← Theories
The frozen fair-leaf weights are not locally optimal for the corrected-score depth-4 search they are deployed in
not-supported-as-testedassessedevidence: public-developmentpublic-policyTH-20260822-depth-native-leaf-weights-caa6f8ba
No explanation has been written for this theory yet. Add
web/content/research/TH-20260822-depth-native-leaf-weights-caa6f8ba.mdx and it will appear here. The registered record is shown below.The registered record
Claim
For the corrected-score fair depth-4 search with the frozen five-stratum chance model (the contract comparator fair-d4), there exists a vector for the eighteen active fair-leaf weights whose mean whole-game score on fresh development seeds exceeds the frozen vector's by more than a 64-game paired cohort's detection floor, and a derivative-free optimiser that evaluates candidates by complete depth-4 games on a fresh seed block every generation can find such a vector within 40 generations of 16 candidates.
Mechanism
The leaf prices what four plies of search cannot see (finding-14). The frozen weights were hand-set for a depth-3 search under historical 7,000-point scoring and have never been refitted under corrected scoring or at the depth they are used at (approaches/fair-expectimax/fair-policy/README.mdx). The two prior weight optimisations failed under conditions that each independently explain failure without implying optimality: the CEM run tuned at depth 3 on rotating three-game batches and transferred its vector to depth 4 unchanged; the heuristic-search evolutions fitted one-ply policies on a fixed seed set and regressed on disjoint seeds. Fresh seeds every generation remove the seed-overfitting channel by construction; depth-native fitness removes the depth-transfer confound; common random numbers within a generation let small perturbations of one policy be ranked with far less variance than two unrelated policies. If the frozen point were a local optimum of mean score at depth 4, the population mean would show no paired gain over the control on fresh seeds and the frozen candidate would fail the held-out screen.
What would prove it wrong
- The preregistered held-out paired screen (64 never-read development games at depth 4, five strata) of the frozen final candidate against the frozen leaf has a one-sided 95% bootstrap lower bound on the mean score delta at or below zero, a Student-t lower bound at or below zero, a lower-quartile regression, or opposite-sign halves: the claim is not supported as tested.
- The paired population-mean-minus-control score delta on fresh training blocks does not exceed +20,000 in any of the last ten completed generations: no measurable gradient exists at this budget, and the claim is not supported as tested.
- Any generation artifact or screen artifact records an incomplete decision, an illegal decision, or a score-identity failure: the run is invalid and cannot support or reject the claim.
- Out of scope and explicitly not tested by this theory: transfer of a five-stratum-evolved vector to the seven-stratum search is measured as a secondary, diagnostic quantity only.
registered 2026-08-22T01:32:50Z by Claude Code / claude-fable-5
Experiments that test it
- CMA-ES over the eighteen fair-leaf weights inside the fast depth-4 five-stratum search, fresh training seeds per generation, one held-out paired screenfast-d4s5-evolved-leaf vs fair-d4 · SCREEN · completed
Results recorded against it
valid run · outcome: failnot-supported-as-testedpublic-developmentRS-20260822T120736Z-662b39ca
Held-out SCREEN of the CMA-ES leaf (distribution mean after 40 generations, stop=max-generations) against the frozen fair leaf, depth 4 five strata, 64 paired never-read games 0xa52b0000+: mean 289720 vs 320020, paired delta -30300 (bootstrap 95% LB -70928, t LB -71500, paired sd 197434, floor 40597), W-T-L 28-0-36, halves -53933/-6667, Q25 delta +8592. Gate: FAIL. Secondary seven-stratum transfer on the same seeds (diagnostic only): delta -47119 (LB -117910). Training-block population-mean-minus-control exceeded +20,000 in at least one of the last 10 generations.
