{ "generated_by": "appendix/collect.py", "page_model": { "queue_before_s": 1080, "queue_after_s": 8, "landing_gap_s": 360.0, "ledger_kernel_left": 0.15 }, "whole_tree_calibration": [ { "slug": "oai-078-bochner-riesz", "baseline_measured_s": 55214.3, "baseline_estimated_s": 81952.3, "baseline_error": 0.484, "full_measured_s": 25435.4, "full_estimated_s": 31448.2, "full_error": 0.236 }, { "slug": "oai-377-infinity-harmonic", "baseline_measured_s": 9454.1, "baseline_estimated_s": 8531.9, "baseline_error": -0.098, "full_measured_s": 6172.8, "full_estimated_s": 6248.0, "full_error": 0.012 }, { "slug": "smooth-knot-quadrisecant", "baseline_measured_s": 4503.3, "baseline_estimated_s": 3832.2, "baseline_error": -0.149, "full_measured_s": 3717.8, "full_estimated_s": 3070.0, "full_error": -0.174 } ], "problems": [ { "slug": "direct-summand", "chain_length": 4, "tree": { "obligations": 514, "started": "2026-10-18T13:41:32Z", "root_accepted": "2026-10-19T04:35:21Z" }, "chain": { "baseline_s": 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"constants_checked": 78988, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 11747, "cpu_s": 1232.7 } ], "one_check_gate_build_s": [ 67.9 ], "root_original": [ { "label": "ds-iso-root-orig", "verdict": "ACCEPT", "seconds": 2238.9, "setup": 10.0, "build": 1090.9, "export": 101.0, "parse": 60.0, "nanoda": 107.0, "lean": 870.0, "kernels_wall": 1037.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 733, "peak_mib": 17818, "cpu_s": 14546.9 } ], "root_full": [ { "label": "ds-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 335.3, "setup": 17.0, "build": 43.0, "export": 112.0, "parse": 63.2, "nanoda": 100.0, "lean": 74.3, "kernels_wall": 163.2, "replay_threads": 12, "ledger_constants_in": 78970, "constants_checked": 20041, "constants_skipped": 78948, "modules_compiled": 0, "peak_mib": 12300, "cpu_s": 1292.1 } ], "cache_build_s": [ 966.8 ] }, "ledger": { "levels_warm": [ 3, 4 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.242, "kernels_wall_left_fraction": 0.909, "nanoda_left_fraction": 0.645, "lean_left_fraction": 0.457, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 550.296, 534.6, 794.4, 788.429 ], "sum_regate_s": 2667.7, "span_s": 2749.4, "regate_own_seconds": [ 550.296, 534.6, 794.4, 788.429 ], "answered_by_prewarm": [ false, false, false, false ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v8, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Direct summand theorem and derived variant", "id": "direct_summand", "collection": "Lean-Eval", "tree_dag": { "obligations": 514, "live_accepted": 307, "depth": 10, "checks": 386, "proof_checks": 294, "regates": 91, "root_checks": 1, "excluded": 268, "chains": [ 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 5, 2, 2, 2, 6, 2, 3, 4 ], "checks_after_coalescing": 352, "historical_check_s": 93775.0, "production": { "max_gate_builds": 48, "check_timeout_s": 10800.0, "solve_pool": 192, "hours": 16.0 } }, "ratios": { "baseline_over_historical": 1.72, "full_over_historical": 0.39 }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 84645.0, "baseline_status": "estimate", "full_s": 48943.5, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "rough", "ratio_used": 1.72 }, "six_step_inputs": { "chain_length": [ 4, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 10.8, "measured: mean over the original levels" ], "build_scratch_s": [ 616.2, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 78.2, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 74.2, "measured: original levels, challenge + solution export" ], "parse_s": [ 38.5, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 43.2, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 377.0, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 99.6, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.242, "measured: constants still checked / all, production levels that started with a warm ledger (L3, L4)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 0.909, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 357.4, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 135.5, "measured" ], "cache_build_s": [ 966.8, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 10039.6 ], [ "+ scheduling and infrastructure", 5751.6 ], [ "+ chain/subtree coalescing", 1167.9 ], [ "+ build reuse", 629.9 ], [ "+ verified-constant ledger", 272.7 ], [ "+ parallel kernel replay", 224.6 ] ] }, { "slug": "oai-078-bochner-riesz", "chain_length": 10, "tree": { "obligations": 214, "started": "2026-10-20T11:19:29Z", "root_accepted": "2026-10-21T07:20:14Z" }, "chain": { "baseline_s": 15849.2, "baseline_status": "measured", "baseline_measured_s": 15849.2, "baseline_estimate_method": null, "full_s": 469.9, "full_status": "measured", "ratio": 33.73, "full_samples_s": [ 469.9 ], "baseline_cpu_h": 39.519, "full_cpu_h": 0.408, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 10, "baseline_levels_measured": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], "baseline_mean_s": 1584.9, "baseline_each_s": [ 1198.5, 1260.1, 1328.6, 1272.5, 1282.9, 1361.9, 1450.2, 1551.6, 2396.8, 2746.1 ], "full_levels_measured": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], "full_mean_s": 292.9, "full_each_s": [ 277.8, 364.6, 241.5, 225.0, 224.9, 362.9, 245.9, 282.6, 308.6, 394.7 ], "historical_in_tree_s": [ 410.9, 433.7, 444.4, 434.8, 438.4, 467.2, 525.3, 472.8, 658.7, 752.3 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 5236.4, "baseline_status": "measured", "full_s": 473.9, "full_gate_build_s": 1035.0, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "br-iso-orig-L1", "verdict": "ACCEPT", "seconds": 1198.5, "setup": 23.0, "build": 922.2, "export": 60.0, "parse": 31.0, "nanoda": 39.0, "lean": 123.3, 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22002, "cpu_s": 26884.5 }, { "label": "br-iso-orig-L10", "verdict": "ACCEPT", "seconds": 2746.1, "setup": 22.0, "build": 2240.1, "export": 100.0, "parse": 49.0, "nanoda": 82.0, "lean": 252.9, "kernels_wall": 384.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 1814, "peak_mib": 24373, "cpu_s": 31429.9 } ], "production": [ { "label": "br-iso-side-L1", "verdict": "ACCEPT", "seconds": 238.5, "setup": 27.0, "build": 53.0, "export": 75.0, "parse": 32.6, "nanoda": 50.8, "lean": 16.6, "kernels_wall": 83.4, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 63532, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 4560, "cpu_s": 599.2, "gate_build_s": 39.3 }, { "label": "br-iso-side-L2", "verdict": "ACCEPT", "seconds": 292.9, "setup": 30.0, "build": 76.0, "export": 90.0, "parse": 45.2, "nanoda": 51.6, "lean": 17.8, "kernels_wall": 96.8, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 66507, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 4699, "cpu_s": 679.7, "gate_build_s": 71.7 }, { "label": "br-iso-side-L3", "verdict": "ACCEPT", "seconds": 218.9, "setup": 26.0, "build": 45.0, "export": 69.0, "parse": 36.6, "nanoda": 42.2, "lean": 8.7, "kernels_wall": 78.9, "replay_threads": 12, "ledger_constants_in": 66486, "constants_checked": 1830, "constants_skipped": 66484, "modules_compiled": 0, "peak_mib": 4908, "cpu_s": 301.1, "gate_build_s": 22.6 }, { "label": "br-iso-side-L4", "verdict": "ACCEPT", "seconds": 202.3, "setup": 26.0, "build": 36.0, "export": 64.0, "parse": 32.8, "nanoda": 43.4, "lean": 8.4, "kernels_wall": 76.2, "replay_threads": 12, "ledger_constants_in": 66486, "constants_checked": 1842, "constants_skipped": 66484, "modules_compiled": 0, "peak_mib": 4660, "cpu_s": 276.3, "gate_build_s": 22.7 }, { "label": "br-iso-side-L5", "verdict": "ACCEPT", "seconds": 202.1, "setup": 26.0, "build": 35.0, "export": 65.0, "parse": 33.6, 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"br-iso-side-L8", "verdict": "ACCEPT", "seconds": 205.1, "setup": 26.0, "build": 31.0, "export": 67.0, "parse": 37.5, "nanoda": 43.6, "lean": 9.3, "kernels_wall": 81.1, "replay_threads": 12, "ledger_constants_in": 