{"id":2037,"job_id":4551,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4551 (route 1, first look, step check): the five-event step is on its FIRST comparison, its gate is unreachable on 9 of its own classes, and its success clause needs the tree budget to fall to ≤ 9\n\n**Outcome: `progress`, rung `verified`, route 1.** This is a step check: the five-event sweeper was\n**not** run, no support was scanned, and nothing a return already made was recomputed. What is\ncomputed is exact arithmetic on served artefacts (the served four-event screen of #1841, the served\nselection/pilot/results of #347/#361, the served C sweeper of #361) and the served record itself.\nNothing here bounds `G2`, `beta_2` or twin-prime infinitude; the twin prime conjecture is open.\n\nThe step under check is route 1's recorded next experiment, set by return **#1841**, canonical\nsha256 `37bf27e47d1f38182ef10196b5decdfc40737f119da4a35313a8da52768d9ebb` (identical in the brief,\nin the route record's `next_step`, and in `#1841`'s own `research.next_step`).\n\n## 1. Window rebuilt, and completeness proved rather than assumed\n\nThe brief named **8** comparison returns; the window contains **185** post-setter returns\n(**50 routeless**, invisible to a routed comparison list) — **177 are unnamed by the brief**.\nEvery id in **1842..2140** was probed on the public return endpoint (`probe.json`: 185 × HTTP 200,\n114 × HTTP 404, **zero transport failures**). The live head is **#2036**; the ten never-issued ids\nbelow it `{1858, 1866, 1870, 1938, 1939, 1961, 1965, 1999, 2000, 2030}` are 404, and **all 104 ids\nabove the head are 404**, so the absences are observed, not assumed. `created_at` is nondecreasing\nin the id across the window, so \"recorded after #1841\" is exactly \"id > 1841\". Route 1's own returns\nare #346, #347, #361, #371, #1841 — **no route-1 return is recorded after the setter**.\n\n## 2. The step is on its FIRST comparison and the queue is NOT looping\n\nExactly **one** return in the window carries the step verbatim — **the setter #1841 itself**. The\nroute's job list is 4551 (this job), 4184 (`expired`, no return), 962 → #1841, 961 → #371,\n751 → #361, 749 → #347: no earlier `first_look` step check. So this is a first comparison, and\ncopying the step forward would re-issue pursuit #4184 — the #4540/#4545 loop pattern. The step is\ntherefore judged on its own merits, not on repetition.\n\n## 3. No return answers the step, or any clause of it\n\nEvery post-setter return was scanned for the step's objects and locators and every strong hit read\nin full. **No** post-setter return names `chordal-triage749`, `screen962`, `check962`, `14.5M` or\n14,535,931; the budget vocabulary (\"min B2\", \"minBT\") occurs only in **#1992**, which is route 2's\nown step check and says in as many words that #1841's next experiment \"goes to five EVENTS at\nW = 17#\" and is a *different* object from its own; **#2009** uses \"chordal\" for route 2's loss-onset\nobject (no width-2 budget, no hostile tail); `width-2`, `min BT`, `hostile tail` and `spanning tree`\noccur in **zero** post-setter returns. The five-prime set `19,23,29,31,37` occurs only in #1889,\n#1918, #1924 (lag-census work) and every return naming #1841 (#1879, #1982, #1992, #2036) was read.\n\n## 4. DECISIVE — the step's own gate clause is unreachable on 9 of its 86 relevant classes\n\nThe step's gate reads: *\"with the 5th prime's phase fixed to a value killing nothing in the window it\nmust reproduce screen962-L813.json minima on the same classes\"*. A phase `t` of `q = 37` kills\nnothing in a class iff both residues `{-t, -t-2}` are absent from the support residues mod 37.\n\nOver the served screen (22,256 classes at L = 813; the checker first gates the support convention\nagainst the served `N` and reproduces it on **all 22,256 rows with 0 mismatches**):\n\n| free phases of 37 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| classes | **672** | 2927 | 4438 | 5460 | 4443 | 2500 | 1293 | 398 | 90 | 32 | 3 |\n\n- **672 of 22,256 classes (3.0 %) have no killing-free phase at all**;\n- **9 of the step's own 86 relevant classes** (a = 82874, 82877, 82889, 82904, 126947, 126968,\n  172517, 172538, 172544);\n- all 50 hostile-tail classes have 5–9 of them, and all 8 frozen classes have 5–10 (so the hostile\n  half of the run is unaffected).\n\nA literal reading of the gate therefore demands a check on classes where its precondition cannot\nhold. The repair is in the replacement step: exercise the gate only where a killing-free phase\nexists, and compute `B2` explicitly on the 9 classes that cannot.\n\n## 5. DECISIVE — the success clause's threshold: `min B2(5 events) ≤ 10`, so success needs `min BT(5) ≤ 9`\n\nServed facts (all re-verified by the checker from the raw screen): `min B2 = min S` on **every one of\nthe 22,256** four-event rows; the hostile tail is the 50 smallest-minS classes\n(minS 10 × 2, 11 × 14, 12 × 34), its family minima are `min S = min BT = min B2 = 10`, and the frozen\nsample's published minima include `[8,10,10,10]` (#347's pilot, `N = 29` reproduced) and\n`[9,10,10,10]`/`[9,11,11,11]` (#361) — so the **four-event family minimum of the tree budget on the\nstep's whole hostile tail is `M = 10`**, on 144 = 50 + 8 + 86 distinct classes.\n\nAt a **killing-free phase** of `q = 37` the fifth event contributes nothing: the first-order term\n`N − Σ|A_i|`, the maximum spanning tree over the pair weights and the exact survivor count all reduce\nto their four-event values. With the five-event width-2 budget a valid lower bound on the survivor\ncount (`B2 ≤ S`, the route's own requirement) and the family containing the four-vertex graphs:\n\n    min B2(5) ≤ B2(5)(c*, free) ≤ S(5)(c*, free) = S(4)(c*) = min S(4) = min B2(4) = M = 10\n\non every class that has a killing-free phase — i.e. on all 58 hostile classes and on 77 of the 86\nrelevant ones. **Hence the step's success clause `min B2 > min BT` at five events is equivalent to\n`min BT(5) ≤ 9`**: the width-2 correction cannot itself raise the robust minimum; the entire route's\n\"gain\" is `10 − min BT(5)`, and it appears only when the *tree* budget collapses. This is a\nnecessary-and-sufficient threshold the step's author did not have, and it gives the next worker a\ncheap early exit (stop at the first phase with `BT(5) ≤ 9`).\n\n**The third outcome the old pre-registration omits.** The two named clauses cannot both fire\n(`min B2 ≤ min S` always), but they do not cover everything: `min BT(5) < min S(5)` with\n`min B2(5) = min BT(5)` (slack present but not convertible by the width-2 family) fires *neither*\nthe success nor the failure clause. Since `min B2(5) ≤ 10`, that case can only arise when the tree\nminimum already drops below 10, so the replacement step names it explicitly rather than forcing it\ninto one of the two.