What it had to pass
- ✓CHECK gates passed before the first training seed (runs/RUN-20260822T013756Z-0f7ab038/gates.log) — observed: 6 of 6 gates passed, 0 mismatches; recorded in RUN-20260822T013756Z-0f7ab038
- ✓incompleteDecisionsTotal 0, illegalDecisionsTotal 0, no score-identity failures across all generation and screen artifacts — observed: incomplete 0, illegal 0, identity failures 0 over 40 generations and 2 screen arms
- ✕held-out d4s5: bootstrap 95% lower bound > 0 AND Student-t 95% lower bound > 0 — observed: mean delta -30300.4, bootstrap LB -70928.5, t LB -71499.9, floor 40597.3
- ✓held-out d4s5: candidate Q25 >= frozen Q25 — observed: Q25 candidate 188540.2 vs frozen 179948.5
- ✕held-out d4s5: paired mean delta > 0 in both halves — observed: halves -53933.4 / -6667.4
- ✓the screened vector is the CMA distribution mean frozen before the held-out lease was opened — observed: candidate-weights.txt sha256 0dd29deb11f0238455353a396098e85c47ba4e02587c48286557bcad5429b637; final.json stop reason max-generations after 40 generations
Recorded metrics
heldOutD4S5
- candidate
- name
- candidate
- games
- 64
- score
- mean
- 289719.6563
- median
- 250811.5000
- sd
- 157309.7762
- q25
- 188540.2500
- min
- 103,274
- max
- 951,994
- moves
- mean
- 85.5313
- q25
- 58.7500
- numberedClearsPerMove
- 1.9731
- coverRevealsPerMove
- 1.0981
- maxChainDepth
- 11
- meanOccupiedCells
- 23.4275
- censoredGames
- 0
- incompleteDecisions
- 0
- illegalDecisions
- 0
- gamesAtOrAboveMillion
- 0
- reference
- name
- frozen
- games
- 64
- score
- mean
- 320020.0469
- median
- 274934.5000
- sd
- 190746.2218
- q25
- 179948.5000
- min
- 102,878
- max
- 933,091
- moves
- mean
- 93.5469
- q25
- 55
- numberedClearsPerMove
- 1.9676
- coverRevealsPerMove
- 1.0810
- maxChainDepth
- 10
- meanOccupiedCells
- 24.3490
- censoredGames
- 0
- incompleteDecisions
- 0
- illegalDecisions
- 0
- gamesAtOrAboveMillion
- 0
- pairedScore
- n
- 64
- meanDelta
- -30300.3906
- pairedSd
- 197433.6487
- bootstrapLower95
- -70928.4727
- bootstrapUpper95
- 9786.4258
- studentTLower95
- -71499.9121
- studentTQuantile
- 1.6694
- detectionFloor
- 40597.2940
- detectionFloorNote
- 1.645 * sd / sqrt(n), the z-based floor defined in docs/research/status.md
- wins
- 28
- ties
- 0
- losses
- 36
- firstHalfMeanDelta
- -53933.4063
- secondHalfMeanDelta
- -6667.3750
- q25Delta
- 8591.7500
- largestSwings
- -593,033
- -533,691
- -514,095
- 438,358
- 365,844
- bootstrapSeedHex
- 0xb0071eaf
- resamples
- 20,000
- pairedMoves
- n
- 64
- meanDelta
- -8.0156
- pairedSd
- 53.1609
- bootstrapLower95
- -18.9531
- bootstrapUpper95
- 2.8125
- studentTLower95
- -19.1090
- studentTQuantile
- 1.6694
- detectionFloor
- 10.9312
- detectionFloorNote
- 1.645 * sd / sqrt(n), the z-based floor defined in docs/research/status.md
- wins
- 27
- ties
- 4
- losses
- 33
- firstHalfMeanDelta
- -14.1563
- secondHalfMeanDelta
- -1.8750
- q25Delta
- 3.7500
- largestSwings
- -160
- -145
- -137
- 115
- 101
- bootstrapSeedHex
- 0xb0071eaf
- resamples
- 20,000
heldOutD4S7Diagnostic
- candidate
- name
- candidate
- games
- 64
- score
- mean
- 346762.6250
- median
- 264269.5000
- sd
- 229722.0652
- q25
- 176323.2500
- min
- 104,372
- max
- 1,090,823
- moves
- mean
- 101.1563
- q25
- 55
- numberedClearsPerMove
- 2.0216
- coverRevealsPerMove
- 1.1240
- maxChainDepth
- 12
- meanOccupiedCells
- 23.4526
- censoredGames
- 0
- incompleteDecisions
- 0
- illegalDecisions
- 0
- gamesAtOrAboveMillion
- 1
- reference
- name
- frozen
- games
- 64
- score
- mean
- 393881.4375
- median
- 320,713
- sd
- 249901.8659
- q25
- 195442.7500
- min
- 102,870
- max
- 1,130,039
- moves
- mean
- 113.7344
- q25
- 60
- numberedClearsPerMove
- 2.0640
- coverRevealsPerMove
- 1.1621
- maxChainDepth
- 10
- meanOccupiedCells
- 23.2727
- censoredGames