68837, "constants_checked": 50, "constants_skipped": 68831, "modules_compiled": 0, "peak_mib": 4749, "cpu_s": 271.0, "gate_build_s": 77.5 }, { "label": "br-iso-side-L9", "verdict": "ACCEPT", "seconds": 285.3, "setup": 26.0, "build": 39.0, "export": 96.0, "parse": 50.5, "nanoda": 73.8, "lean": 16.8, "kernels_wall": 124.2, "replay_threads": 12, "ledger_constants_in": 68866, "constants_checked": 14395, "constants_skipped": 68858, "modules_compiled": 0, "peak_mib": 6834, "cpu_s": 555.4, "gate_build_s": 23.3 }, { "label": "br-iso-side-L10", "verdict": "ACCEPT", "seconds": 370.4, "setup": 27.0, "build": 51.0, "export": 134.0, "parse": 84.9, "nanoda": 73.5, "lean": 17.8, "kernels_wall": 158.4, "replay_threads": 12, "ledger_constants_in": 68866, "constants_checked": 14503, "constants_skipped": 68858, "modules_compiled": 0, "peak_mib": 6826, "cpu_s": 683.3, "gate_build_s": 24.3 } ], "one_check": [ { "label": "br-iso-one-1", "verdict": "ACCEPT", "seconds": 351.5, "setup": 27.0, "build": 87.0, "export": 102.0, "parse": 51.8, "nanoda": 83.7, "lean": 28.5, "kernels_wall": 135.5, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 83370, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 7261, "cpu_s": 1243.0 } ], "one_check_gate_build_s": [ 118.4 ], "root_original": [ { "label": "br-iso-root-orig", "verdict": "ACCEPT", "seconds": 5236.4, "setup": 28.0, "build": 4561.1, "export": 154.0, "parse": 94.0, "nanoda": 87.0, "lean": 312.2, "kernels_wall": 493.3, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 2927, "peak_mib": 28647, "cpu_s": 61100.4 } ], "root_full": [ { "label": "br-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 473.9, "setup": 42.0, "build": 60.0, "export": 197.0, "parse": 113.0, "nanoda": 61.9, "lean": 20.9, "kernels_wall": 174.9, "replay_threads": 12, "ledger_constants_in": 83358, "constants_checked": 9908, "constants_skipped": 83338, "modules_compiled": 0, "peak_mib": 9978, "cpu_s": 781.3 } ], "cache_build_s": [ 4218.9 ] }, "ledger": { "levels_warm": [ 3, 4, 5, 6, 7, 8, 9, 10 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.051, "kernels_wall_left_fraction": 1.095, "nanoda_left_fraction": 0.995, "lean_left_fraction": 0.632, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 410.893, 433.726, 444.389, 434.793, 438.406, 467.206, 525.262, 472.811, 658.712, 752.265 ], "sum_regate_s": 5038.5, "span_s": 1413.2, "regate_own_seconds": [ 410.893, 433.726, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "answered_by_prewarm": [ false, false, true, true, true, true, true, true, true, true ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v10, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Bochner–Riesz Multipliers in Three Dimensions", "id": "078", "collection": "OpenAI math", "tree_dag": { "obligations": 214, "live_accepted": 126, "depth": 11, "checks": 191, "proof_checks": 154, "regates": 36, "root_checks": 1, "excluded": 221, "chains": [ 2, 4, 7, 10 ], "checks_after_coalescing": 172, "historical_check_s": 53526.8, "production": { "max_gate_builds": 32, "check_timeout_s": 10800.0, "solve_pool": 128, "hours": 72.0 } }, "ratios": { "baseline_over_historical": 3.091, "full_over_historical": 0.593 }, "whole_tree": { "status": "measured", "lanes": 2, "lane": "8 whole cores (16 CPUs), 64 GiB, isolated", "baseline_s": 55214.3, "baseline_status": "measured to the 12 h cut + estimate", "baseline_measured_s": 43152.3, "baseline_estimate_method": "181 checks measured in this tree (79509 s on one lane; their historical 43854 s). The other 10: the closing cascade the chain example measured (6 levels) and the root take the chain example's isolated ORIGINAL times (measured in the chain example (same isolation)); other closing-cascade REGATEs take their historical seconds x 3.15 (the chain example's measured ORIGINAL/historical ratio: the tree's REGATEs were seeded and prewarmed); the rest their historical seconds x 1.81 (this tree's measured ratio); all placed on the same two lanes. The naive estimate (every unmeasured check x 1.81) is in estimate_s_naive", "full_s": 25435.4, "full_status": "measured", "baseline_checks": 191, "full_checks": 172, "baseline_sequential_s": 79508.9, "full_sequential_s": 48429.5, "baseline_cpu_h": 98.232, "full_cpu_h": 37.161, "final_official_check_s": 4413.6, "historical_check_s": 53526.8 }, "six_step_inputs": { "chain_length": [ 10, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 22.5, "measured: mean over the original levels" ], "build_scratch_s": [ 1241.4, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 84.6, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 72.3, "measured: original levels, challenge + solution export" ], "parse_s": [ 35.6, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 52.5, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 160.6, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 90.1, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.051, "measured: constants still checked / all, production levels that started with a warm ledger (L3, L4, L5, L6, L7, L8, L9, L10)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 1.095, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 469.9, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 135.5, "measured" ], "cache_build_s": [ 4218.9, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 29889.0 ], [ "+ scheduling and infrastructure", 19169.0 ], [ "+ chain/subtree coalescing", 1592.9 ], [ "+ build reuse", 436.1 ], [ "+ verified-constant ledger", 255.0 ], [ "+ parallel kernel replay", 236.5 ] ] }, { "slug": "oai-304-hilbert-smith", "chain_length": 12, "tree": { "obligations": 209, "started": "2026-10-20T10:59:27Z", "root_accepted": "2026-10-24T19:39:20Z" }, "chain": { "baseline_s": 480832.6, "baseline_status": "cut_at_12h", "baseline_measured_s": 43228.2, "baseline_estimate_method": "level 1 ran to the end (42035 s, measured); level 2 was stopped at the 12 h cut after 1193 s, in its solution_build stage (1106 s in it, Lake at 9964/10072); its remainder, 10410 s, is the rest of that stage (1451 s, at least 0) plus the later stages (8960 s): level 1's measured run (42035 s)'s stages times 0.274 (the build had compiled 860 of the 1988 Submission modules in the import closure in 1106 s (whole build ~2556 s, linear)); levels 3-12 not started (the 12 h of timeline were used up): each estimated as level 1's time (42035 s, measured) times the square root of the import-closure ratio (L3 1999, L4 2001, L5 2002, L6 2003, L7 2006, L8 2007, L9 2011, L10 2015, L11 2027, L12 2473 vs 1987 Submission modules; time ~ sqrt(closure): on the seven finished examples' original runs, median error 7% per level, -39%..+30%). The 12 h are displayed timeline: the levels' measured durations inside their containers, one after another", "full_s": 4674.1, "full_status": "measured", "ratio": 102.87, "full_samples_s": [ 4674.1 ], "baseline_cpu_h": 27.879, "full_cpu_h": 17.077, "worker": { "cores": 8, "cpus": 16, "memory_gib": 128 } }, "single_node": { "nodes": 12, "baseline_levels_measured": [ 1 ], "baseline_mean_s": 42035.2, "baseline_each_s": [ 42035.2 ], "full_levels_measured": [], "full_mean_s": 4674.1, "full_each_s": [], "historical_in_tree_s": [ 19918.4, 6923.5, 7590.5, 7965.9, 1568.9, 6141.5, 2032.5, 917.0, 2023.9, 6065.9, 968.3, 1488.8 ], "baseline_status": "measured on 1 of 12 levels", "full_status": "estimate", "full_note": "estimate: the measured one check of the whole chain (gate build + check, 4,674 s); each level's import closure is 80-100% of the top level's (1,987-2,473 Submission modules), so one level with an empty ledger takes about as long" }, "root": { "baseline_s": 52714.8, "baseline_status": "cut_at_12h", "full_s": 607.0, "full_gate_build_s": 176.8, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "hs-iso-orig-L1", "verdict": "ACCEPT", "seconds": 42035.2, "setup": 34.0, "build": 9338.6, "export": 117.0, "parse": 63.0, "nanoda": 2663.3, "lean": 29819.2, "kernels_wall": 