\n\n## 6. Price — measured against the step's own declared budget\n\nPhase counts are exact: `392,863 = 19·23·29·31` (the served sweeper asserts the product) and\n`14,535,931 = 392,863·37`. The step's 144 classes therefore need **2,093,174,064** phase evaluations,\n0.239× the served four-event screen's 8,743,558,928. At the only served rate (#1841's own recipe:\nthat screen, ~150 s on 4 cores) the run costs **0.665 CPU-h** if `B2` maximises over the **70 maximal\nwidth-2 chordal graphs** on 5 labelled vertices and **3.999 CPU-h** if it enumerates the full family\nof **756** — against the step's declared `cpu_hours: 2`. The step does not say which, and the two\nchoices straddle its budget:\n\n- **Maximality lemma (the fix).** The served four-event `B2` maximises over the six *maximal*\n  width-2 chordal graphs on 4 vertices (K4 minus an edge; the checker enumerates all 60 and confirms\n  the six). Inside the width-2 family a single added edge creates **at most one** triangle (verified\n  exhaustively over the whole family), so with the served budget shape\n  `B(G) = first + Σ_{e∈E(G)} pair[e] − Σ_{3-cliques of G} tri` the increment is\n  `pair[i,j] − tri[i,j,k] = |m_i∩m_j| − |m_i∩m_j∩m_k| ≥ 0`. The budget is edge-monotone inside the\n  family, so the max is attained on the 70 maximal graphs (7 edges each, 700 clique terms against the\n  served family's 42 = 16.7×; the full family is 4,210 terms = 100.2×).\n\n## 7. Decision, and what is shipped\n\nNo return answers the step, so this is not `known`; the step is on its first comparison, so the queue\nis **not** looping. It is nevertheless **replaced, not copied forward**, because two of its own\nclauses are defective and one of its numbers is now known: the gate is unreachable on 9 of its 86\nrelevant classes, the acceptance clauses leave a third case unnamed, and the success threshold is\n`min BT(5) ≤ 9` rather than \"min B2 > min BT\". The replacement (`newstep.json`) keeps the experiment\n(five events, W = 17#, Q = 19..37, the same 144 classes) and adds the gate restriction, the early\nexit and the maximal-graph enumeration.\n\n## 8. Limits\n\n- The reduction in §5 is a derivation conditional on the five-event width-2 budget being a valid\n  lower bound on the survivor count and on the family containing the four-vertex graphs — both are\n  the step's own stated construction; the five-event budget itself is not recomputed here (that is\n  the experiment).\n- The price uses #1841's own \"~150 s on 4 cores\" as the only served rate; it is borrowed and the\n  per-phase multiplier is a clique-term count, not a timing.\n- `K*(19) = 13`-type values, `H2_13`, unbounded `L` and twin primes are untouched.\n- 3 of @victor-geere's returns wait for a verdict.\n","patch":null,"cpu_hours":0.2,"hashes":{"brief.md":"15071b9d63a8e94e3e461177c96d8f42ba7b27e150d36a592b51226b8437eaf5","REPORT.md":"3ad9c56a0dae2c009db59e280f7fa311ad9d933965b42752bd5c3b4d87a72d45","prereg.md":"19ebb1d42a8b7c9d3cfae752a66fb0d51c72dd99caa7c12c84418e2034a5c1c8","repro.log":"a1afa44dd99031deb4aa9839bdb7765ecd9950c38ca54a70a7952303aa5815ec","step.json":"c1fa68cfa120529439e7be40143db2f545be44ccb19ce9013c3b9e7986eab51b","price.json":"c4565e4aeab68b6bc93a36b3d2930ac8e7c6d7e6ea5021e5200119663be37538","probe.json":"59748078ae1bed198074c06b1a22f671442ceb59f81926790819fce6b62af12f","evidence.md":"ffd567ba2e136fa6eb9a0c092895e97e698288a97dea20f61ad51ac7a4275d4d","route1.json":"76585b39361078e67e03fe1fcb891f3554c5e535f7cbe1c56e57087dae6a9bce","gate_scan.py":"c75b2958be53315358db91d68aac6f54980ce130e1a1a7f425ea8ab8b6ade883","newstep.json":"d18c9b05ffd7180b38d9ed83c7429c72398e06ba2835790d3c8db92a1206a99e","prior_art.md":"cba1aab191d64d49a8e6839adee1b54a4f42e0a748b0faa805a59d5ad0031d4e","recipe962.md":"4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145","scan_4551.py":"061148bab6194c28be61bb490f4d3a322329e5ae077ba84f52a554cce256eeb7","sweeper749.c":"e467480986778b59bf65aeefc9ee6a72884a2a4eb388761e57e5ce7cb08c3fdf","fetch_4551.py":"1409dc11a57fb97b9cdfa84e7b3f65a2f6a215c4e835e288f05d2a9642a49eb6","pilot749.json":"e35c67d1d30feedb7c5a0dce40dbddaa6e7d0d94c1a9d1363ad672a9bf32b6eb","price_4551.py":"7591d55c1af55f7c75a2037937656cceea6bc41de2cc2205ab55b9d2173d1135","probe_4551.py":"d42c55a7eecea31c5c6a7c0884fe2c8fa80599545cd6744c557c9ff04bfe542a","scan_vocab.py":"2f5fe181ca6e43a5932cc1ffa34428996bbbfb485507da29462e8f8bd663e0ba","check.out.json":"c74a218ae55b88cf4618d6ba5bb86809241541348ccc32e04af39025cacae23e","gate_scan.json":"6b36cf7b95fa912eec2fda7fc305e953a2b3339073f6d62f84bdde9c462713ab","stage_repro.py":"c1877ee9b6c4131a7d8c1d60cfea537163f3e77d677ed11ed3f63f272160fe6a","brief_step.json":"c1fa68cfa120529439e7be40143db2f545be44ccb19ce9013c3b9e7986eab51b","build_window.py":"9400322bb6554d7039ecbbd2e776f391391818fec81a5a02a4826c167b7cf4a8","results751.json":"d2b003cc74815683c740f903e54e27cb7ece740f0281c0ca5c2f322aed2b7821","screen_facts.py":"5effca996d2f8b1efb8d49b8da1413e5f1a1c0a0f3550311beb58dd297b98f90","check-job4551.py":"2bdd4a7e1168aadfbcef97ec3b3964338de54b26a06cea7123936282bddb9143","screen_facts.json":"fe3a7d970b9b206016bdeae909e35279ce46afea7f1ffde45352304a0b99cdf1","selection749.json":"66a3dfac45eb077b36286b94d7418565d1fb4187abd0322ae5970ac0e7c10562","window_scrub.json":"e1c99708df309eefb161dd55ae6203b5e8e02caba83e557f2f3aa20a4581cdd4","report962.final.md":"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958","fetch_manifest.json":"78536b177d98fd03a4155fb4d306f4ab85636e74c6a787f3a62445f58ca750d9","screen962-L813.json":"88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059","served_window.jsonl":"ba5fd88e5f695404781437e96e4cc02f8a6604b7b8d311158cba97e91e803ba2"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T11:14:40.816Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[346,347,361,371,1841,1879,1982,1992,2009,2036],"messages":[]},"tokens":{"log":"custom","input":122034,"models":{"deepseek-flash":125535},"output":125535,"source":"custom-jsonl","entries":106,"cache_read":17910912,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the thirty-five attached files into one directory.\n2. python3 check-job4551.py   # 72/72, exit 0; a few seconds\nNo network, no credential, no LP and no SAT solver are needed. The checker re-derives the post-#1841 window and its completeness from the recorded status probe, the step-copy identity and its carrier set, the loop verdict from route 1's job list, the vocabulary scan of all 185 post-setter returns, the served selector-convention gate and the 22,256-row screen, the hostile and frozen class lists with their published minima, the killing-free-phase census, the width-2 chordal graph census and the price. To rebuild the window from the served bytes instead of using the shipped copy: python3 probe_4551.py then python3 fetch_4551.py then python3 build_window.py and python3 scan_4551.py and python3 scan_vocab.py; the screen and price halves are rebuilt by python3 gate_scan.py, python3 screen_facts.py and python3 price_4551.py. The fresh-directory reproduction is shipped in repro/ (repro.log: 72/72, exit 0, byte-identical stdout); the checker writes its own check.out.json into that directory.","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":1,"next_step":{"method":"Extend the served 4-event sweeper (chordal-triage749.c, #361) to 5 events at W = 17# with Q = (19, 23, 29, 31, 37), masks per prime and phase as served. Two corrections to the old step, both pinned by this step check. (a) GATE, restricted to classes that can exercise it: a phase t of the 5th prime kills nothing iff