- 0
- incompleteDecisions
- 0
- illegalDecisions
- 0
- gamesAtOrAboveMillion
- 2
- pairedScore
- n
- 64
- meanDelta
- -47118.8125
- pairedSd
- 352065.1287
- bootstrapLower95
- -117909.7625
- bootstrapUpper95
- 25407.0273
- studentTLower95
- -120586.1010
- studentTQuantile
- 1.6694
- detectionFloor
- 72393.3921
- detectionFloorNote
- 1.645 * sd / sqrt(n), the z-based floor defined in docs/research/status.md
- wins
- 29
- ties
- 1
- losses
- 34
- firstHalfMeanDelta
- 28192.9063
- secondHalfMeanDelta
- -122430.5313
- q25Delta
- -19119.5000
- largestSwings
- -937,256
- 827,839
- -822,882
- -820,654
- 660,216
- bootstrapSeedHex
- 0xb0071eaf
- resamples
- 20,000
- pairedMoves
- n
- 64
- meanDelta
- -12.5781
- pairedSd
- 96.0415
- bootstrapLower95
- -31.8758
- bootstrapUpper95
- 7.2344
- studentTLower95
- -32.6196
- studentTQuantile
- 1.6694
- detectionFloor
- 19.7485
- detectionFloorNote
- 1.645 * sd / sqrt(n), the z-based floor defined in docs/research/status.md
- wins
- 28
- ties
- 5
- losses
- 31
- firstHalfMeanDelta
- 7.5938
- secondHalfMeanDelta
- -32.7500
- q25Delta
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- largestSwings
- -255
- 230
- -225
- -225
- 180
- bootstrapSeedHex
- 0xb0071eaf
- resamples
- 20,000
evolution
- generationsCompleted
- 40
- stopReason
- max-generations
- finalSigma
- 0.0652
- wallHours
- 9.7180
- seedsConsumedEndExclusiveHex
- 0xa5290500
- candidateWeights
- open_columns
- 148.0413
- height_load
- -30.0776
- solid_cells
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- cracked_cells
- -326.7377
- numbered_cells
- -25.3490
- high_low_numbers
- -60.4035
- direct_potential
- 1230.7800
- latent_chain_potential
- 608.4009
- cracked_exposure
- 131.4615
- solid_exposure
- 29.9260
- adjacent_ones
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- triple_twos
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- dead_low_numbers
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- covered_height_risk
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- low_number_height_risk
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- danger_height_squared
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- rise_pressure
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- next_disc_vertical_options
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- progress
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- populationBest
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- bestIndex
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- populationWorst
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- meanPairedDeltaVsControl
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- medianPairedSdVsControl
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- sigma
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- condition
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- wallSeconds
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- evaluatorWallSeconds
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- gen
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- populationMean
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- meanPairedDeltaVsControl
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- sigma
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- evaluatorWallSeconds
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- gen
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- controlMean
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- populationMean
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- populationBest
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- meanPairedDeltaVsControl
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- medianPairedSdVsControl