32545.5, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 2010, "peak_mib": 59996, "cpu_s": 100365.1 }, { "label": "hs-iso-orig-L2", "verdict": "stopped at the 12 h cut", "seconds": 1198.0, "setup": null, "build": null, "export": null, "parse": null, "nanoda": null, "lean": null, "kernels_wall": null, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 860, "peak_mib": null, "cpu_s": null } ], "production": [], "one_check": [ { "label": "hs-iso-one-1", "verdict": "ACCEPT", "seconds": 4522.9, "setup": 31.0, "build": 66.0, "export": 137.0, "parse": 77.6, "nanoda": 4211.3, "lean": 3878.3, "kernels_wall": 4288.8, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 141560, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 113254, "cpu_s": 61067.6 } ], "one_check_gate_build_s": [ 151.2 ], "root_original": [ { "label": "hs-iso-root-orig", "verdict": "stopped at the 12 h cut", "seconds": 43232.9, "setup": null, "build": null, "export": null, "parse": null, "nanoda": null, "lean": null, "kernels_wall": null, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 5533, "peak_mib": null, "cpu_s": null } ], "root_full": [ { "label": "hs-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 607.0, "setup": 47.0, "build": 74.0, "export": 288.0, "parse": 157.2, "nanoda": 40.7, "lean": 27.6, "kernels_wall": 197.9, "replay_threads": 12, "ledger_constants_in": 141538, "constants_checked": 6366, "constants_skipped": 141526, "modules_compiled": 0, "peak_mib": 10531, "cpu_s": 833.7 } ], "cache_build_s": [ 17042.9 ] }, "ledger": null, "historical": { "regate_seconds": [ 19918.439, 6923.47, 7590.467, 7965.867, 1568.888, 6141.47, 2032.457, 916.954, 2023.903, 6065.91, 968.301, 1488.807 ], "sum_regate_s": 63604.9, "span_s": 36585.6, "regate_own_seconds": [ 19918.439, 6923.47, 7590.467, 0.0, 1568.888, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "answered_by_prewarm": [ false, false, false, true, false, true, true, true, true, true, true, true ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v12, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "The Hilbert–Smith conjecture in every finite dimension", "id": "304", "collection": "OpenAI math", "tree_dag": { "obligations": 209, "live_accepted": 164, "depth": 13, "checks": 257, "proof_checks": 205, "regates": 51, "root_checks": 1, "excluded": 278, "chains": [ 2, 3, 2, 2, 4, 3, 2, 4, 3, 4, 2, 12 ], "checks_after_coalescing": 226, "historical_check_s": 541355.0, "production": { "max_gate_builds": 32, "check_timeout_s": 57600.0, "solve_pool": 128, "hours": 72.0 } }, "ratios": { "baseline_over_historical": 2.11, "full_over_historical": null }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 596259.2, "baseline_status": "estimate", "full_s": 241380.0, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "low", "ratio_used": 2.11 }, "six_step_inputs": { "chain_length": [ 12, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 34.0, "measured: mean over the original levels" ], "build_scratch_s": [ 9338.6, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 217.2, "estimate: the one check's gate build + its seeded build (no production levels were measured)" ], "export_s": [ 117.0, "measured: original levels, challenge + solution export" ], "parse_s": [ 63.0, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 2663.3, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 29819.2, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 4288.8, "measured: the one check's kernels (nanoda-t 4,211 s, parallel Lean replay 3,878 s at the same time); no single-level production run" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ null, "no production level started with a warm ledger" ], "ledger_parallel_kernels_warm_over_cold_measured": [ null, "-" ], "one_check_s": [ 4674.1, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 4288.8, "measured" ], "cache_build_s": [ 17042.9, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ], "note": "original: level 1 measured to its end (42,035 s); levels 2-12 estimated. The main page's model uses this tree's earlier node measurement: build 10,920 s, nanoda 46 min, serial Lean 26,422 s, parallel 53 min" }, "page_model_chain_steps": [ [ "baseline", 521341.2 ], [ "+ scheduling and infrastructure", 508477.2 ], [ "+ chain/subtree coalescing", 42043.1 ], [ "+ build reuse", 32921.7 ], [ "+ verified-constant ledger", 5311.6 ], [ "+ parallel kernel replay", 1082.5 ] ] }, { "slug": "oai-377-infinity-harmonic", "chain_length": 2, "tree": { "obligations": 48, "started": "2026-10-20T09:19:07Z", "root_accepted": "2026-10-20T11:14:26Z" }, "chain": { "baseline_s": 721.0, "baseline_status": "measured", "baseline_measured_s": 721.0, "baseline_estimate_method": null, "full_s": 247.7, "full_status": "measured", "ratio": 2.91, "full_samples_s": [ 247.7 ], "baseline_cpu_h": 1.103, "full_cpu_h": 0.168, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 2, "baseline_levels_measured": [ 1, 2 ], "baseline_mean_s": 360.5, "baseline_each_s": [ 309.3, 411.7 ], "full_levels_measured": [ 1, 2 ], "full_mean_s": 179.0, "full_each_s": [ 178.9, 179.1 ], "historical_in_tree_s": [ 272.6, 257.2 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 735.1, "baseline_status": "measured", "full_s": 238.0, "full_gate_build_s": 92.2, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "ih-iso-orig-L1", "verdict": "ACCEPT", "seconds": 309.3, "setup": 7.0, "build": 171.1, "export": 41.0, "parse": 18.0, "nanoda": 15.0, "lean": 57.2, "kernels_wall": 90.2, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 79, "peak_mib": 11477, "cpu_s": 1349.1 }, { "label": "ih-iso-orig-L2", "verdict": "ACCEPT", "seconds": 411.7, "setup": 7.0, "build": 237.3, "export": 47.0, "parse": 21.0, "nanoda": 20.0, "lean": 79.4, "kernels_wall": 120.4, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 156, "peak_mib": 10295, "cpu_s": 2620.4 } ], "production": [ { "label": "ih-iso-side-L1", "verdict": "ACCEPT", "seconds": 127.3, "setup": 8.0, "build": 41.0, "export": 42.0, "parse": 18.5, "nanoda": 17.8, "lean": 8.9, "kernels_wall": 36.3, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 44737, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 2730, "cpu_s": 297.7, "gate_build_s": 51.6 }, { "label": "ih-iso-side-L2", "verdict": "ACCEPT", "seconds": 139.4, "setup": 8.0, "build": 40.0, "export": 45.0, "parse": 21.0, "nanoda": 25.3, "lean": 10.5, "kernels_wall": 46.4, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 51186, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 3210, "cpu_s": 348.5, "gate_build_s": 39.7 } ], "one_check": [ { "label": "ih-iso-one-1", "verdict": "ACCEPT", "seconds": 161.6, "setup": 8.0, "build": 55.0, "export": 49.0, "parse": 22.8, "nanoda": 26.8, "lean": 11.4, "kernels_wall": 49.6, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 51187, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 3433, "cpu_s": 400.9 } ], "one_check_gate_build_s": [ 86.1 ], "root_original": [ { "label": "ih-iso-root-orig", "verdict": "ACCEPT", "seconds": 735.1, "setup": 7.0, "build": 465.5, "export": 97.0, "parse": 26.0, "nanoda": 29.0, "lean": 110.6, "kernels_wall": 165.6, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 249, "peak_mib": 10471, "cpu_s": 4905.1 } ], "root_full": [ { "label": "ih-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 238.0, "setup": 14.0, "build": 65.0, "export": 94.0, "parse": 43.7, "nanoda": 21.3, "lean": 9.6, "kernels_wall": 65.0, "replay_threads": 12, "ledger_constants_in": 51167, "constants_checked": 8876, "constants_skipped": 51163, "modules_compiled": 0, "peak_mib": 3815, "cpu_s": 383.3 } ], "cache_build_s": [ 231.4 ] }, "ledger": null, "historical": { "regate_seconds": [ 272.63, 257.248 ], "sum_regate_s": 529.9, "span_s": 363.9, "regate_own_seconds": [ 272.63, 0.0 ], "answered_by_prewarm": [ false, true ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v10, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Uniform Interior C^{1,α} Estimates for Infinity-Harmonic