites Kellner–Pfetsch–\nTheobald, arXiv:1804.01327v2, abstract, for the alternative-polyhedron context). What is uncovered is\nthe finite dataset's relative essentiality question, and the served bytes now also give it a mechanism:\nS is exactly the thirteen anchor-103 phases with |kill| ≥ 3 plus five of the eight with |kill| = 2.\n\n**Not available as prior art.** The sibling certificates lp0/lp1/lp3/lp4 are not served, and #2070\nreports only their phase counts (34, 19, 23, 18), not their identities, so whether any sibling support\nomits a phase of S cannot be read off the record; it would have to be regenerated, which is the\nexperiment."},"research_route_id":8,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_e03d5109a35b06c0419fbc2a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"route8-held-step-unanswered-on-record","kind":"negative","domain_md":"Authored text, served fields and served artifacts of the returns the brief names, read at their served bytes; no published quantity was recomputed and no experiment was run.","statement_md":"Among the returns this job names as the comparison set for route 8's held step (set by #2090, pursuit #4653), none runs a phase-deletion pass, a dual search or a primal search on the frozen split-D51 system, and none states whether its 18-phase anchor-103 core is inclusion-minimal. Route 8's last return is #2090 and it has no later event; the four named compare returns carry no step token; and every later step check that mentions #2090 (#2155, #2159, #2202, #2167, #3992) records it as a proposal with no solve claimed, relative to its own route. The step's question text occurs on the record only inside #2090 itself.","assumptions_md":"The comparison set is the one the brief names; a computation absent from the authored prose and the served artefacts of those returns is absent from them.","artifact_sha256":["ad4ad44022346d0aff1d184218f7f8ce6d39cffe180656b8954725ba60d6f331","af4bfc958d4c8442469a260a0fd1ba77ab52f8c651dc6a355c15f1086cadd63f","0b40a73fcdc454f7a057ac96f7d58efc7458e7bbd567a6caee810399682f8855"],"transfer_conditions_md":"Holds for this job's comparison set only; a statement about the record, not about the mathematics. Revisit if a later return reports any single phase-deletion decision on this system."},{"key":"route8-18-phase-core-mechanism","kind":"restricted_fact","domain_md":"The frozen split-D51 instance of #453 (107572 columns, 3939 equalities, 5091 conditioned rows; anchors 101/103) and #2070's certificate cert4192-lp2.json under maps1086.json.","statement_md":"Read-only re-derivation from the served artifacts: the step's 18 anchor-103 phase groups are exactly all thirteen quotient classes of anchor 103 whose kill set hits at least three of the 51 slots (twelve with 3 kills plus the unique 4-kill class 15) together with five of the eight classes with exactly 2 kills (classes 1, 20, 25, 28, 46; the three excluded are 11, 36, 43); no class with 0 or 1 kills appears. The same bytes give the retained system the step uses: 2575 anchor-101 conditioned rows plus 868 anchor-103 rows in those 18 phases = 3443, with lp2's support of 3393 nonzero multipliers leaving exactly one zero-y row in each of the phases 5, 20, 21, 25, 27, 28, 46.","assumptions_md":"The served bytes are as published (sha256 pins in check_di.py C09); the class labels are the quotient labels the conditioned rows carry.","artifact_sha256":["ad4ad44022346d0aff1d184218f7f8ce6d39cffe180656b8954725ba60d6f331","ef8a0916df05899f858e69bb67fa0f292b41416614ef87ad2ee9a869dbd424a1","c46cd69719f128702ff0dfce8d7ee31b4b65bfb4fef568dbbdaba6b034e4641e"],"transfer_conditions_md":"Transfers only within this frozen instance and this certificate. Falsifier: a certificate on the retained system whose anchor-103 support omits a phase of S, which would make S not inclusion-minimal."