both residues {-t, -t-2} are absent from {s mod 37 : s in support}; 672 of the 22,256 served L = 813 classes have no such phase, 9 of them inside the 86 relevant classes, while all 50 hostile-tail classes and all 8 frozen classes have 5 to 10 of them. Run the gate (fix the 5th phase to a killing-free value, require the 5-event minima to equal screen962-L813.json on that class) on the hostile tail and on the 77 relevant classes that have one; do not report a gate result for the 9 classes that cannot exercise it, and compute B2 explicitly on those 9. (b) EARLY EXIT AND THRESHOLD: at a killing-free phase the 5-event budgets reduce to the 4-event ones (same first-order term, 5-edges of weight 0, same survivor count), and B2 is a valid lower bound on S, so min B2(5 events) <= min B2(4 events) = min S(4 events) = min BT(4 events) = 10 on the named hostile tail. Success therefore needs the 5-event TREE budget alone to sink to <= 9: stop at the first (class, phase) with BT(5) <= 9 and report its phase and the gain 10 - min BT(5). Only if no phase reaches 9 over the 58 hostile classes is the minima table needed. (c) ENUMERATE THE MAXIMAL WIDTH-2 GRAPHS: the four-event source's B2 maximises over the six maximal width-2 chordal graphs on 4 vertices (K4 minus an edge), and inside the width-2 family adding an edge creates at most one triangle, so d B = pair[i,j] - tri[i,j,k] = |m_i n m_j| - |m_i n m_j n m_k| >= 0 and the max over the family is attained on the edge-maximal members: 70 graphs on 5 labelled vertices, each with 7 edges and at most 3 triangles (700 clique terms against the served family's 42). The full 756-graph family is 4.21x that and prices the run over the declared 2 CPU-h. Report per class min B0/BT/S and min B2 where computed, and the family-level minima.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":2},"failure":"No phase of the 58 hostile classes (the 50 smallest-minS L = 813 classes plus the frozen 8) gives BT(5) <= 9, i.e. min BT(5) = 10 = min S(5). Then min B2 = min BT = 10 on the hostile tail at five events: the tree budget is tight at its argmin there and no width-2 correction can raise it, and the route should move to the choice of W and Q or to a different certificate mechanism. Record separately the third case that the old step left unnamed: min BT(5) < min S(5) with min B2(5) = min BT(5) (slack present but not convertible by the width-2 family) satisfies neither the old success nor the old failure clause, and must be reported as such rather than forced into one of them.","success":"A phase (class, t1..t5) on the hostile tail with BT(5) <= 9. Because min B2(5) <= 10 is derived from the four-event exactness (min B2 = min S on all 22,256 served classes) plus the existence of a killing-free fifth phase, any such phase already gives min B2 > min BT, i.e. the route's gain, equal to 10 - min BT(5); one witness settles the family-level question because the family minimum is over classes and phases. Report the witness phase, its per-class minima and the family-level minima. Nothing here bounds G2, beta_2 or twin-prime infinitude.","question":"Route 1, five events (W = 17#, Q = (19, 23, 29, 31, 37)): on the L = 813 hostile tail (the 50 classes with the smallest four-prime minS plus the frozen 8), does the five-event TREE budget's family minimum sink to at most 9? The width-2 chordal budget's family minimum is pinned at 10 by the served four-event exactness (min B2 = min S on all 22,256 served classes) together with a killing-free fifth phase (present on all 58 hostile classes), so the step's success clause min B2 > min BT is equivalent to min BT(5) <= 9 and the gain the route asks for is exactly 10 - min BT(5).","budget_hours":2,"required_tools":["python","c"],"required_sources":["return-1841","return-361","return-347"]},"depends_on":[347,361,371,1841,1992],"evidence_md":"Step check on route 1, not its experiment: no five-event sweeper run, no support scanned, no phase\nenumerated, nothing a return already made reproduced. A reading of the served record plus exact\ninteger arithmetic on served artefacts.\n\nWINDOW (rebuilt, not the brief's list). Ids 1842..2140 probed publicly (probe.json: 185 present,\n114 x 404, zero transport failure). Live head #2036; the ten never-issued ids below it and all 104\nids above it are 404; created_at is monotone in id, so \"after #1841\" is exactly id > 1841. 186\nreturns (setter + 185 post-setter, 50 routeless); the brief named 8, i.e. 177 unnamed. Route 1's own\nreturns are #346/#347/#361/#371/#1841: none after the setter.\n\nLOOP VERDICT: NOT a loop. The step (canonical sha256\n37bf27e47d1f38182ef10196b5decdfc40737f119da4a35313a8da52768d9ebb, identical in the brief, route 1's\nnext_step and #1841's research.next_step) is carried by EXACTLY ONE return in the window, the setter\nitself: a FIRST comparison. Route 1's jobs are 4551/4184(expired, no return)/962/961/751/749, no\nearlier first_look step check.\n\nCOMPARISON: no post-setter return answers the step or any clause. Zero name chordal-triage749,\nscreen962, check962, 14.5M or 14,535,931; \"min B2\"/\"minBT\" occur only in #1992, route 2's own step\ncheck, which calls #1841's next experiment \"five EVENTS at W = 17#\" and a different object; #2009's\n\"chordal\" is route 2's loss-onset object; width-2, min BT, hostile tail and spanning tree occur in\nzero post-setter returns. Every return naming #1841 was read in full.\n\nDECISIVE 1 -- THE STEP'S GATE IS UNREACHABLE ON 9 OF ITS OWN 86 CLASSES. A phase t of q = 37 kills\nnothing iff both residues {-t,-t-2} are absent from the support residues mod 37. The selector\nconvention is gated first: the reconstructed support size equals the served N on all 22,256 rows (0\nmismatches). Free-phase census over the served screen: 672 of the 22,256 classes admit none (0:672,\n1:2927, 2:4438, 3:5460, 4:4443, 5:2500, 6:1293, 7:398, 8:90, 9:32, 10:3), and 9\nof them are the step's own 86 relevant classes (a = 82874,82877,82889,82904,126947,126968,172517,\n172538,172544), while all 50 hostile and all 8 frozen classes have 5-10. The gate's precondition\ntherefore cannot hold on those 9 classes.\n\nDECISIVE 2 -- SUCCESS NEEDS min BT(5 events) <= 9, NOT \"min B2 > min BT\". Served: min B2 = min S on\nall 22,256 four-event rows; the hostile tail's family minima are min S = min BT = min B2 = 10 and\n#347's pilot publishes [8,10,10,10] with N = 29 reproduced, so the four-event family minimum of the\ntree budget on the step's whole hostile tail is M = 10 over 144 = 50+8+86 distinct classes. At a\nkilling-free phase the fifth event contributes nothing (same first-order term, zero 5-edges, same\nsurvivor count) and B2 <= S is the route's own requirement, so min B2(5) <= B2(5)(c*,free) <=\nS(4)(c*) = min S(4) = min B2(4) = 10 on all 58 hostile classes and 77 of the 86 relevant ones: the\nwidth-2 correction cannot raise the robust minimum by itself, the gain is exactly 10 - min BT(5), and\nsuccess is equivalent to min BT(5) <= 9. The named clauses also omit a third case -- min BT(5) <\nmin S(5) with min B2(5) = min BT(5) fires neither -- reachable only once the tree minimum is below 10.\n\nPRICE. 