Depth-3 factored reveal quadrature (N=7, M=6) beats fair depth-4 five-stratum search on the shared cohort
web/content/research/TH-20260823-d3-reveal-quadrature-beats-d4s5-paired-4ee1d5fe.mdx and it will appear here. The registered record is shown below.The registered record
Claim
The depth-3 factored-chance fair search with seven disc strata and six reveal samples (D3 N7M6, fair leaf, finding-16) beats the frozen fair depth-4 five-stratum search (D4 s5, N5 M1, finding-05) on the shared development cohort 0xa51d1000-0xa51d103f by a paired per-game score margin whose one-sided 95% whole-game bootstrap lower bound and Student-t lower bound are both above zero.
Mechanism
finding-16 recorded 376,442 for D3 N7M6 and finding-05 recorded 297,327 for D4 s5 on the same 64 seeds, a +79,115 difference of means, but the two arms were never contrasted as paired per-game deltas: every published bound for D3 N7M6 was taken against D3 M=1, D3 M=12 or D4 N7 arms. The K2 program (runs/RUN-20260823T191900Z-b9f8f80d, section 1.4 and section 8 row C0) leans on this +79k as the head start of its fallback route (c). The mechanism claimed is that decorrelating the reveal draw at depth 3 buys more than the fourth ply buys at five strata (finding-05 measured the fourth ply at -7,723 NS at s5), so the shallower, better-quadratured search should dominate pairwise and not merely in means. If the paired bound does not clear zero the +79k is a heavy-tail artefact of 64 games and cannot be quoted as a head start.
What would prove it wrong
- The paired D3 N7M6 minus D4 s5 score delta over the 64 shared seeds has a one-sided 95% percentile bootstrap lower bound (20,000 resamples, seed 0xb0071eaf) at or below zero.
- The paired D3 N7M6 minus D4 s5 Student-t one-sided 95% lower bound is at or below zero.
- The two cohort halves in seed order disagree in sign, or W-T-L shows the mean is carried by fewer than a quarter of the games.
Experiments that test it
- C0: paired D3 N7M6 minus D4 s5 contrast from retained per-game recordsD3 N7M6: factored-chance-fair-search, depth 3, discSamples 7, revealSamples 6, terminalUtility -1000000, maximumWork 51084852, 2000-move cap, corrected 17,000-point Hardcore scoring (finding-16 arm, RUN-20260821T035407Z-00483c6c) vs D4 s5: parameterized-fair-search, depth 4, chanceSamples 5 (N5 M1), terminalUtility -1000000, maximumWork 3200000, 2000-move cap, corrected 17,000-point Hardcore scoring (finding-05 fresh-s5 arm, runs/RUN-A51D-s7confirm/fresh-s5.json; byte-identical games to runs/RUN-A52-LEAF/eval/s5-w000.json) · CHECK · completed
Results recorded against it
C0 reanalysis (K2 program section 8 row 0): the paired per-game bound behind the +79,115 head start is now printed, and it clears zero. On the 64 shared seeds 0xa51d1000-0xa51d103f, depth 3 with seven disc strata and six reveal samples (fair leaf, finding-16) scores 376,442 against fair depth 4 at five strata's 297,327 (finding-05): paired +79,115, one-sided 95% percentile bootstrap lower bound +29,033 (upper +129,722; 20,000 resamples, seed 0xb0071eaf), Student-t lower bound +27,548, W-T-L 35-0-29, halves +88,138 / +70,092, Q25 +34,872 (227,224 vs 192,352), median 322,859 vs 260,415, median paired delta +32,926, moves +22.30 (LB +8.67), paired sd 247,113, detection floor 50,813, at 3.27x the logical work per move (4,244,020 vs 1,296,034). Both gate bounds are positive, so the experiment passes and the theory is supported-as-tested at public-development tier. READ THE CAVEATS: the means and their difference were published before this gate was written, so this is a bound attached to a known sign on already-read development data, not a discovery; it is not promotable above this tier on this cohort. The delta is heavy-tailed: the five largest paired gains (seeds 0xa51d1012 +747,416, 0xa51d1020 +684,129, 0xa51d1008 +643,799, 0xa51d1001 +643,344, 0xa51d1033 +558,163) carry 64.7% of the summed delta, the sixteen largest carry 134% (the remaining 48 games net negative), and the worst loss is -332,950 (0xa51d103c); the minimum leave-one-out mean is still +68,507, so no single game is load-bearing, but against a detection floor of 50,813 the mean sits 1.56 floors above zero and the bootstrap lower bound only 0.57 floors above it. The flow statistics move with the score: numbered clears per move 2.0447 vs 1.9489, cover reveals per move 1.1423 vs 1.0697 (paired clears +53.9 per game, LB +21.1; reveals +31.8, LB +12.6), mean occupancy 23.49 vs 24.29. SECONDARY, not gated: against fair depth 4 at seven strata (398,498) the same arm is -22,056 with bounds (-92,005, +45,490), t lower bound -92,330, W-T-L 30-0-34, halves -27,121 / -16,991, Q25 +14,360, moves -5.20, at 0.86x the work; this reproduces finding-16's -22,056 point estimate exactly and its bootstrap lower bound to within 2,138 (finding-16 printed -89,867 from its own resampler; this run's pinned seed gives -92,005), and remains a wash. So the head start the K2 fallback route (c) stands on is real against D4 s5 but the same arm does not separate from D4 s7, which is the stronger comparator and the one the program's end state must beat on the strength-cost frontier.