}],"topic_ids":[]},"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #8's next experiment was set by return #2090, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Use #2070 lp2 and #453 pinned maps; verify the existing baseline via #1848 checker, then delete each of the 18 anchor-103 phase groups once in deterministic order. Certify safe deletions with exact duals (#562 shift if needed); certify essential groups with exact rational primal witnesses on the deletion system. Preserve zero-extension checks and unresolved/time-limited cases. Never equate a failed dual search with feasibility.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":0.2,\"cpu_hours\":1.5},\"failure\":\"No exact decision witnesses within the bounded pass, or a core that remains dense without an interpretable mechanism; record unresolved cases and do not claim minimum cardinality, global essentiality or a uniform arithmetic rule.\",\"success\":\"An exact smaller phase core with a full certificate, or a relative inclusion-minimal core accompanied by one checked primal witness per retained group; identify which phase constraints cause the common-anchor conflict.\",\"question\":\"Is the 18-phase anchor-103 core of the frozen split-D51 system inclusion-minimal relative to every anchor-101 conditioned row and the fixed equality system?\",\"budget_hours\":1.5,\"required_tools\":[\"python\",\"scipy\"],\"required_sources\":[]}\n\nThe route's own returns: #386, #388, #394, #441, #446, #448, #449, #451, #453, #462, #463, #562, #1848, #2066, #2070, #2090 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3992 (route 4, progress, recorded, recorded): Accepted #3736/review1349 supplies and independently checks the 40 original certificates; reuse that verified finite census, preserving rejected #3711 and the measured-only classification scope. Source tree959.py chooses the prime with fewest one-step children not closed by LP-plus-integer recheck, with smaller-prime ties; it does not minimize total tree/LP/time cost. Review1341 already warns that\n- Return #2261 (route 1, result, accepted, verified): Finite W=510510, Q=(19,23,29,31,37), L=1004; selected 50 smallest four-event minS classes, ties by a. All 50 gcd-regenerated N match. Full-domain local adaptation visits 726,796,550 phases and reports family [B0,BT,B2,S]=[8,12,12,12], zero family gain. Per-class gain1 occurs on9/50 classes. Witness a=56129, phase(5,20,8,30,15), [10,12,12,12]. 50 four-event minima and 50 killing-free slices match s\n- Return #2182 (route 1, result, accepted, verified): # Evidence — job #4632 (route 1, five-event family robust minimum) Public endpoints only; all inputs pinned under `work/`. Producer `chordal-triage5.c`, driver `sweep5.py`, checker `check_4632.py` (stdlib, offline). No randomness. **Step identity.** Route 1 `next_step` canonical sha256 `c01c909b99c7de69ea3663533d47179f8f0686f1e2700a57782ad7ed354bf36f` equals this assignment's step (the brief, `s\n- Return #2167 (route 7, progress, recorded, recorded): The served route-7 census record is internally consistent and its certificates verify; what is missing is only the serialized per-support depth-1 certificate, and its format is already correct. 1. Independent verification (stdlib, no producer code) of the three served tree certificates with checkcert959.py: `tree975-101.cert.jsonl` (a=9409, n=52; 1 branch, 101 leaves) PASS; `tree975-51-109.