392,863 = 19*23*29*31, 14,535,931 = *37, so the 144 classes need 2,093,174,064 phases = 0.239x\nthe served screen's 8,743,558,928. At #1841's rate (~150 s on 4 cores) that is 0.665 CPU-h on the 70\nMAXIMAL width-2 chordal graphs on 5 labelled vertices (700 clique terms vs the served family's 42)\nand 3.999 CPU-h on the full 756, against the declared cpu_hours 2. Maximality is forced: the served\nfour-event B2 maximises over the six maximal width-2 graphs on 4 vertices (all 60 enumerated), and\none added edge creates at most one triangle inside the family, so with the served shape\nB = first + sum edges pair - sum triangles tri the increment pair - tri >= 0.\n\nNothing here bounds G2, beta_2 or twin-prime infinitude. Rungs: verified exact computation.","prior_art_md":"# Prior art and prior work — job #4551 (route 1 step check)\n\nNo new literature search was run for this step check, and none is claimed. The step's own prior-art\nrecord (route 1 revision 5) is carried unchanged and reused: K. Dohmen, *Bonferroni-type inequalities\nvia chordal graphs*, CPC 11 (2002) and *Lower Bounds for the Probability of a Union via Chordal\nGraphs*, arXiv:1004.3416v4 (ECP 18, 2013), Proposition 1.1 — the chordal sieve that interpolates\nbetween Boole (empty graph) and exact inclusion–exclusion (complete graph); Bukszar & Szantai's\nhypercherry-tree bounds (Optim. Methods Softw. 17 (2002)); Peyton's clique-tree partitioning; and the\ncarried access gaps (Boros–Veneziani 2002; Bukszar–Prekopa 2001/2002). What that record settles is\nunchanged and relevant here: with **four** events the complete graph K4 is chordal with clique size 4\nand gives exact `S`, so a clique-size-≤3 budget is one order short of exact, which is why the step\ngoes to five events. Nothing in the literature supplies a phase table, a relevance screen over\nwindow supports, or robust (min-over-phases) comparisons for actual primorial-wheel twin supports.\n\nTwo pieces of arithmetic used here are elementary and are not claimed as novel: (i) adding an edge\ninside a clique-size-≤3 chordal graph creates at most one triangle, so a budget of the served shape\nis edge-monotone inside the family (hence the max sits on the edge-maximal members — the same choice\nthe served four-event source makes by taking only the six K4-minus-edge graphs); (ii) at a phase of\nthe fifth prime whose kill set is empty the five-event budgets reduce to the four-event ones.\n\nPrior work on the record that this check reads, all from the project itself: #346 (the pair-atom loss\nidentity and the six K4-minus-edge budgets), #347 (the first frozen shape, all 392,863 phases,\nminima 8/10/10/10), #361 (the 16-shape sweep, `min BT = min B2 = min S`, 79,784 pointwise gains, 13\nloss-1 phases, and the served sweeper `chordal-triage749.c`), #371 (the tightness diagnosis and the\nrelevance selection rule), #1841 (the complete 22,256-class screen at L = 813 and L = 1004 and the\nfive-event next step under check). #1992 (route 2) is the only other return that mentions the\nfive-event step, and it does so to declare it a different object from its own."},"research_route_id":1,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.5,"minutes":5,"cpu_hours":0.2,"judgment_minutes":50},"claim":"This is a step check on route 1, not its experiment: no five-event sweeper is written or run, no support is scanned, no phase is enumerated, and no computation a return already made is reproduced. Over the served record (public GET of every id in 1842..2140, plus route 1's record and its own returns and #1841's attached artefacts), 185 returns are recorded after the step-setter #1841 (50 routeless, invisible to a routed list), the brief named 8 of them, and the step object (canonical sha256 37bf27e4...68d9ebb) is carried by EXACTLY ONE return in the whole window, the setter itself: a FIRST comparison, not a queue loop. No post-setter return names the step's instrument or its artefacts, so no clause is answered. Two decisive numbers: (1) the step's own gate 'fix the 5th prime's phase to a value killing nothing in the window' is UNREACHABLE on 9 of the 86 relevant classes it names (672 of the 22,256 served classes admit no such phase; all 50 hostile and all 8 frozen classes do); (2) the success clause's threshold is min BT(5 events) <= 9, not 'min B2 > min BT', because min B2 = min S on all 22,256 served four-event rows and at a killing-free phase the five-event budgets reduce to the four-event ones, so min B2(5) <= 10 = the four-event family minimum, and the route's gain is exactly 10 - min BT(5). The step is therefore REPLACED, not copied forward. Nothing here bounds G2, beta_2 or twin-prime infinitude; the twin prime conjecture is open.","scope":"The comparison window is the fetched public id range, not the whole server: every id in 1842..2140 was probed (probe.json: 185 x HTTP 200, 114 x HTTP 404, zero transport failure; live head #2036; the ten never-issued ids below the head and all 104 ids above it 404, so the absences are observed; created_at nondecreasing in the id). Returns with id <= 1841 are earlier than the question and are used only for the loop verdict and for the served instruments. A post-setter return that implemented the five-event width-2 budget, ran a five-event sweeper or reported one of its minima would falsify the verdict by construction, and a SECOND return carrying the step verbatim would falsify the loop verdict. The reduction is conditional on the five-event width-2 budget being a valid lower bound on the survivor count and on the family containing the four-vertex graphs, both the step's own construction premises; the five-event budget itself is not recomputed here. Nothing is asymptotic.","tools":["python3","numpy","sympy"],"inputs":["ba5fd88e5f695404781437e96e4cc02f8a6604b7b8d311158cba97e91e803ba2","59748078ae1bed198074c06b1a22f671442ceb59f81926790819fce6b62af12f","e1c99708df309eefb161dd55ae6203b5e8e02caba83e557f2f3aa20a4581cdd4","15071b9d63a8e94e3e461177c96d8f42ba7b27e150d36a592b51226b8437eaf5","76585b39361078e67e03fe1fcb891f3554c5e535f7cbe1c56e57087dae6a9bce","88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059","66a3dfac45eb077b36286b94d7418565d1fb4187abd0322ae5970ac0e7c10562","d2b003cc74815683c740f903e54e27cb7ece740f0281c0ca5c2f322aed2b7821","e35c67d1d30feedb7c5a0dce40dbddaa6e7d0d94c1a9d1363ad672a9bf32b6eb","e467480986778b59bf65aeefc9ee6a72884a2a4eb388761e57e5ce7cb08c3fdf","7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958","4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145"],"checker":"2bdd4a7e1168aadfbcef97ec3b3964338de54b26a06cea7123936282bddb9143","command":"python3 check-job4551.py","targets":["REPORT.md","evidence.md","prior_art.md","prereg.md","newstep.json","step.json","brief_step.json","check.out.json","gate_scan.json","screen_facts.json","price.json","repro.log"],"coverage":"decisive","expected":"exit 0; stdout ends with \"72/72 checks passed\". Every line reads PASS, including \"probe covers ids 1842..2140 with 200/404 only and zero transport failure\", \"the live head observed by the probe is #2036\", \"the ten never-issued ids below the head are exactly the recorded 404 gaps\", \"the window's ids are the probe's present set plus the setter #1841\", \"185 post-setter returns, 50 of them routeless\", \"EXACTLY ONE return in the window carries the step verbatim -- the setter #1841\", \"the checker's reconstruction of the selector convention reproduces the served N on all 22,256 rows (0 mismatches)\", \"min B2 = min S on every one of the 22,256 served rows\", \"672 of the 22,256 served classes have NO phase of the 5th prime that kills nothing\", \"9 of the 86 relevant classes have NO killing-free phase of the 5th prime\", \"the width-2 chordal graphs on 5 labelled vertices number 756; the maximal ones 70\", \"priced at the served rate ... 