Functions", "id": "377", "collection": "OpenAI math", "tree_dag": { "obligations": 48, "live_accepted": 39, "depth": 4, "checks": 63, "proof_checks": 52, "regates": 10, "root_checks": 1, "excluded": 31, "chains": [ 2, 2 ], "checks_after_coalescing": 61, "historical_check_s": 11517.1, "production": { "max_gate_builds": 32, "check_timeout_s": 10800.0, "solve_pool": 128, "hours": 72.0 } }, "ratios": { "baseline_over_historical": 1.368, "full_over_historical": 0.676 }, "whole_tree": { "status": "measured", "lanes": 2, "lane": "8 whole cores (16 CPUs), 64 GiB, isolated", "baseline_s": 9454.1, "baseline_status": "measured", "baseline_measured_s": 9454.1, "baseline_estimate_method": null, "full_s": 6172.8, "full_status": "measured", "baseline_checks": 63, "full_checks": 61, "baseline_sequential_s": 17116.1, "full_sequential_s": 11567.2, "baseline_cpu_h": 11.512, "full_cpu_h": 5.333, "final_official_check_s": 620.5, "historical_check_s": 11517.1 }, "six_step_inputs": { "chain_length": [ 2, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 7.0, "measured: mean over the original levels" ], "build_scratch_s": [ 204.2, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 86.2, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 44.0, "measured: original levels, challenge + solution export" ], "parse_s": [ 19.5, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 17.5, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 68.3, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 41.3, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ null, "no production level started with a warm ledger" ], "ledger_parallel_kernels_warm_over_cold_measured": [ null, "-" ], "one_check_s": [ 247.7, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 49.6, "measured" ], "cache_build_s": [ 231.4, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 3241.0 ], [ "+ scheduling and infrastructure", 1097.0 ], [ "+ chain/subtree coalescing", 368.5 ], [ "+ build reuse", 250.5 ], [ "+ verified-constant ledger", 177.6 ], [ "+ parallel kernel replay", 170.9 ] ] }, { "slug": "shafarevich-solvable-galois", "chain_length": 5, "tree": { "obligations": 148, "started": "2026-10-11T13:21:28Z", "root_accepted": "2026-10-13T16:48:37Z" }, "chain": { "baseline_s": 5637.1, "baseline_status": "measured", "baseline_measured_s": 5637.1, "baseline_estimate_method": null, "full_s": 390.3, "full_status": "measured", "ratio": 14.44, "full_samples_s": [ 388.7, 391.9 ], "baseline_cpu_h": 9.473, "full_cpu_h": 0.3535, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 5, "baseline_levels_measured": [ 1, 2, 3, 4, 5 ], "baseline_mean_s": 1127.4, "baseline_each_s": [ 852.4, 809.9, 1034.5, 1366.4, 1573.9 ], "full_levels_measured": [ 1, 2, 3, 4, 5 ], "full_mean_s": 278.0, "full_each_s": [ 292.3, 268.2, 215.8, 309.7, 304.0 ], "historical_in_tree_s": [ 618.6, 567.3, 631.5, 625.3, 693.4 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 2488.6, "baseline_status": "measured", "full_s": 346.3, "full_gate_build_s": 1087.6, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "sh-iso-orig-L1", "verdict": "ACCEPT", "seconds": 852.4, "setup": 9.0, "build": 398.3, "export": 125.0, "parse": 66.0, "nanoda": 49.0, "lean": 205.1, "kernels_wall": 320.1, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 136, "peak_mib": 9848, "cpu_s": 3218.4 }, { "label": "sh-iso-orig-L2", "verdict": "ACCEPT", "seconds": 809.9, "setup": 9.0, "build": 418.3, "export": 80.0, "parse": 50.0, "nanoda": 49.0, "lean": 203.6, "kernels_wall": 302.6, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 148, "peak_mib": 9866, "cpu_s": 3379.3 }, { "label": "sh-iso-orig-L3", "verdict": "ACCEPT", "seconds": 1034.5, "setup": 9.0, "build": 507.8, "export": 114.0, "parse": 77.0, "nanoda": 63.0, "lean": 263.6, "kernels_wall": 403.6, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 331, "peak_mib": 11218, "cpu_s": 6313.6 }, { "label": "sh-iso-orig-L4", "verdict": "ACCEPT", "seconds": 1366.4, "setup": 10.0, "build": 788.1, "export": 129.0, "parse": 72.0, "nanoda": 71.0, "lean": 296.2, "kernels_wall": 439.3, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 333, "peak_mib": 10646, "cpu_s": 9214.4 }, { "label": "sh-iso-orig-L5", "verdict": "ACCEPT", "seconds": 1573.9, "setup": 10.0, "build": 965.4, "export": 150.0, "parse": 70.0, "nanoda": 69.0, "lean": 309.5, "kernels_wall": 448.5, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 435, "peak_mib": 12344, "cpu_s": 11978.1 } ], "production": [ { "label": "sh-iso-side-L1", "verdict": "ACCEPT", "seconds": 214.6, "setup": 10.0, "build": 29.0, "export": 69.0, "parse": 38.2, "nanoda": 68.4, "lean": 27.7, "kernels_wall": 106.6, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 89374, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 5785, "cpu_s": 727.0, "gate_build_s": 77.7 }, { "label": "sh-iso-side-L2", "verdict": "ACCEPT", "seconds": 217.3, "setup": 10.0, "build": 31.0, "export": 71.0, "parse": 39.1, "nanoda": 66.2, "lean": 27.5, "kernels_wall": 105.3, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 89461, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 5689, "cpu_s": 741.7, "gate_build_s": 50.9 }, { "label": "sh-iso-side-L3", "verdict": "ACCEPT", "seconds": 193.3, "setup": 10.0, "build": 30.0, "export": 78.0, "parse": 44.3, "nanoda": 31.0, "lean": 14.5, "kernels_wall": 75.3, "replay_threads": 12, "ledger_constants_in": 89440, "constants_checked": 7433, "constants_skipped": 89438, "modules_compiled": 0, "peak_mib": 6424, "cpu_s": 372.7, "gate_build_s": 22.5 }, { "label": "sh-iso-side-L4", "verdict": "ACCEPT", "seconds": 262.1, "setup": 10.0, "build": 37.0, "export": 106.0, "parse": 78.3, "nanoda": 30.7, "lean": 15.1, "kernels_wall": 109.0, "replay_threads": 12, "ledger_constants_in": 89440, "constants_checked": 7485, "constants_skipped": 89438, "modules_compiled": 0, "peak_mib": 6267, "cpu_s": 473.3, "gate_build_s": 47.6 }, { "label": "sh-iso-side-L5", "verdict": "ACCEPT", "seconds": 213.0, "setup": 11.0, "build": 31.0, "export": 88.0, "parse": 48.5, "nanoda": 22.2, "lean": 34.4, "kernels_wall": 83.0, "replay_threads": 12, "ledger_constants_in": 96904, "constants_checked": 1475, "constants_skipped": 96900, "modules_compiled": 0, "peak_mib": 6665, "cpu_s": 329.8, "gate_build_s": 91.0 } ], "one_check": [ { "label": "sh-iso-one-1", "verdict": "ACCEPT", "seconds": 273.5, "setup": 11.0, "build": 44.0, "export": 82.0, "parse": 48.8, "nanoda": 87.7, "lean": 53.2, "kernels_wall": 136.5, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 98379, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 6911, "cpu_s": 996.6 }, { "label": "sh-iso-one-2", "verdict": "ACCEPT", "seconds": 271.5, "setup": 10.0, "build": 44.0, "export": 83.0, "parse": 49.6, "nanoda": 84.9, "lean": 52.6, "kernels_wall": 134.5, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 98379, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 6706, "cpu_s": 988.1 } ], "one_check_gate_build_s": [ 115.2, 120.4 ], "root_original": [ { "label": "sh-iso-root-orig", "verdict": "ACCEPT", "seconds": 2488.6, "setup": 15.0, "build": 1650.0, "export": 111.0, "parse": 58.0, "nanoda": 118.0, "lean": 536.6, "kernels_wall": 712.6, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 1583, "peak_mib": 20449, "cpu_s": 23912.6 } ], "root_full": [ { "label": "sh-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 346.3, "setup": 26.0, "build": 34.0, "export": 117.0, "parse": 62.0, "nanoda": 107.2, "lean": 45.3, "kernels_wall": 169.2, "replay_threads": 12, "ledger_constants_in": 98362, "constants_checked": 24610, "constants_skipped": 98352, "modules_compiled": 0, "peak_mib": 10121, "cpu_s": 1009.6 } ], "cache_build_s": [ 973.5 ] }, "ledger": { "levels_warm": [ 3, 4, 5 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.056, "kernels_wall_left_fraction": 0.841, "nanoda_left_fraction": 0.416, "lean_left_fraction": 0.773, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 618.636, 567.303, 631.501, 625.259, 