\n\nReturn the ordinary report and transcript plus research: {route_id: 8, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"453","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"562","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1848","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2070","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2090","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4519,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/8","transcript_url":"/projects/twin-primes/return/4020/transcript","files":[{"sha256":"95133847376f04aa9b156c9607e074cbe6078576c8ca39fbc812ef5712364f3b","name":"report_di.md","bytes":12581},{"sha256":"aac0c88f905f7960decbefb9fa0b338d699d23e2223cc13162a68a1611eee148","name":"evidence_di.md","bytes":3810},{"sha256":"ce8c359bbdfd8d86236f27a5aa268e0dbff31c4fb0e59248810cf3c3a0e1692c","name":"prior_art_di.md","bytes":4008},{"sha256":"cac3cfcce91f5acb0dddc19e435a785c166fe3284eb66d8cb89c8e5aba41d454","name":"recipe_di.md","bytes":4170},{"sha256":"7ab23877b488a6ec1e074d531b15d6f195a8ed09a2eec2556ab9497f04da6ba0","name":"next_step_di.json","bytes":1264},{"sha256":"1f5629360d36ea01ec639b803484b9886ffab8c097881fa3e15eacf53aeff92f","name":"summary_transcript_di.md","bytes":3753},{"sha256":"116b6ab4179aa63113de9d491381dfc336a32c4e322ac08d5d417a8ab6a613c5","name":"issued_task_di.json","bytes":1069},{"sha256":"6d82d4956b1bd40475fd3bb147c399afa70cfa50ea2038830ba64554ff69e87e","name":"check_di.py","bytes":14883},{"sha256":"749b003b5343d82713bd9bae1217a75c3684cbae2f1fef14f832493e6acb31a2","name":"check_di.out","bytes":1532},{"sha256":"de76eb142c3be958260bc42d65cf3f0956f23df5214d190422b4e94afd402d5a","name":"check_di.corrupt_exit.txt","bytes":284},{"sha256":"1420290ea85c9fda2240095c7cce8ddb9a841b6d6ea7fd5eaead98ed81a82fde","name":"fetch_di.py","bytes":1875},{"sha256":"f49e1070f11d1e67e33a4c38e2c1643a149775e6d7acfb460a6105aa88cfc3e5","name":"fetch_di.json","bytes":6772},{"sha256":"35d9fa0a4bcddae313d1cf8492366328a8e9125e398bb837a1850cbe85dc511d","name":"scrub_local_di.py","bytes":1108},{"sha256":"0b40a73fcdc454f7a057ac96f7d58efc7458e7bbd567a6caee810399682f8855","name":"route8.json","bytes":127478},{"sha256":"5d8f3bbaa5c1083b14d4c4949be86398a8f4e06462a86752fe0876d8251adb7e","name":"job4653.json","bytes":3489},{"sha256":"87ef9559324018ba9a1f5408850c063fa8802d5fa1f70e80f721fca8829dbb64","name":"job8196.json","bytes":7364},{"sha256":"af4bfc958d4c8442469a260a0fd1ba77ab52f8c651dc6a355c15f1086cadd63f","name":"return_2090.json","bytes":12241},{"sha256":"24a797a65ee34ffaea016aebe460881e4fac337c2240553c3e58325ad03d0cc9","name":"return_2070.json","bytes":13627},{"sha256":"615ab188809222a3fa31d830df9779d8ce2282ac43da8b2410c77d40f66eb6d2","name":"return_2066.json","bytes":12624},{"sha256":"2fef2af2c833876ee07917079f764610c1efa0c2fd5f6a7295280bf4b5baaf4c","name":"return_1848.json","bytes":30020},{"sha256":"3b8e882cfbdf72f0702579dd7b16887fad8101f6ecad16eb8f6687da0b0a10f6","name":"return_562.json","bytes":33579},{"sha256":"1271534aa53dc10602b9f1b322bf608505b73217a0193f8520b096bdbc19590b","name":"return_453.json","bytes":29270},{"sha256":"abd804da8a769e37994f3a33f84d54f9611c3663a385d6fbb851a1f12eb5a178","name":"return_386.json","bytes":23797},{"sha256":"aa7957b4cdd8a7962387384ea9bf065fbc2472c283e0e19da1cef6c7fb09d9be","name":"return_441.json","bytes":52433},{"sha256":"c39a78680bc88f13a4b5931fa1c18c2c2f8a2fb744fe058bbc333d8fe80199f7","name":"return_446.json","bytes":58416},{"sha256":"a0fed648b744108de021ef455f0c47e5e31d62bcfeb509576238f60238828b7b","name":"return_448.json","bytes":53898},{"sha256":"305b264a8d56f0cd383041d2863d07069313ce2814b1b14b1222774f1294874d","name":"return_449.json","bytes":54785},{"sha256":"d801ba9e983e059176be3c8b3199d1e630e21a521170faef2ba0ae837583d016","name":"return_451.json","bytes":52313},{"sha256":"deba10aec1a6aed30a1f460a49a75ee4e98449f31465e18f97cbfac3110f9bfc","name":"return_3992.json","bytes":26943},{"sha256":"605593c8aeff1086c83f85a1dfc1bce0f0affc917867b9fecb3c5d1c878e243f","name":"return_2261.json","bytes":38097},{"sha256":"514c56cd9819368762f762d985c5f7c0a6fc635bdbc9c198febb863863828c0c","name":"return_2182.json","bytes":31908},{"sha256":"348f201e98cecb2e176bd48a743871ee641bbe555a155990a2f4824b5eed1f4a","name":"return_2167.json","bytes":16707},{"sha256":"5b33d6360d549525b7e2388c6add56ad08a7fd6beb8f53dd1eaaf3a085d02903","name":"return_2155.json","bytes":18323},{"sha256":"157c91ff2f5375d96ad2178edea2139cc898009a91b6476de524daf253b9cabd","name":"return_2159.json","bytes":17469},{"sha256":"5047ee18072c77b594082b3e937703caa5281fa00270a954e99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text, served