- ✓Both arms are drop7-lifetime-cohort-v1 artifacts covering exactly the same 64 seeds 0xa51d1000-0xa51d103f in order, 0 censored games, 2000-move cap, terminalUtility -1000000, seedLease SEEDLEASE-A51D — observed: seed lists identical and in order for d3-n7-m6.json, fresh-s5.json, fresh-s7.json and s5-w000.json; censoredGames 0 in all; maximumMoves 2000; terminalUtility -1000000; seedLease SEEDLEASE-A51D; dataRole exploratory-development-diagnostic. Work bounds differ by design (51,084,852 vs 3,200,000 vs 16,000,000): they are the arms' own budgets, not a scoring setting. fresh-s5.json and s5-w000.json carry identical scores and moves on every game.
- ✓D3 N7M6 minus D4 s5: percentile bootstrap 95% lower bound > 0 AND Student-t 95% lower bound > 0 — observed: bootstrap LB +29,033, Student-t LB +27,548 (t quantile 1.6694, df 63); mean +79,115; W-T-L 35-0-29; halves +88,138 / +70,092
Recorded metrics
- artifact
- runs/RUN-A525-reveal/d3-n7-m6.json
- sha256
- 36aa1d0f0ec29b0ec70bd540e7d06758e37147a521f6891c0fde930943aa83fc
- meanScore
- 376442.1406
- median
- 322,859
- q25
- 227224.5000
- min
- 103,015
- max
- 1,002,557
- sd
- 223365.7773
- meanMoves
- 109.4531
- workPerMove
- 4244020.0805
- maximumWork
- 51,084,852
- censoredGames
- 0
- gamesAtOrAboveMillion
- 1
- artifact
- runs/RUN-A51D-s7confirm/fresh-s5.json
- sha256
- d6c1dbd403dbf5b477f1b0905b4aa440e443c2dfba8eef29085b7f5bee024d9a
- meanScore
- 297327.3906
- median
- 260,415
- q25
- 192,352
- min
- 86,935
- max
- 836,427
- sd
- 150549.5574
- meanMoves
- 87.1563
- workPerMove
- 1296033.6877
- maximumWork
- 3,200,000
- censoredGames
- 0
- gamesAtOrAboveMillion
- 0
- artifact
- runs/RUN-A51D-s7confirm/fresh-s7.json
- sha256
- 0c95442620a78ef5a928a4b8cdab9f57b3bdb8a3d7df5fcd1a6d818785bd4209
- meanScore
- 398498.2344
- median
- 344630.5000
- q25
- 212,864
- meanMoves
- 114.6563
- workPerMove
- 4956614.2652
- maximumWork
- 16,000,000
- censoredGames
- 0
- n
- 64
- meanScoreDelta
- 79114.7500
- pairedSd
- 247112.6017
- bootstrapLower95
- 29032.5102
- bootstrapUpper95
- 129721.6797
- studentTLower95
- 27548.4592
- studentTQuantile
- 1.6694
- detectionFloor
- 50812.5287
- winTieLoss
- 35-0-29
- firstHalfMeanDelta
- 88137.8438
- secondHalfMeanDelta
- 70091.6563
- q25Delta
- 34872.5000
- medianPairedDelta
- 32925.5000
- minLeaveOneOutMeanDelta
- 68506.7900
- top5Share
- 0.6470
- top16Share
- 1.3400
- meanMovesDelta
- 22.2969
- movesBootstrapLower95
- 8.6719
- movesStudentTLower95
- 8.2664
- numberedClearedDelta
- 53.9375
- numberedClearedLower95
- 21.1406
- coversRevealedDelta
- 31.7969
- coversRevealedLower95
- 12.6094
- workRatio
- 3.2746
- bootstrapSeedHex
- 0xb0071eaf
- resamples
- 20,000
- n
- 64
- meanScoreDelta
- -22056.0938
- pairedSd
- 336763.8340
- bootstrapLower95
- -92004.8930
- bootstrapUpper95
- 45490.1641
- studentTLower95
- -92330.3803
- detectionFloor
- 69247.0634
- winTieLoss
- 30-0-34
- firstHalfMeanDelta
- -27121.1250
- secondHalfMeanDelta
- -16991.0625
- q25Delta
- 14360.5000
- meanMovesDelta
- -5.2031
- movesBootstrapLower95
- -24.0313
- workRatio
- 0.8562
- finding16PointEstimate
- -22,056
- finding16BootstrapLower95
- -89,867
- Bound computation on already-read development data whose means and sign were published (finding-16, finding-05) before the gate was written; diagnostic, not promotable above public-development on this cohort. A fresh-development replication under a new protocol is required before the +79k is used as anything but a planning prior.
- The two arms were played in different runs (RUN-20260821T035407Z-00483c6c for D3 N7M6; the finding-05 fresh-s5 arm) by different binaries (factored-chance-fair-search vs parameterized-fair-search); the seed lists, move cap, terminal utility and scoring are identical but the pairing is across builds, not within one runner invocation. Engine parity between these families was established separately (finding-09/16 checks; finding-15 engine control), not re-run here.
- Heavy tail: five games carry 64.7% of the summed delta; the bootstrap lower bound sits 0.57 detection floors above zero. 64 games cannot resolve anything below about 50,800.
- The arm does not separate from D4 s7 (-22,056, bounds -92,005 to +45,490), so 'beats D4 s5' does not transfer to 'beats the current best fair comparator'.
- The wrapper pinned at freeze failed to import (module-name collision) and was amended before any output existed; the amendment changed no statistic. The first pinned wrapper hash is retained in expectedArtifacts and the amended hash in amendments.