693.393 ], "sum_regate_s": 3136.1, "span_s": 3334.1, "regate_own_seconds": [ 618.636, 567.303, 631.501, 625.259, 693.393 ], "answered_by_prewarm": [ false, false, false, false, false ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v8, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Shafarevich's theorem on solvable Galois groups", "id": "shafarevich_solvable_galois", "collection": "Lean-Eval", "tree_dag": { "obligations": 148, "live_accepted": 106, "depth": 9, "checks": 180, "proof_checks": 151, "regates": 27, "root_checks": 2, "excluded": 270, "chains": [ 2, 5, 6, 2, 2 ], "checks_after_coalescing": 168, "historical_check_s": 209252.0, "production": { "max_gate_builds": 4, "check_timeout_s": 10800.0, "solve_pool": 40, "hours": 48.0 } }, "ratios": { "baseline_over_historical": 1.78, "full_over_historical": 0.444 }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 184765.0, "baseline_status": "estimate", "full_s": 26652.3, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "rough", "ratio_used": 1.78 }, "six_step_inputs": { "chain_length": [ 5, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 9.4, "measured: mean over the original levels" ], "build_scratch_s": [ 615.6, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 89.5, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 119.6, "measured: original levels, challenge + solution export" ], "parse_s": [ 67.0, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 60.2, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 255.6, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 105.9, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.056, "measured: constants still checked / all, production levels that started with a warm ledger (L3, L4, L5)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 0.841, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 388.7, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 136.5, "measured" ], "cache_build_s": [ 973.5, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 12477.0 ], [ "+ scheduling and infrastructure", 7117.0 ], [ "+ chain/subtree coalescing", 1135.4 ], [ "+ build reuse", 609.3 ], [ "+ verified-constant ledger", 340.9 ], [ "+ parallel kernel replay", 309.4 ] ] }, { "slug": "smooth-knot-quadrisecant", "chain_length": 4, "tree": { "obligations": 47, "started": "2026-10-17T15:10:49Z", "root_accepted": "2026-10-17T17:10:39Z" }, "chain": { "baseline_s": 759.5, "baseline_status": "measured", "baseline_measured_s": 759.5, "baseline_estimate_method": null, "full_s": 200.6, "full_status": "measured", "ratio": 3.79, "full_samples_s": [ 205.1, 196.0 ], "baseline_cpu_h": 0.479, "full_cpu_h": 0.13, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 4, "baseline_levels_measured": [ 1, 2, 3, 4 ], "baseline_mean_s": 189.9, "baseline_each_s": [ 115.8, 192.2, 200.0, 251.5 ], "full_levels_measured": [ 1, 2, 3, 4 ], "full_mean_s": 134.6, "full_each_s": [ 109.6, 144.4, 141.2, 143.3 ], "historical_in_tree_s": [ 131.5, 181.0, 205.8, 224.8 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 336.5, "baseline_status": "measured", "full_s": 114.0, "full_gate_build_s": 22.0, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "sk-iso-orig-L1", "verdict": "ACCEPT", "seconds": 115.8, "setup": 6.0, "build": 71.0, "export": 25.0, "parse": 5.0, "nanoda": 2.0, "lean": 6.7, "kernels_wall": 13.7, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 4, "peak_mib": 1939, "cpu_s": 157.6 }, { "label": "sk-iso-orig-L2", "verdict": "ACCEPT", "seconds": 192.2, "setup": 6.0, "build": 85.0, "export": 40.0, "parse": 17.0, "nanoda": 9.0, "lean": 35.2, "kernels_wall": 61.2, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 10, "peak_mib": 4336, "cpu_s": 333.5 }, { "label": "sk-iso-orig-L3", "verdict": "ACCEPT", "seconds": 200.0, "setup": 6.0, "build": 88.0, "export": 38.0, "parse": 17.0, "nanoda": 10.0, "lean": 40.9, "kernels_wall": 68.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 17, "peak_mib": 6510, "cpu_s": 403.6 }, { "label": "sk-iso-orig-L4", "verdict": "ACCEPT", "seconds": 251.5, "setup": 6.0, "build": 120.0, "export": 37.0, "parse": 17.0, "nanoda": 14.0, "lean": 57.4, "kernels_wall": 88.5, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 43, "peak_mib": 10696, "cpu_s": 829.9 } ], "production": [ { "label": "sk-iso-side-L1", "verdict": "ACCEPT", "seconds": 84.3, "setup": 7.0, "build": 42.0, "export": 27.0, "parse": 5.2, "nanoda": 3.0, "lean": 1.8, "kernels_wall": 8.3, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 14908, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 1385, "cpu_s": 130.3, "gate_build_s": 25.3 }, { "label": "sk-iso-side-L2", "verdict": "ACCEPT", "seconds": 120.5, "setup": 7.0, "build": 43.0, "export": 41.0, "parse": 16.8, "nanoda": 12.6, "lean": 6.4, "kernels_wall": 29.4, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 39149, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 2295, "cpu_s": 243.4, "gate_build_s": 23.9 }, { "label": "sk-iso-side-L3", "verdict": "ACCEPT", "seconds": 114.8, "setup": 7.0, "build": 42.0, "export": 41.0, "parse": 18.0, "nanoda": 6.7, "lean": 4.0, "kernels_wall": 24.7, "replay_threads": 12, "ledger_constants_in": 39128, "constants_checked": 1906, "constants_skipped": 39126, "modules_compiled": 0, "peak_mib": 2387, "cpu_s": 164.5, "gate_build_s": 26.4 }, { "label": "sk-iso-side-L4", "verdict": "ACCEPT", "seconds": 113.6, "setup": 7.0, "build": 36.0, "export": 40.0, "parse": 18.0, "nanoda": 12.5, "lean": 5.9, "kernels_wall": 30.6, "replay_threads": 12, "ledger_constants_in": 39128, "constants_checked": 8795, "constants_skipped": 39126, "modules_compiled": 0, "peak_mib": 2676, "cpu_s": 203.5, "gate_build_s": 29.7 } ], "one_check": [ { "label": "sk-iso-one-1", "verdict": "ACCEPT", "seconds": 157.3, "setup": 7.0, "build": 59.0, "export": 48.0, "parse": 21.2, "nanoda": 22.2, "lean": 9.4, "kernels_wall": 43.3, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 47924, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 3767, "cpu_s": 391.0 }, { "label": "sk-iso-one-2", "verdict": "ACCEPT", "seconds": 145.7, "setup": 7.0, "build": 52.0, "export": 44.0, "parse": 20.5, "nanoda": 22.1, "lean": 9.4, "kernels_wall": 42.7, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 47924, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 3742, "cpu_s": 369.6 } ], "one_check_gate_build_s": [ 47.8, 50.3 ], "root_original": [ { "label": "sk-iso-root-orig", "verdict": "ACCEPT", "seconds": 336.5, "setup": 6.0, "build": 182.1, "export": 43.0, "parse": 18.0, "nanoda": 18.0, "lean": 69.4, "kernels_wall": 105.4, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 58, "peak_mib": 12036, "cpu_s": 1409.4 } ], "root_full": [ { "label": "sk-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 114.0, "setup": 11.0, "build": 37.0, "export": 40.0, "parse": 18.7, "nanoda": 7.3, "lean": 4.7, "kernels_wall": 26.0, "replay_threads": 12, "ledger_constants_in": 47906, "constants_checked": 1547, "constants_skipped": 47898, "modules_compiled": 0, "peak_mib": 2710, "cpu_s": 161.9 } ], "cache_build_s": [ 110.0 ] }, "ledger": { "levels_warm": [ 3, 4 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.115, "kernels_wall_left_fraction": 1.467, "nanoda_left_fraction": 1.231, "lean_left_fraction": 1.207, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 131.466, 180.994, 205.752, 224.821 ], "sum_regate_s": 743.0, "span_s": 766.9, "regate_own_seconds": [ 131.466, 180.994, 205.752, 224.821 ], "answered_by_prewarm": [ false, false, false, false ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v8, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Pannwitz–Kuperberg quadrisecant theorem", "id": "smooth_knot_has_quadrisecant", "collection": "Lean-Eval", "tree_dag": { "obligations": 47, "live_accepted": 36, "depth": 6, "checks": 44, "proof_checks": 33, "regates": 10, "root_checks": 1, "excluded": 22, "chains": [ 2, 4 ], "checks_after_coalescing": 40, "historical_check_s": 