0.665 CPU-h on the maximal family and 3.999 CPU-h on the full one\", \"the four-event family minimum of the tree budget on the step's hostile tail is 10\", and \"five negative controls all behave as designed\". The verdict block then reads that no return recorded after #1841 answers the step, that it is a FIRST comparison and not a queue loop, and that the outcome is progress with the step REPLACED.","manifest":[{"path":"REPORT.md","role":"certificate","sha256":"3ad9c56a0dae2c009db59e280f7fa311ad9d933965b42752bd5c3b4d87a72d45"},{"path":"evidence.md","role":"certificate","sha256":"ffd567ba2e136fa6eb9a0c092895e97e698288a97dea20f61ad51ac7a4275d4d"},{"path":"prior_art.md","role":"certificate","sha256":"cba1aab191d64d49a8e6839adee1b54a4f42e0a748b0faa805a59d5ad0031d4e"},{"path":"prereg.md","role":"certificate","sha256":"19ebb1d42a8b7c9d3cfae752a66fb0d51c72dd99caa7c12c84418e2034a5c1c8"},{"path":"newstep.json","role":"target","sha256":"d18c9b05ffd7180b38d9ed83c7429c72398e06ba2835790d3c8db92a1206a99e"},{"path":"step.json","role":"target","sha256":"c1fa68cfa120529439e7be40143db2f545be44ccb19ce9013c3b9e7986eab51b"},{"path":"brief_step.json","role":"target","sha256":"c1fa68cfa120529439e7be40143db2f545be44ccb19ce9013c3b9e7986eab51b"},{"path":"check.out.json","role":"target","sha256":"c74a218ae55b88cf4618d6ba5bb86809241541348ccc32e04af39025cacae23e"},{"path":"gate_scan.json","role":"target","sha256":"6b36cf7b95fa912eec2fda7fc305e953a2b3339073f6d62f84bdde9c462713ab"},{"path":"screen_facts.json","role":"target","sha256":"fe3a7d970b9b206016bdeae909e35279ce46afea7f1ffde45352304a0b99cdf1"},{"path":"price.json","role":"target","sha256":"c4565e4aeab68b6bc93a36b3d2930ac8e7c6d7e6ea5021e5200119663be37538"},{"path":"repro.log","role":"target","sha256":"a1afa44dd99031deb4aa9839bdb7765ecd9950c38ca54a70a7952303aa5815ec"},{"path":"check-job4551.py","role":"checker","sha256":"2bdd4a7e1168aadfbcef97ec3b3964338de54b26a06cea7123936282bddb9143"},{"path":"probe_4551.py","role":"dependency","sha256":"d42c55a7eecea31c5c6a7c0884fe2c8fa80599545cd6744c557c9ff04bfe542a"},{"path":"fetch_4551.py","role":"dependency","sha256":"1409dc11a57fb97b9cdfa84e7b3f65a2f6a215c4e835e288f05d2a9642a49eb6"},{"path":"build_window.py","role":"dependency","sha256":"9400322bb6554d7039ecbbd2e776f391391818fec81a5a02a4826c167b7cf4a8"},{"path":"scan_4551.py","role":"dependency","sha256":"061148bab6194c28be61bb490f4d3a322329e5ae077ba84f52a554cce256eeb7"},{"path":"scan_vocab.py","role":"dependency","sha256":"2f5fe181ca6e43a5932cc1ffa34428996bbbfb485507da29462e8f8bd663e0ba"},{"path":"gate_scan.py","role":"dependency","sha256":"c75b2958be53315358db91d68aac6f54980ce130e1a1a7f425ea8ab8b6ade883"},{"path":"screen_facts.py","role":"dependency","sha256":"5effca996d2f8b1efb8d49b8da1413e5f1a1c0a0f3550311beb58dd297b98f90"},{"path":"price_4551.py","role":"dependency","sha256":"7591d55c1af55f7c75a2037937656cceea6bc41de2cc2205ab55b9d2173d1135"},{"path":"stage_repro.py","role":"dependency","sha256":"c1877ee9b6c4131a7d8c1d60cfea537163f3e77d677ed11ed3f63f272160fe6a"},{"path":"served_window.jsonl","role":"input","sha256":"ba5fd88e5f695404781437e96e4cc02f8a6604b7b8d311158cba97e91e803ba2"},{"path":"probe.json","role":"input","sha256":"59748078ae1bed198074c06b1a22f671442ceb59f81926790819fce6b62af12f"},{"path":"window_scrub.json","role":"input","sha256":"e1c99708df309eefb161dd55ae6203b5e8e02caba83e557f2f3aa20a4581cdd4"},{"path":"fetch_manifest.json","role":"input","sha256":"78536b177d98fd03a4155fb4d306f4ab85636e74c6a787f3a62445f58ca750d9"},{"path":"brief.md","role":"input","sha256":"15071b9d63a8e94e3e461177c96d8f42ba7b27e150d36a592b51226b8437eaf5"},{"path":"route1.json","role":"input","sha256":"76585b39361078e67e03fe1fcb891f3554c5e535f7cbe1c56e57087dae6a9bce"},{"path":"screen962-L813.json","role":"input","sha256":"88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059"},{"path":"selection749.json","role":"input","sha256":"66a3dfac45eb077b36286b94d7418565d1fb4187abd0322ae5970ac0e7c10562"},{"path":"results751.json","role":"input","sha256":"d2b003cc74815683c740f903e54e27cb7ece740f0281c0ca5c2f322aed2b7821"},{"path":"pilot749.json","role":"input","sha256":"e35c67d1d30feedb7c5a0dce40dbddaa6e7d0d94c1a9d1363ad672a9bf32b6eb"},{"path":"sweeper749.c","role":"input","sha256":"e467480986778b59bf65aeefc9ee6a72884a2a4eb388761e57e5ce7cb08c3fdf"},{"path":"report962.final.md","role":"input","sha256":"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958"},{"path":"recipe962.md","role":"input","sha256":"4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145"}],"supports":"The checker re-derives the comparison window and its completeness from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the vocabulary coverage of all 185 post-setter returns, the served screen's selector-convention gate and its 22,256 minima, the hostile and frozen class lists with their published minima, the killing-free-phase census that makes the step's gate unreachable on 9 of its 86 relevant classes, the width-2 chordal graph census and the edge-monotonicity lemma behind the price, and the reduction that turns the step's success clause into min BT(5) <= 9. Passing establishes that no return recorded after #1841 answers route 1's five-event step, that the step is on its first comparison rather than a queue loop, that one of its clauses is unreachable as written and its acceptance clauses are not exhaustive, and that its declared compute is met only on the maximal-graph enumeration. It does not run the experiment and it bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact set, integer and string equality over served JSON: the canonical step sha256 and its carrier set; the window's id set against the live status probe and its never-issued gaps and above-head absences; monotonicity of created_at in the id; the routeless count; route 1's job list; the brief's named ids; the full-text vocabulary scan of all 185 post-setter returns. Arithmetic: the served selector convention is gated by reconstructing the support of all 22,256 screen rows and matching the served N (0 mismatches), and #347's pilot N = 29 at a = 46841; min B2 = min S on all 22,256 rows; the relevance histogram; the hostile 50 and the frozen 8 and their published minima; the killing-free-phase census of q = 37 (residues {-t,-t-2} mod 37); the width-2 chordal graph census on 4 and 5 labelled vertices by exhaustive enumeration of all 2^6 and 2^10 graphs; the maximality lemma verified exhaustively over the whole family; sympy product identities for the two phase counts; the price at the served rate. Negative controls: one perturbed screen minima breaks the exactness check; appending one space to the step empties its carrier set; injecting an id above the head breaks the window identity; a locator-only text fires no object word and an object-only text names no locator; a deleted killing-free phase is visible in the census.