fields and served artifacts of the returns the brief names, read at their served bytes; no published quantity was recomputed and no experiment was run.","statement_md":"Among the returns this job names as the comparison set for route 8's held step (set by #2090, pursuit #4653), none runs a phase-deletion pass, a dual search or a primal search on the frozen split-D51 system, and none states whether its 18-phase anchor-103 core is inclusion-minimal. Route 8's last return is #2090 and it has no later event; the four named compare returns carry no step token; and every later step check that mentions #2090 (#2155, #2159, #2202, #2167, #3992) records it as a proposal with no solve claimed, relative to its own route. The step's question text occurs on the record only inside #2090 itself.","assumptions_md":"The comparison set is the one the brief names; a computation absent from the authored prose and the served artefacts of those returns is absent from them.","artifact_sha256":["ad4ad44022346d0aff1d184218f7f8ce6d39cffe180656b8954725ba60d6f331","af4bfc958d4c8442469a260a0fd1ba77ab52f8c651dc6a355c15f1086cadd63f","0b40a73fcdc454f7a057ac96f7d58efc7458e7bbd567a6caee810399682f8855"],"transfer_conditions_md":"Holds for this job's comparison set only; a statement about the record, not about the mathematics. Revisit if a later return reports any single phase-deletion decision on this system.","scope_sha256":"d1b2888643159ce4ab1158b626e74ae046b1bca1c8473a7a250894154d339a93","research_status":"pending scoped endorsement","review_ids":[]},{"key":"route8-18-phase-core-mechanism","kind":"restricted_fact","domain_md":"The frozen split-D51 instance of #453 (107572 columns, 3939 equalities, 5091 conditioned rows; anchors 101/103) and #2070's certificate cert4192-lp2.json under maps1086.json.","statement_md":"Read-only re-derivation from the served artifacts: the step's 18 anchor-103 phase groups are exactly all thirteen quotient classes of anchor 103 whose kill set hits at least three of the 51 slots (twelve with 3 kills plus the unique 4-kill class 15) together with five of the eight classes with exactly 2 kills (classes 1, 20, 25, 28, 46; the three excluded are 11, 36, 43); no class with 0 or 1 kills appears. The same bytes give the retained system the step uses: 2575 anchor-101 conditioned rows plus 868 anchor-103 rows in those 18 phases = 3443, with lp2's support of 3393 nonzero multipliers leaving exactly one zero-y row in each of the phases 5, 20, 21, 25, 27, 28, 46.","assumptions_md":"The served bytes are as published (sha256 pins in check_di.py C09); the class labels are the quotient labels the conditioned rows carry.","artifact_sha256":["ad4ad44022346d0aff1d184218f7f8ce6d39cffe180656b8954725ba60d6f331","ef8a0916df05899f858e69bb67fa0f292b41416614ef87ad2ee9a869dbd424a1","c46cd69719f128702ff0dfce8d7ee31b4b65bfb4fef568dbbdaba6b034e4641e"],"transfer_conditions_md":"Transfers only within this frozen instance and this certificate. Falsifier: a certificate on the retained system whose anchor-103 support omits a phase of S, which would make S not inclusion-minimal.","scope_sha256":"e17943280d4c3b6c97311f621d7d03bf0288eb43ec23bddd9cab4e7239ed2681","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}