6161.6, "production": { "max_gate_builds": 8, "check_timeout_s": 10800.0, "solve_pool": 24, "hours": 4.0 } }, "ratios": { "baseline_over_historical": 1.008, "full_over_historical": 0.739 }, "whole_tree": { "status": "measured", "lanes": 2, "lane": "8 whole cores (16 CPUs), 64 GiB, isolated", "baseline_s": 4503.3, "baseline_status": "measured", "baseline_measured_s": 4503.3, "baseline_estimate_method": null, "full_s": 3717.8, "full_status": "measured", "baseline_checks": 44, "full_checks": 40, "baseline_sequential_s": 6699.7, "full_sequential_s": 5538.3, "baseline_cpu_h": 2.92, "full_cpu_h": 2.382, "final_official_check_s": 290.3, "historical_check_s": 6161.6 }, "six_step_inputs": { "chain_length": [ 4, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 6.0, "measured: mean over the original levels" ], "build_scratch_s": [ 91.0, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 67.1, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 35.0, "measured: original levels, challenge + solution export" ], "parse_s": [ 14.0, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 8.8, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 35.0, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 18.9, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.115, "measured: constants still checked / all, production levels that started with a warm ledger (L3, L4)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 1.467, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 205.1, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 43.3, "measured" ], "cache_build_s": [ 110.0, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 6159.2 ], [ "+ scheduling and infrastructure", 1871.2 ], [ "+ chain/subtree coalescing", 197.8 ], [ "+ build reuse", 173.9 ], [ "+ verified-constant ledger", 136.7 ], [ "+ parallel kernel replay", 132.9 ] ] }, { "slug": "sphere-theorem", "chain_length": 3, "tree": { "obligations": 167, "started": "2026-10-11T13:24:54Z", "root_accepted": "2026-10-13T00:23:51Z" }, "chain": { "baseline_s": 4527.9, "baseline_status": "measured", "baseline_measured_s": 4527.9, "baseline_estimate_method": null, "full_s": 389.2, "full_status": "measured", "ratio": 11.63, "full_samples_s": [ 389.2 ], "baseline_cpu_h": 10.014, "full_cpu_h": 0.338, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 3, "baseline_levels_measured": [ 1, 2, 3 ], "baseline_mean_s": 1509.3, "baseline_each_s": [ 1286.9, 1522.3, 1718.7 ], "full_levels_measured": [ 1, 2, 3 ], "full_mean_s": 371.0, "full_each_s": [ 468.5, 328.4, 316.2 ], "historical_in_tree_s": [ 1731.2, 1710.5, 1690.1 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 2799.5, "baseline_status": "measured", "full_s": 506.7, "full_gate_build_s": 271.6, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "sp-iso-orig-L1", "verdict": "ACCEPT", "seconds": 1286.9, "setup": 14.0, "build": 785.9, "export": 95.0, "parse": 50.0, "nanoda": 61.0, "lean": 281.0, "kernels_wall": 392.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 300, "peak_mib": 11170, "cpu_s": 9364.4 }, { "label": "sp-iso-orig-L2", "verdict": "ACCEPT", "seconds": 1522.3, "setup": 14.0, "build": 967.6, "export": 110.0, "parse": 61.0, "nanoda": 62.0, "lean": 307.6, "kernels_wall": 430.6, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 482, "peak_mib": 13192, "cpu_s": 12466.8 }, { "label": "sp-iso-orig-L3", "verdict": "ACCEPT", "seconds": 1718.7, "setup": 14.0, "build": 1150.8, "export": 107.0, "parse": 73.0, "nanoda": 63.0, "lean": 310.8, "kernels_wall": 446.8, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 489, "peak_mib": 13264, "cpu_s": 14218.5 } ], "production": [ { "label": "sp-iso-side-L1", "verdict": "ACCEPT", "seconds": 361.1, "setup": 17.0, "build": 78.0, "export": 123.0, "parse": 63.1, "nanoda": 79.9, "lean": 36.8, "kernels_wall": 143.0, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 70415, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 5004, "cpu_s": 1034.2, "gate_build_s": 107.4 }, { "label": "sp-iso-side-L2", "verdict": "ACCEPT", "seconds": 281.2, "setup": 17.0, "build": 45.0, "export": 83.0, "parse": 44.2, "nanoda": 92.0, "lean": 41.7, "kernels_wall": 136.2, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 75283, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 6367, "cpu_s": 1050.1, "gate_build_s": 47.2 }, { "label": "sp-iso-side-L3", "verdict": "ACCEPT", "seconds": 290.2, "setup": 16.0, "build": 71.0, "export": 107.0, "parse": 77.2, "nanoda": 18.9, "lean": 15.8, "kernels_wall": 96.1, "replay_threads": 12, "ledger_constants_in": 75262, "constants_checked": 301, "constants_skipped": 75260, "modules_compiled": 0, "peak_mib": 5702, "cpu_s": 430.5, "gate_build_s": 26.0 } ], "one_check": [ { "label": "sp-iso-one-1", "verdict": "ACCEPT", "seconds": 286.5, "setup": 16.0, "build": 58.0, "export": 79.0, "parse": 44.9, "nanoda": 88.6, "lean": 39.2, "kernels_wall": 133.5, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 75563, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 6341, "cpu_s": 1046.7 } ], "one_check_gate_build_s": [ 102.7 ], "root_original": [ { "label": "sp-iso-root-orig", "verdict": "ACCEPT", "seconds": 2799.5, "setup": 14.0, "build": 1973.8, "export": 111.0, "parse": 59.0, "nanoda": 110.0, "lean": 531.7, "kernels_wall": 700.7, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 1337, "peak_mib": 19550, "cpu_s": 27698.5 } ], "root_full": [ { "label": "sp-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 506.7, "setup": 23.0, "build": 85.0, "export": 208.0, "parse": 118.1, "nanoda": 72.5, "lean": 37.9, "kernels_wall": 190.6, "replay_threads": 12, "ledger_constants_in": 75544, "constants_checked": 16575, "constants_skipped": 75538, "modules_compiled": 0, "peak_mib": 7541, "cpu_s": 1031.9 } ], "cache_build_s": [ 1536.0 ] }, "ledger": { "levels_warm": [ 3 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.004, "kernels_wall_left_fraction": 0.688, "nanoda_left_fraction": 0.22, "lean_left_fraction": 0.403, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 1731.157, 1710.529, 1690.066 ], "sum_regate_s": 5131.8, "span_s": 6111.4, "regate_own_seconds": [ 1731.157, 1710.529, 1690.066 ], "answered_by_prewarm": [ false, false, false ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v8, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Differentiable sphere theorem (Brendle–Schoen)", "id": "sphere_theorem_differentiable", "collection": "Lean-Eval", "tree_dag": { "obligations": 167, "live_accepted": 111, "depth": 8, "checks": 143, "proof_checks": 112, "regates": 27, "root_checks": 4, "excluded": 133, "chains": [ 2, 2, 2, 2, 2, 3, 3, 2 ], "checks_after_coalescing": 133, "historical_check_s": 240386.1, "production": { "max_gate_builds": 4, "check_timeout_s": 10800.0, "solve_pool": 40, "hours": 48.0 } }, "ratios": { "baseline_over_historical": 0.883, "full_over_historical": 0.217 }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 109312.6, "baseline_status": "estimate", "full_s": 27669.6, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "rough", "ratio_used": 0.883 }, "six_step_inputs": { "chain_length": [ 3, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 14.0, "measured: mean over the original levels" ], "build_scratch_s": [ 968.1, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 124.9, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 104.0, "measured: original levels, challenge + solution export" ], "parse_s": [ 61.3, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 62.0, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 299.8, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 139.6, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.004, "measured: constants still checked / all, production levels that started with a warm ledger (L3)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 0.688, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 389.2, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 133.5, "measured" ], "cache_build_s": [ 