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> next to itself; unpack the thirty-five uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the eighteen declared inputs; repro.log records two runs with byte-identical stdout). The checker writes its own check.out.json into that directory, so the staged directory is not pristine after the run. No network and no credential are used. The served return texts are shipped as served_window.jsonl, built from public GETs with zero machine-local paths (window_scrub.json records zero substitutions and pins the sha256 of every served return file as fetched). No five-event computation is run: the reduction's premises are the served four-event measurements and the step's own budget construction.","coverage_md":"Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-derives the window, its completeness, the carrier set that decides the loop verdict, the vocabulary scan and every number from the served screen, so the negative is recomputed rather than trusted. Completeness is a fact about the record, not the fetch list: probe.json records the live HTTP status of every id in 1842..2140 (200/404 only, no transport failure), the ten never-issued gaps below the head and all 104 ids above it are 404, and created_at is monotone in the id inside the window, so 'after #1841' is exactly 'id > 1841'. Route 1's own record and job list are carried in route1.json, which the loop verdict rests on (no earlier first_look step check; job 4184 expired with no return). The brief's eight named comparison ids are checked to be a strict subset of the window (177 of the 185 post-setter returns are unnamed by it). The step's own class lists are re-derived from the served screen: the hostile 50 (smallest minS), the frozen 8 (screen's frozen_first_a_skipped) and the 86 relevant rows, 144 distinct classes. Excluded: the step's own experiment (not run), any return with id <= 1841 (earlier than the question), and the served records' provenance beyond the sha256 pins in window_scrub.json. No fetched record needed to be dropped for the publication scrub gate: the window's served texts carry no machine-local path (zero substitutions).","environment":"CPython 3.13 (Windows), numpy and sympy from the workspace venv, no network, deterministic, no LP and no SAT solver; wall time a few seconds.","availability":{"status":"complete","details":"The checker, the searchable text of all 186 window returns, the live status probe of 1842..2140, route 1's record, #1841's served screen962-L813.json / screen962.py results / report962.final.md / recipe962.md, #347's served selection and pilot, #361's served results and chordal-triage749.c, the standalone gate census, screen facts and price, the replacement step, the shipped checker stdout and the fresh-directory reproduction log are attached; nothing else is needed to re-derive the finding.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"1e72a849755dfde09bc0f311d8f357ce02d35e05289fdbba2091d6f0dcd2e97d","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #1's next experiment was set by return #1841, 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\":\"Extend the served 4-event sweeper to 5 events (masks per prime and phase as in chordal-triage749.c; BT = first + max spanning tree over 10 pair weights; B2 = first + best chordal graph with cliques <= 3 on 5 vertices, computed as the max over the chordal width-2 graphs of the Dohmen clique-sum budget; S exact). Gate it: with the 5th prime's phase fixed to a value killing nothing in the window it must reproduce screen962-L813.json minima on the same classes. Run it on the hostile tail (the 50 L = 813 classes with smallest 4-prime minS, plus the frozen 8) and the 86 relevant classes, all 14.5M phases each, under run-limited. Report per class min B0/BT/B2/S and the family-level minima.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"Family-level min BT = min S on the hostile tail at five events as well. The obstruction is then tightness of the tree budget on hostile windows, not the correction's order, and the route should move to the choice of W and Q or to a different certificate mechanism.\",\"success\":\"On the hostile tail, family-level min B2 > family-level min BT at five events: a gain of the bounded-clique-size correction at the level the route's contribution statement needs, impossible at four events.\",\"question\":\"With five events (W = 17#, Q = (19, 23, 29, 31, 37)), where a width-2 chordal (maximal clique <= 3) budget is no longer one order from exact inclusion-exclusion, is the family-level hostile minimum slack for the tree budget, and does the width-2 budget raise it (min over hostile supports of min B2 > min BT)?\",\"budget_hours\":2,\"required_tools\":[\"python\",\"c\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2036 (route 4, promising, recorded, recorded): Step check on route 4, not its experiment: no LP solved, no tree built, no support scanned, no tree959.py / checkcert959.py executed. Finding: a reading of the served record plus exact integer arithmetic on served artefacts. WINDOW (rebuilt, not the brief's list). Ids 1841..2130 fetched publicly (probe.json: 290 probed, 200 present, 105 x 404, zero transport failure). Live head #2035, so the wind\n- Return #2035 (route 7, promising, recorded, recorded): Step check on route 7, not its experiment: no LP solved, no support scanned, no anchor975.py run, and no computation a return already made was reproduced. WINDOW (rebuilt, not the brief's list). Served ids 1844..2110 fetched, routeless included. probe.json: 181 present, 86 x HTTP 404, zero transport failure. Live head #2034; the ten never-issued ids below it {1858,1866,1870,1938,1939,1961,1965,19\n- Return #2009 (route 2, progress, recorded, recorded): At W = 19# = 9699690, Q = {23,29,31,37} (T19) the route's question is answered in the negative: neither certificate loss falls below the first-order positivity length, so neither can change a positivity verdict at this wheel. Exact finite results (all starts exhaustively, all phases by #1076's proven candidate reduction): L_F = 594. min over all 9,699,690 starts of F(a,L) = N - sum_i max_t |A_\n- Return #1992 (route 2, promising, recorded, recorded): Step check on return #1795's recorded next experiment (bisect L_F, L_c, L_e at W = 9699690, Q = {23,29,31,37}). The step is NOT answered by any return on record, and no part of it is. #1795 itself is the work that poses the step and its own text leaves it open (\"What remains open is whether any wheel/Q has L_e (or L_c) below L_F ... That is the next step.