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- sigma
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- condition
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- wallSeconds
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- evaluatorWallSeconds
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- gen
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- games
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- controlMean
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- populationMean
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- populationBest
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- meanPairedDeltaVsControl
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- medianPairedSdVsControl
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- sigma
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- evaluatorWallSeconds
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- gen
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- games
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- meanPairedDeltaVsControl
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- gen
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- wallSeconds
- 816.9897
- evaluatorWallSeconds
- 816.9740
- gen
- 25
- seedStartHex
- 0xa5290320
- games
- 32
- controlMean
- 394248.8125
- populationMean
- 318951.4746
- populationBest
- 371139.2813
- bestIndex
- 14
- populationWorst
- 257599.8438
- meanPairedDeltaVsControl
- -75297.3379
- medianPairedSdVsControl
- 355548.1631
- sigma
- 0.0888
- condition
- 1.4694
- wallSeconds
- 933.6182
- evaluatorWallSeconds
- 933.6092
- gen
- 26
- seedStartHex
- 0xa5290340
- games
- 32
- controlMean
- 373975.8438
- populationMean
- 305625.9570
- populationBest
- 372646.2813
- bestIndex
- 12
- populationWorst
- 263425.0938
- meanPairedDeltaVsControl
- -68349.8867
- medianPairedSdVsControl
- 248534.7412
- sigma
- 0.0860
- condition
- 1.4752
- wallSeconds
- 856.1095
- evaluatorWallSeconds
- 856.0943
- gen
- 27
- seedStartHex
- 0xa5290360
- games
- 32
- controlMean
- 306527.3438
- populationMean
- 311577.5840
- populationBest
- 361121.5313
- bestIndex
- 14
- populationWorst
- 261,334
- meanPairedDeltaVsControl
- 5050.2402
- medianPairedSdVsControl
- 244600.9454
- sigma
- 0.0860
- condition
- 1.4856
- wallSeconds
- 864.5847
- evaluatorWallSeconds
- 864.5752
- gen
- 28
- seedStartHex
- 0xa5290380
- games
- 32
- controlMean
- 425243.6250
- populationMean
- 336869.3926
- populationBest
- 392982.9063
- bestIndex
- 4
- populationWorst
- 294603.5000
- meanPairedDeltaVsControl
- -88374.2324
- medianPairedSdVsControl
- 272346.5070
- sigma
- 0.0815
- condition
- 1.5208
- wallSeconds
- 967.0923
- evaluatorWallSeconds
- 967.0789
- gen
- 29
- seedStartHex
- 0xa52903a0
- games
- 32
- controlMean
- 352649.8750
- populationMean
- 305152.9082
- populationBest
- 358598.1563
- bestIndex
- 4
- populationWorst
- 247336.2188
- meanPairedDeltaVsControl
- -47496.9668
- medianPairedSdVsControl
- 258355.8448
- sigma
- 0.0777
- condition
- 1.5243
- wallSeconds
- 855.1493
- evaluatorWallSeconds
- 855.1336
- gen
- 30
- seedStartHex
- 0xa52903c0
- games
- 32
- controlMean
- 260597.2188
- populationMean
- 320306.2441
- populationBest
- 386149.7500
- bestIndex
- 0
- populationWorst
- 283558.7813
- meanPairedDeltaVsControl
- 59709.0254
- medianPairedSdVsControl
- 213531.5884
- sigma
- 0.0726
- condition
- 1.5277
- wallSeconds
- 885.3881
- evaluatorWallSeconds
- 885.3722
- gen
- 31
- seedStartHex
- 0xa52903e0
- games
- 32
- controlMean
- 359296.3125
- populationMean
- 327388.4082
- populationBest
- 387984.2813
- bestIndex
- 4
- populationWorst
- 273712.4688
- meanPairedDeltaVsControl
- -31907.9043
- medianPairedSdVsControl
- 246018.3954
- sigma
- 0.0699
- condition
- 1.5327
- wallSeconds
- 915.2263
- evaluatorWallSeconds