1536.0, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 8487.6 ], [ "+ scheduling and infrastructure", 5271.6 ], [ "+ chain/subtree coalescing", 1517.2 ], [ "+ build reuse", 674.0 ], [ "+ verified-constant ledger", 366.5 ], [ "+ parallel kernel replay", 333.1 ] ] }, { "slug": "wang-zahl-kakeya", "chain_length": 3, "tree": { "obligations": 234, "started": "2026-10-11T13:27:49Z", "root_accepted": "2026-10-13T23:39:45Z" }, "chain": { "baseline_s": 736.8, "baseline_status": "measured", "baseline_measured_s": 736.8, "baseline_estimate_method": null, "full_s": 168.3, "full_status": "measured", "ratio": 4.38, "full_samples_s": [ 169.1, 167.5 ], "baseline_cpu_h": 0.385, "full_cpu_h": 0.1035, "worker": { "cores": 8, "cpus": 16, "memory_gib": 64 } }, "single_node": { "nodes": 3, "baseline_levels_measured": [ 1, 2, 3 ], "baseline_mean_s": 245.6, "baseline_each_s": [ 223.8, 227.0, 286.0 ], "full_levels_measured": [ 1, 2, 3 ], "full_mean_s": 137.1, "full_each_s": [ 142.0, 138.6, 130.7 ], "historical_in_tree_s": [ 233.1, 278.9, 258.5 ], "baseline_status": "measured", "full_status": "measured" }, "root": { "baseline_s": 5122.0, "baseline_status": "measured", "full_s": 599.4, "full_gate_build_s": 3569.5, "full_mode": "fast_root" }, "runs": { "original": [ { "label": "wz-iso-orig-L1", "verdict": "ACCEPT", "seconds": 223.8, "setup": 6.0, "build": 96.0, "export": 41.0, "parse": 18.0, "nanoda": 14.0, "lean": 48.8, "kernels_wall": 80.8, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 14, "peak_mib": 4182, "cpu_s": 336.3 }, { "label": "wz-iso-orig-L2", "verdict": "ACCEPT", "seconds": 227.0, "setup": 6.0, "build": 102.0, "export": 39.0, "parse": 19.0, "nanoda": 12.0, "lean": 49.0, "kernels_wall": 80.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 17, "peak_mib": 4173, "cpu_s": 353.9 }, { "label": "wz-iso-orig-L3", "verdict": "ACCEPT", "seconds": 286.0, "setup": 6.0, "build": 136.0, "export": 43.0, "parse": 20.0, "nanoda": 17.0, "lean": 64.0, "kernels_wall": 101.0, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 39, "peak_mib": 6611, "cpu_s": 694.6 } ], "production": [ { "label": "wz-iso-side-L1", "verdict": "ACCEPT", "seconds": 116.9, "setup": 7.0, "build": 35.0, "export": 40.0, "parse": 19.0, "nanoda": 15.8, "lean": 7.9, "kernels_wall": 34.9, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 46899, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 2751, "cpu_s": 267.2, "gate_build_s": 25.1 }, { "label": "wz-iso-side-L2", "verdict": "ACCEPT", "seconds": 117.0, "setup": 6.0, "build": 35.0, "export": 41.0, "parse": 18.2, "nanoda": 16.7, "lean": 7.6, "kernels_wall": 35.0, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 46921, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 2574, "cpu_s": 260.8, "gate_build_s": 21.6 }, { "label": "wz-iso-side-L3", "verdict": "ACCEPT", "seconds": 109.6, "setup": 6.0, "build": 35.0, "export": 41.0, "parse": 19.7, "nanoda": 7.9, "lean": 4.7, "kernels_wall": 27.6, "replay_threads": 12, "ledger_constants_in": 46900, "constants_checked": 2198, "constants_skipped": 46898, "modules_compiled": 0, "peak_mib": 2765, "cpu_s": 160.4, "gate_build_s": 21.1 } ], "one_check": [ { "label": "wz-iso-one-1", "verdict": "ACCEPT", "seconds": 131.9, "setup": 7.0, "build": 48.0, "export": 40.0, "parse": 19.5, "nanoda": 17.4, "lean": 8.3, "kernels_wall": 36.9, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 49098, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 3093, "cpu_s": 313.0 }, { "label": "wz-iso-one-2", "verdict": "ACCEPT", "seconds": 130.4, "setup": 6.0, "build": 48.0, "export": 39.0, "parse": 19.4, "nanoda": 17.9, "lean": 8.3, "kernels_wall": 37.4, "replay_threads": 12, "ledger_constants_in": 0, "constants_checked": 49098, "constants_skipped": 0, "modules_compiled": 0, "peak_mib": 2994, "cpu_s": 315.8 } ], "one_check_gate_build_s": [ 37.2, 37.1 ], "root_original": [ { "label": "wz-iso-root-orig", "verdict": "ACCEPT", "seconds": 5122.0, "setup": 25.0, "build": 4554.2, "export": 124.0, "parse": 57.0, "nanoda": 79.0, "lean": 282.7, "kernels_wall": 418.8, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 3466, "peak_mib": 25586, "cpu_s": 69550.0 } ], "root_full": [ { "label": "wz-iso-root-fast-1", "verdict": "ACCEPT", "seconds": 599.4, "setup": 43.0, "build": 62.0, "export": 215.0, "parse": 177.9, "nanoda": 101.4, "lean": 34.9, "kernels_wall": 279.3, "replay_threads": 12, "ledger_constants_in": 49079, "constants_checked": 31231, "constants_skipped": 49073, "modules_compiled": 0, "peak_mib": 8921, "cpu_s": 1311.1 } ], "cache_build_s": [ 115.2 ] }, "ledger": { "levels_warm": [ 3 ], "levels_cold": [ 1, 2 ], "constants_left_fraction": 0.045, "kernels_wall_left_fraction": 0.79, "nanoda_left_fraction": 0.486, "lean_left_fraction": 0.606, "note": "warm = a production check that started with constants already in the ledger (learned from the levels below); fractions are warm/cold means of the same chain's levels, parallel replay on" }, "historical": { "regate_seconds": [ 233.117, 278.931, 258.535 ], "sum_regate_s": 770.6, "span_s": 830.4, "regate_own_seconds": [ 233.117, 278.931, 258.535 ], "answered_by_prewarm": [ false, false, false ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v8, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Wang–Zahl: the three-dimensional Kakeya conjecture", "id": "wang_zahl_kakeya_dimH", "collection": "Lean-Eval", "tree_dag": { "obligations": 234, "live_accepted": 134, "depth": 10, "checks": 193, "proof_checks": 156, "regates": 33, "root_checks": 4, "excluded": 241, "chains": [ 3, 3, 2, 2, 2, 4, 7, 4 ], "checks_after_coalescing": 174, "historical_check_s": 321342.9, "production": { "max_gate_builds": 4, "check_timeout_s": 10800.0, "solve_pool": 40, "hours": 48.0 } }, "ratios": { "baseline_over_historical": 0.96, "full_over_historical": 0.537 }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 162513.4, "baseline_status": "estimate", "full_s": 20736.2, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "rough", "ratio_used": 0.96 }, "six_step_inputs": { "chain_length": [ 3, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 6.0, "measured: mean over the original levels" ], "build_scratch_s": [ 111.3, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 57.6, "measured: mean over the production levels (LOT's gate build seeded from the kept build + check.sh's build seeded with it)" ], "export_s": [ 41.0, "measured: original levels, challenge + solution export" ], "parse_s": [ 19.0, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 14.3, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 53.9, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 35.0, "measured: production levels with an empty ledger, nanoda-t and the parallel Lean replay (12 threads) at the same time, wall" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ 0.045, "measured: constants still checked / all, production levels that started with a warm ledger (L3)" ], "ledger_parallel_kernels_warm_over_cold_measured": [ 0.79, "measured: kernel wall of the warm levels / the cold levels, parallel replay on (different levels: closure sizes differ; with parallel replay the kernel phase is already short)" ], "one_check_s": [ 169.1, "measured: gate build + one check of the whole chain, all optimizations on" ], "one_check_kernels_s": [ 36.9, "measured" ], "cache_build_s": [ 115.2, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ] }, "page_model_chain_steps": [ [ "baseline", 4696.5 ], [ "+ scheduling and infrastructure", 1480.5 ], [ "+ chain/subtree coalescing", 253.5 ], [ "+ build reuse", 199.8 ], [ "+ verified-constant ledger", 141.8 ], [ "+ parallel kernel replay", 136.8 ] ] }, { "slug": "oai-074-kakeya-four", "chain_length": 5, "tree": { "obligations": 296, "started": "2026-10-21T01:44:08Z", "root_accepted": "2026-10-22T20:30:36Z" }, "chain": { "baseline_s": 57166.3, "baseline_status": "cut_at_12h", "baseline_measured_s": 43233.1, "baseline_estimate_method": "levels 1-3 ran to the end (36706 s, measured); level 4 was stopped at the 12 h cut after 6527 s, in its solution_export stage (235 s in it); its remainder, 1483 s, is the rest of that stage (136 s, at least 0) plus the later stages (1347 s): level 3's measured run (12415 s)'s stages times 0.642 (its solution_build stage took 6191 s against the reference's 9639 s); level 5 not started (the 12 h of timeline were used up): each estimated as level 3's time (12415 s, measured) times the square root of the import-closure ratio (L5 7476 vs 7434 Submission modules; time ~ sqrt(closure): on the seven finished examples' original runs, median error 7% per level, -39%..