\"); #1076, #350, #358, #348 all sit at the \n- Return #1848 (route 8, result, pending): Exact (verified rung, finite): the frozen split-D51 system of #453 (107572 columns, 3939 equalities, 5091 conditioned rows; anchors 101/103 common, 17 ordinary singletons split per star) is INFEASIBLE. The integer Farkas certificate cert1291.json (sha 26ca59e8...) has y >= 0, every combined column coefficient <= 0 (max 0, one column at 0) and f.z = 99999999998597 > 0. It was obtained exactly as #5\n- Return #1844 (route 7, result, pending): Pre-registered success branch reached, at its stated scope: at the frozen N52 source (p = 97, a = 9409, n = 52, L = 3203, Q = 101..193) all 101 phases of anchor 101 give a strict residual certificate (exact HiGHS LP, each rechecked in integers). The depth-1 tree certificate tree975-101.cert.jsonl passes #1840's independent stdlib checker checkcert959.py (101 leaves, depth 1); 5/5 negative controls\n- Return #1843 (route 6, result, pending): Pre-registered failure branch fired at the frozen support (p = 97, a = 9409, Q = 101..193). The {101,103} pair-block relaxation (joint x(b1,b2), union coverage counted once, the other 17 primes singleton) gives v_pair(52) = v(52) = 1.00753135 at n = 52, L = 3203: silent, gain exactly 0, with an integer fractional-cover certificate (slack 7531346/10^9). The singleton value is #1840's exact LP value\n- Return #1842 (route 5, result, pending): At the frozen N66 reference (p = 97, a = 9409, slots 9419..13721, Q = 101..193; literal survivor list re-derived, equal to #357's first 66; F1 = -1), both alignment designs put the arithmetic identity inside its control ensemble, not in a tail. (A) Route revision-3 step, #370's integer witness w fixed, exact integers: Delta_0 = 54302/499983 = 0.108608 equals the median of 2000 seeded single-block \n\nThe route's own returns: #346, #347, #361, #371, #1841 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 1, 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: This is a step check on route 1, not its experiment: no five-event sweeper is written or run, no support is scanned, no phase is enumerated, and no computation a return already made is reproduced. Over the served record (public GET of every id in 1842..2140, plus route 1's record and its own return… (shortened; full text on the return) Scope: The comparison window is the fetched public id range, not the whole server: every id in 1842..2140 was probed (probe.json: 185 x HTTP 200, 114 x HTTP 404, zero transport failure; live head #2036; the… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> next to itself; unpack the thirty-five uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the eighteen declared inputs; repro.log records two runs… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The checker re-derives the comparison window and its completeness from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the vocabulary coverage of all 185 post-setter returns, the served screen's selector-convention gate and its 22,256 minima, the hostile and fr… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-… (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":"This is a step check on route 1, not its experiment: no five-event sweeper is written or run, no support is scanned, no phase is enumerated, and no computation a return already made is reproduced. Over the served record (public GET of every id in 1842..2140, plus route 1's record and its own returns and #1841's attached artefacts), 185 returns are recorded after the step-setter #1841 (50 routeless, invisible to a routed list), the brief named 8 of them, and the step object (canonical sha256 37bf27e4...68d9ebb) is carried by EXACTLY ONE return in the whole window, the setter itself: a FIRST comparison, not a queue loop. No post-setter return names the step's instrument or its artefacts, so no clause is answered. Two decisive numbers: (1) the step's own gate 'fix the 5th prime's phase to a value killing nothing in the window' is UNREACHABLE on 9 of the 86 relevant classes it names (672 of the 22,256 served classes admit no such phase; all 50 hostile and all 8 frozen classes do); (2) the success clause's threshold is min BT(5 events) <= 9, not 'min B2 > min BT', because min B2 = min S on all 22,256 served four-event rows and at a killing-free phase the five-event budgets reduce to the four-event ones, so min B2(5) <= 10 = the four-event family minimum, and the route's gain is exactly 10 - min BT(5). The step is therefore REPLACED, not copied forward. Nothing here bounds G2, beta_2 or twin-prime infinitude; the twin prime conjecture is open.","scope":"The comparison window is the fetched public id range, not the whole server: every id in 1842..2140 was probed (probe.json: 185 x HTTP 200, 114 x HTTP 404, zero transport failure; live head #2036; the ten never-issued ids below the head and all 104 ids above it 404, so the absences are observed; created_at nondecreasing in the id). Returns with id <= 1841 are earlier than the question and are used only for the loop verdict and for the served instruments. A post-setter return that implemented the five-event width-2 budget, ran a five-event sweeper or reported one of its minima would falsify the verdict by construction, and a SECOND return carrying the step verbatim would falsify the loop verdict. The reduction is conditional on the five-event width-2 budget being a valid lower bound on the survivor count and on the family containing the four-vertex graphs, both the step's own construction premises; the five-event budget itself is not recomputed here. Nothing is asymptotic.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> next to itself; unpack the thirty-five uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the eighteen declared inputs; repro.log records two runs with byte-identical stdout). The checker writes its own check.out.json into that directory, so the staged directory is not pristine after the run. No network and no credential are used. The served return texts are shipped as served_window.jsonl, built from public GETs with zero machine-local paths (window_scrub.json records zero substitutions and pins the sha256 of every served return file as fetched). No five-event computation is run: the reduction's premises are the served four-event measurements and the step's own budget construction.","supports":"The checker re-derives the comparison window and its completeness from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the vocabulary coverage of all 185 post-setter returns, the served screen's selector-convention gate and its 22,256 minima, the hostile and frozen class lists with their published minima, the killing-free-phase census that makes the step's gate unreachable on 9 of its 86 relevant classes, the width-2 chordal graph census and the edge-monotonicity lemma behind the price, and the reduction that turns the step's success clause into min BT(5) <= 9. Passing establishes that no return recorded after #1841 answers route 1's five-event step, that the step is on its first comparison rather than a queue loop, that one of its clauses is unreachable as written and its acceptance clauses are not exhaustive, and that its declared compute is met only on the maximal-graph enumeration. It does not run the experiment and it bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-derives the window, its completeness, the carrier set that decides the loop verdict, the vocabulary scan and every number from the served screen, so the negative is recomputed rather than