- 915.2098
- gen
- 32
- seedStartHex
- 0xa5290400
- games
- 32
- controlMean
- 277942.3750
- populationMean
- 303626.5098
- populationBest
- 343677.5000
- bestIndex
- 1
- populationWorst
- 252287.8125
- meanPairedDeltaVsControl
- 25684.1348
- medianPairedSdVsControl
- 213494.7003
- sigma
- 0.0708
- condition
- 1.5431
- wallSeconds
- 876.0767
- evaluatorWallSeconds
- 876.0621
- gen
- 33
- seedStartHex
- 0xa5290420
- games
- 32
- controlMean
- 379779.7813
- populationMean
- 316443.3535
- populationBest
- 371682.6875
- bestIndex
- 3
- populationWorst
- 275071.9688
- meanPairedDeltaVsControl
- -63336.4277
- medianPairedSdVsControl
- 280981.8576
- sigma
- 0.0707
- condition
- 1.5663
- wallSeconds
- 886.5113
- evaluatorWallSeconds
- 886.4983
- gen
- 34
- seedStartHex
- 0xa5290440
- games
- 32
- controlMean
- 304261.7813
- populationMean
- 319626.4297
- populationBest
- 363,269
- bestIndex
- 1
- populationWorst
- 295119.8125
- meanPairedDeltaVsControl
- 15364.6484
- medianPairedSdVsControl
- 272748.8985
- sigma
- 0.0680
- condition
- 1.5899
- wallSeconds
- 889.6517
- evaluatorWallSeconds
- 889.6369
- gen
- 35
- seedStartHex
- 0xa5290460
- games
- 32
- controlMean
- 255848.6563
- populationMean
- 331995.6289
- populationBest
- 377511.2500
- bestIndex
- 14
- populationWorst
- 289589.3750
- meanPairedDeltaVsControl
- 76146.9727
- medianPairedSdVsControl
- 221086.8710
- sigma
- 0.0653
- condition
- 1.5876
- wallSeconds
- 923.6854
- evaluatorWallSeconds
- 923.6700
- gen
- 36
- seedStartHex
- 0xa5290480
- games
- 32
- controlMean
- 267823.7813
- populationMean
- 290865.1133
- populationBest
- 322046.1875
- bestIndex
- 11
- populationWorst
- 262735.1250
- meanPairedDeltaVsControl
- 23041.3320
- medianPairedSdVsControl
- 177721.0672
- sigma
- 0.0660
- condition
- 1.6020
- wallSeconds
- 831.9670
- evaluatorWallSeconds
- 831.9511
- gen
- 37
- seedStartHex
- 0xa52904a0
- games
- 32
- controlMean
- 310436.4375
- populationMean
- 309239.6777
- populationBest
- 359385.4688
- bestIndex
- 2
- populationWorst
- 271522.4688
- meanPairedDeltaVsControl
- -1196.7598
- medianPairedSdVsControl
- 271233.4125
- sigma
- 0.0675
- condition
- 1.6150
- wallSeconds
- 859.6889
- evaluatorWallSeconds
- 859.6734
- gen
- 38
- seedStartHex
- 0xa52904c0
- games
- 32
- controlMean
- 324310.9688
- populationMean
- 339401.6621
- populationBest
- 394045.8750
- bestIndex
- 2
- populationWorst
- 303462.0625
- meanPairedDeltaVsControl
- 15090.6934
- medianPairedSdVsControl
- 275916.6619
- sigma
- 0.0663
- condition
- 1.6348
- wallSeconds
- 931.3985
- evaluatorWallSeconds
- 931.3823
- gen
- 39
- seedStartHex
- 0xa52904e0
- games
- 32
- controlMean
- 300656.6250
- populationMean
- 280208.6367
- populationBest
- 308910.5313
- bestIndex
- 2
- populationWorst
- 246365.3125
- meanPairedDeltaVsControl
- -20447.9883
- medianPairedSdVsControl
- 206957.2805
- sigma
- 0.0652
- condition
- 1.6499
- wallSeconds
- 844.4164
- evaluatorWallSeconds
- 844.4023
detectionFloorNote
A 64-game paired cohort cannot resolve effects below roughly the stated floor; a fail rejects this exact configuration and does not show the frozen weights are optimal.
Limitations
- Single 64-game development-tier screen on one machine; no replication yet (192 seeds of the held-out lease remain reserved for one).
- Evolution and screen ran while a GPU training sweep shared the machine; wall times are not timing-grade, decisions are deterministic and unaffected.
- The seven-stratum arm replays already-read held-out seeds and is diagnostic only.
- The population-mean trajectory on training blocks carries the perturbation penalty of sampling at sigma and does not measure the candidate's own fitness.
- Scripted-round (leaderboard) play of any vector is a demonstration and is not part of this result.