+30%). The 12 h are displayed timeline: the levels' measured durations inside their containers, one after another", "full_s": null, "full_status": "pending", "ratio": null, "full_samples_s": null, "baseline_cpu_h": 122.816, "full_cpu_h": null, "worker": { "cores": 8, "cpus": 16, "memory_gib": 128 } }, "single_node": { "nodes": 5, "baseline_levels_measured": [ 1, 2, 3 ], "baseline_mean_s": 12235.4, "baseline_each_s": [ 13076.0, 11215.0, 12415.3 ], "full_levels_measured": [], "full_mean_s": 1300.0, "full_each_s": [], "historical_in_tree_s": [ 2322.3, 2448.3, 2529.2, 2626.3, 2632.7 ], "baseline_status": "measured on 3 of 5 levels", "full_status": "estimate", "full_note": "estimate, as the chain's one check (see the inputs): the five levels' closures differ by under 1% (7,434-7,476 Submission modules); re-measure pending the nanoda-t fix" }, "root": { "baseline_s": 16048.1, "baseline_status": "measured", "full_s": null, "full_gate_build_s": null, "full_mode": "node_whatif" }, "runs": { "original": [ { "label": "kk-iso-orig-L1", "verdict": "ACCEPT", "seconds": 13076.0, "setup": 74.0, "build": 10418.7, "export": 517.1, "parse": 222.0, "nanoda": 225.0, "lean": 1619.1, "kernels_wall": 2066.2, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 6142, "peak_mib": 60749, "cpu_s": 158743.8 }, { "label": "kk-iso-orig-L2", "verdict": "ACCEPT", "seconds": 11215.0, "setup": 66.0, "build": 8633.7, "export": 409.0, "parse": 293.0, "nanoda": 230.0, "lean": 1583.1, "kernels_wall": 2106.2, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 7376, "peak_mib": 70225, "cpu_s": 134700.2 }, { "label": "kk-iso-orig-L3", "verdict": "ACCEPT", "seconds": 12415.3, "setup": 63.0, "build": 9661.4, "export": 594.1, "parse": 379.0, "nanoda": 217.0, "lean": 1500.7, "kernels_wall": 2096.8, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 7434, "peak_mib": 51964, "cpu_s": 148693.0 }, { "label": "kk-iso-orig-L4", "verdict": "stopped at the 12 h cut", "seconds": 6529.0, "setup": null, "build": null, "export": null, "parse": null, "nanoda": null, "lean": null, "kernels_wall": null, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 7435, "peak_mib": null, "cpu_s": null } ], "production": [], "one_check": [], "one_check_gate_build_s": [ 104.0 ], "root_original": [ { "label": "kk-iso-root-orig", "verdict": "ACCEPT", "seconds": 16048.1, "setup": 108.0, "build": 13458.7, "export": 501.1, "parse": 273.0, "nanoda": 222.0, "lean": 1485.2, "kernels_wall": 1980.3, "replay_threads": 1, "ledger_constants_in": null, "constants_checked": null, "constants_skipped": null, "modules_compiled": 10625, "peak_mib": 78512, "cpu_s": 210414.8 } ], "root_full": [], "cache_build_s": [ 9016.4 ] }, "ledger": null, "historical": { "regate_seconds": [ 2322.32, 2448.272, 2529.163, 2626.258, 2632.673 ], "sum_regate_s": 12558.7, "span_s": 2662.2, "regate_own_seconds": [ 2322.32, 0.0, 0.0, 0.0, 0.0 ], "answered_by_prewarm": [ false, true, true, true, true ], "span_note": "from the bottom level's REGATE start to the top level's acceptance, as the tree ran it (LOT at the time with checker trusted-v10wz, its build reuse, prewarms, queueing and the scheduler's ticks included)" }, "title": "Every four-dimensional Kakeya set has full Hausdorff dimension", "id": "074", "collection": "OpenAI math", "tree_dag": { "obligations": 296, "live_accepted": 241, "depth": 12, "checks": 358, "proof_checks": 284, "regates": 73, "root_checks": 1, "excluded": 305, "chains": [ 2, 3, 4, 2, 3, 3, 2, 2, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 5 ], "checks_after_coalescing": 319, "historical_check_s": 198507.4, "production": { "max_gate_builds": 32, "check_timeout_s": 10800.0, "solve_pool": 128, "hours": 72.0 } }, "ratios": { "baseline_over_historical": 5.04, "full_over_historical": null }, "whole_tree": { "status": "estimate", "lanes": 2, "lane": "8 whole cores (16 CPUs), as the measured replays", "baseline_s": 543051.7, "baseline_status": "estimate", "full_s": 100166.2, "full_status": "estimate", "method": "whole-tree estimate on two lanes, the measured replays' list scheduling over the tree's own check plan:\n BASELINE every check = its historical seconds x r_o (the chain example's isolated-baseline/historical ratio\n of the same tree), the root = the chain example's measured official root check;\n FULL the cache build first, then every check = the chain example's measured single-node full mean (gate build\n + check, production levels), each closing cascade = one check timed as the chain example's measured one check,\n the root = the measured fast root + its gate build. Without a measured single-node full mean (304, 074) every\n check = its historical seconds x 1.0 (the tree ran with build reuse already).", "confidence": "low", "ratio_used": 5.04 }, "six_step_inputs": { "chain_length": [ 5, "measured" ], "checks_after_coalescing": [ 1, "measured (the chain is one check)" ], "queue_before_s": [ 1080, "uniform: median wait before a check started, 16-20 min before the scheduling work (Gorenstein-Walter tree, 2026-10-15); page model 18 min" ], "queue_after_s": [ 8, "uniform: about 8 s after it (same tree)" ], "landing_gap_s": [ 360.0, "uniform: closing a chain level by level adds 0.05-0.2 h per level (production trees); page model 0.1 h" ], "setup_s": [ 67.7, "measured: mean over the original levels" ], "build_scratch_s": [ 9571.3, "measured: mean over the original levels (challenge + solution build, from scratch)" ], "build_reuse_s": [ 275.0, "estimate: the one check's measured gate build (104 s) + setup and seeded build 171 s (nanoda investigation)" ], "export_s": [ 506.7, "measured: original levels, challenge + solution export" ], "parse_s": [ 298.0, "measured: original levels, parse (kernel_prep)" ], "nanoda_s": [ 224.0, "measured: original levels, the toolchain's nanoda 0.4.17" ], "lean_serial_s": [ 1567.6, "measured: original levels, the serial Lean replay" ], "parallel_kernels_s": [ 420.0, "estimate: the parallel Lean replay 287 s (par:12, measured on this chain's export) beside nanoda 0.4.17 247 s (measured on the same export): 300-420 s with the fixed nanoda-t; the pinned nanoda-t 0.4.6-beta never finishes two theorems of this proof" ], "ledger_kernel_left": [ 0.15, "uniform: the kernel phase was 85% shorter with the ledger on a large tree with serial kernels (Gorenstein-Walter, 93.1% of constants skipped, 7/7 spot checks identical); page model 0.15" ], "ledger_constants_left_measured": [ null, "no production level started with a warm ledger" ], "ledger_parallel_kernels_warm_over_cold_measured": [ null, "-" ], "one_check_s": [ 1300.0, "estimate: gate build 104 s + setup/seeded build 171 s + export 393 s + parse 269 s + kernels 300-420 s (≈1,240-1,360 s), once nanoda-t is on 0.4.17 (re-measure pending)" ], "one_check_kernels_s": [ null, "measured" ], "cache_build_s": [ 9016.4, "measured: the lib's first build from scratch (S0), a premise of build reuse, not counted" ], "note": "original: levels 1-3 measured to their end, level 4 to the 12 h cut, level 5 estimated" }, "page_model_chain_steps": [ [ "baseline", 68016.5 ], [ "+ scheduling and infrastructure", 62656.5 ], [ "+ chain/subtree coalescing", 12243.3 ], [ "+ build reuse", 2947.0 ], [ "+ verified-constant ledger", 1424.1 ], [ "+ parallel kernel replay", 1218.4 ] ] } ] }