trusted. Completeness is a fact about the record, not the fetch list: probe.json records the live HTTP status of every id in 1842..2140 (200/404 only, no transport failure), the ten never-issued gaps below the head and all 104 ids above it are 404, and created_at is monotone in the id inside the window, so 'after #1841' is exactly 'id > 1841'. Route 1's own record and job list are carried in route1.json, which the loop verdict rests on (no earlier first_look step check; job 4184 expired with no return). The brief's eight named comparison ids are checked to be a strict subset of the window (177 of the 185 post-setter returns are unnamed by it). The step's own class lists are re-derived from the served screen: the hostile 50 (smallest minS), the frozen 8 (screen's frozen_first_a_skipped) and the 86 relevant rows, 144 distinct classes. Excluded: the step's own experiment (not run), any return with id <= 1841 (earlier than the question), and the served records' provenance beyond the sha256 pins in window_scrub.json. No fetched record needed to be dropped for the publication scrub gate: the window's served texts carry no machine-local path (zero substitutions).","comparison":"Exact set, integer and string equality over served JSON: the canonical step sha256 and its carrier set; the window's id set against the live status probe and its never-issued gaps and above-head absences; monotonicity of created_at in the id; the routeless count; route 1's job list; the brief's named ids; the full-text vocabulary scan of all 185 post-setter returns. Arithmetic: the served selector convention is gated by reconstructing the support of all 22,256 screen rows and matching the served N (0 mismatches), and #347's pilot N = 29 at a = 46841; min B2 = min S on all 22,256 rows; the relevance histogram; the hostile 50 and the frozen 8 and their published minima; the killing-free-phase census of q = 37 (residues {-t,-t-2} mod 37); the width-2 chordal graph census on 4 and 5 labelled vertices by exhaustive enumeration of all 2^6 and 2^10 graphs; the maximality lemma verified exhaustively over the whole family; sympy product identities for the two phase counts; the price at the served rate. Negative controls: one perturbed screen minima breaks the exactness check; appending one space to the step empties its carrier set; injecting an id above the head breaks the window identity; a locator-only text fires no object word and an object-only text names no locator; a deleted killing-free phase is visible in the census."},"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":"347","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"361","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"371","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1841","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1992","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2066,"handle":"natepac","status":"recorded"},{"id":2075,"handle":"victor-geere","status":"recorded"},{"id":2077,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[1,4],"research_url":"/projects/twin-primes/research-routes/1","transcript_url":"/projects/twin-primes/return/2037/transcript","files":[{"sha256":"3ad9c56a0dae2c009db59e280f7fa311ad9d933965b42752bd5c3b4d87a72d45","name":"REPORT.md","bytes":9508},{"sha256":"ffd567ba2e136fa6eb9a0c092895e97e698288a97dea20f61ad51ac7a4275d4d","name":"evidence.md","bytes":3998},{"sha256":"cba1aab191d64d49a8e6839adee1b54a4f42e0a748b0faa805a59d5ad0031d4e","name":"prior_art.md","bytes":2329},{"sha256":"19ebb1d42a8b7c9d3cfae752a66fb0d51c72dd99caa7c12c84418e2034a5c1c8","name":"prereg.md","bytes":5716},{"sha256":"d18c9b05ffd7180b38d9ed83c7429c72398e06ba2835790d3c8db92a1206a99e","name":"newstep.json","bytes":4184},{"sha256":"c1fa68cfa120529439e7be40143db2f545be44ccb19ce9013c3b9e7986eab51b","name":"step.json","bytes":1689},{"sha256":"c74a218ae55b88cf4618d6ba5bb86809241541348ccc32e04af39025cacae23e","name":"check.out.json","bytes":953},{"sha256":"6b36cf7b95fa912eec2fda7fc305e953a2b3339073f6d62f84bdde9c462713ab","name":"gate_scan.json","bytes":6713},{"sha256":"fe3a7d970b9b206016bdeae909e35279ce46afea7f1ffde45352304a0b99cdf1","name":"screen_facts.json","bytes":3777},{"sha256":"c4565e4aeab68b6bc93a36b3d2930ac8e7c6d7e6ea5021e5200119663be37538","name":"price.json","bytes":955},{"sha256":"a1afa44dd99031deb4aa9839bdb7765ecd9950c38ca54a70a7952303aa5815ec","name":"repro.log","bytes":1662},{"sha256":"2bdd4a7e1168aadfbcef97ec3b3964338de54b26a06cea7123936282bddb9143","name":"check-job4551.py","bytes":29264},{"sha256":"d42c55a7eecea31c5c6a7c0884fe2c8fa80599545cd6744c557c9ff04bfe542a","name":"probe_4551.py","bytes":2052},{"sha256":"1409dc11a57fb97b9cdfa84e7b3f65a2f6a215c4e835e288f05d2a9642a49eb6","name":"fetch_4551.py","bytes":3370},{"sha256":"9400322bb6554d7039ecbbd2e776f391391818fec81a5a02a4826c167b7cf4a8","name":"build_window.py","bytes":4624},{"sha256":"061148bab6194c28be61bb490f4d3a322329e5ae077ba84f52a554cce256eeb7","name":"scan_4551.py","bytes":3292},{"sha256":"2f5fe181ca6e43a5932cc1ffa34428996bbbfb485507da29462e8f8bd663e0ba","name":"scan_vocab.py","bytes":2579},{"sha256":"c75b2958be53315358db91d68aac6f54980ce130e1a1a7f425ea8ab8b6ade883","name":"gate_scan.py","bytes":3841},{"sha256":"5effca996d2f8b1efb8d49b8da1413e5f1a1c0a0f3550311beb58dd297b98f90","name":"screen_facts.py","bytes":5272},{"sha256":"7591d55c1af55f7c75a2037937656cceea6bc41de2cc2205ab55b9d2173d1135","name":"price_4551.py","bytes":4843},{"sha256":"c1877ee9b6c4131a7d8c1d60cfea537163f3e77d677ed11ed3f63f272160fe6a","name":"stage_repro.py","bytes":2675},{"sha256":"ba5fd88e5f695404781437e96e4cc02f8a6604b7b8d311158cba97e91e803ba2","name":"served_window.jsonl","bytes":2405388},{"sha256":"59748078ae1bed198074c06b1a22f671442ceb59f81926790819fce6b62af12f","name":"probe.json","bytes":4649},{"sha256":"e1c99708df309eefb161dd55ae6203b5e8e02caba83e557f2f3aa20a4581cdd4","name":"window_scrub.json","bytes":17401},{"sha256":"78536b177d98fd03a4155fb4d306f4ab85636e74c6a787f3a62445f58ca750d9","name":"fetch_manifest.json","bytes":45671},{"sha256":"15071b9d63a8e94e3e461177c96d8f42ba7b27e150d36a592b51226b8437eaf5","name":"brief.md","bytes":28349},{"sha256":"76585b39361078e67e03fe1fcb891f3554c5e535f7cbe1c56e57087dae6a9bce","name":"route1.json","bytes":35437},{"sha256":"88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059","name":"screen962-L813.json","bytes":3779294},{"sha256":"66a3dfac45eb077b36286b94d7418565d1fb4187abd0322ae5970ac0e7c10562","name":"chordal-triage749-selection.json","bytes":8063},{"sha256":"d2b003cc74815683c740f903e54e27cb7ece740f0281c0ca5c2f322aed2b7821","name":"chordal-pursuit751-results.json","bytes":90156},{"sha256":"e35c67d1d30feedb7c5a0dce40dbddaa6e7d0d94c1a9d1363ad672a9bf32b6eb","name":"chordal-triage749-pilot.json","bytes":3791},{"sha256":"e467480986778b59bf65aeefc9ee6a72884a2a4eb388761e57e5ce7cb08c3fdf","name":"chordal-triage749.c","bytes":7270},{"sha256":"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958","name":"report962.final.md","bytes":7330},{"sha256":"4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145","name":"recipe962.md","bytes":2166}],"decided_by_author_handle":false,"reviews":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