ResultPrevalence, lead time and incremental lifetime signal of entombed numbered discs in the existing training corpus
Corpus analysis of entombed numbered discs (value n with column height > n and horizontal run > n) over 4,863,627 non-explored positions.
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Technical recordMetrics, gate checks and limitations
Corpus analysis of entombed numbered discs (value n with column height > n and horizontal run > n) over 4,863,627 non-explored positions. Prevalence: an entombed disc of value >= 3 is on the board in 19.1% of depth-4 behaviour states overall, rising from 7.6% more than 40 moves before death to 69.8% within 5 moves of it. At death: 579 of 768 complete depth-4 games (75.4%) end with one on the board (criterion 1 holds). Lead time from first persistent appearance to death: median 11 moves, quartiles 5.5-15, 57% at least 10 moves, 8% at least 20 (criterion 2 holds, narrowly). Incremental signal: held-out R^2 for log1p(moves to death) is 0.6952 with the 18 frozen leaf features + occupancy + rise clock and 0.6955 with the entombed features added (+0.0003); the held-out partial correlation of the entombed count is -0.023 (threshold -0.05). Criterion 3 fails. Occupancy-matched, an entombed >= 3 disc shortens mean remaining life by about two moves (e.g. 35.0 vs 37.4 at 24-27 occupied cells; 24.6 vs 26.3 at 28-31). Reading: the disc is a reliable marker of the policy's last two rises, but the leaf's value-blind height and cover terms already carry almost all of its lifetime information; as a static foresight term it is not what the search is missing. Gate: FAIL (not-supported-as-tested).
- ✓analysis completes on all non-explored records with finite leaf values — observed: 4863627 records analysed, 393554 explored records excluded, 0 invalid leaf rows
- ✓depth-4 fracAtDeath >= 0.5 — observed: 0.7539
- ✓depth-4 lead-time median >= 10 moves — observed: median 11.0, q25 5.5, q75 15.0
- ✕held-out partial correlation <= -0.05 AND incremental R^2 >= 0.005 — observed: partial -0.0234; incremental R^2 0.00031; depth-4-only incremental R^2 0.00043
Technical recordRecorded metrics
- depth1
- states
- 664,432
- fracWithEntombedGe3
- 0.2291
- fracWithEntombedLe2
- 0.7340
- byMovesToDeath
- death<=5
- states
- 70,086
- fracWithEntombedGe3
- 0.6572
- meanEntombedGe3
- 1.5275
- meanOccupancy
- 38.0101
- fracWithEntombed34
- 0.6525
- death6-15
- states
- 142,831
- fracWithEntombedGe3
- 0.4339
- meanEntombedGe3
- 0.7169
- meanOccupancy
- 31.2209
- fracWithEntombed34
- 0.4324
- death16-40
- states
- 323,577
- fracWithEntombedGe3
- 0.1177
- meanEntombedGe3
- 0.1483
- meanOccupancy
- 22.1048
- fracWithEntombed34
- 0.1174
- death>40
- states
- 127,938
- fracWithEntombedGe3
- 0.0477
- meanEntombedGe3
- 0.0580
- meanOccupancy
- 17.3375
- fracWithEntombed34
- 0.0477
- depth2
- states
- 3,840,470
- fracWithEntombedGe3
- 0.2056
- fracWithEntombedLe2
- 0.7731
- byMovesToDeath
- death<=5
- states
- 302,037
- fracWithEntombedGe3
- 0.6640
- meanEntombedGe3
- 1.5443
- meanOccupancy
- 38.6116
- fracWithEntombed34
- 0.6588
- death6-15
- states
- 609,783
- fracWithEntombedGe3
- 0.4542
- meanEntombedGe3
- 0.7616
- meanOccupancy
- 31.7454
- fracWithEntombed34
- 0.4527
- death16-40
- states
- 1,472,663
- fracWithEntombedGe3
- 0.1487
- meanEntombedGe3
- 0.1933
- meanOccupancy
- 23.8524
- fracWithEntombed34
- 0.1484
- death>40
- states
- 1,455,987
- fracWithEntombedGe3
- 0.0640
- meanEntombedGe3
- 0.0787
- meanOccupancy
- 19.2009
- fracWithEntombed34
- 0.0639
- depth3
- states
- 295,894
- fracWithEntombedGe3
- 0.1981
- fracWithEntombedLe2
- 0.7871
- byMovesToDeath
- death<=5
- states
- 19,429
- fracWithEntombedGe3
- 0.6915
- meanEntombedGe3
- 1.5718
- meanOccupancy
- 39.2730
- fracWithEntombed34
- 0.6840
- death6-15
- states
- 39,219
- fracWithEntombedGe3
- 0.4741
- meanEntombedGe3
- 0.8055
- meanOccupancy
- 32.2350
- fracWithEntombed34
- 0.4727
- death16-40
- states
- 95,924
- fracWithEntombedGe3
- 0.1716
- meanEntombedGe3
- 0.2273
- meanOccupancy
- 24.5149
- fracWithEntombed34
- 0.1714
- death>40
- states
- 141,322
- fracWithEntombedGe3
- 0.0716
- meanEntombedGe3
- 0.0883
- meanOccupancy
- 19.7004
- fracWithEntombed34
- 0.0716
- depth4
- states
- 62,831
- fracWithEntombedGe3
- 0.1912
- fracWithEntombedLe2
- 0.7960
- byMovesToDeath
- death<=5
- states
- 3,709
- fracWithEntombedGe3
- 0.6983
- meanEntombedGe3
- 1.5980
- meanOccupancy
- 40.0768
- fracWithEntombed34
- 0.6945
- death6-15
- states
- 7,461
- fracWithEntombedGe3
- 0.4832
- meanEntombedGe3
- 0.8128
- meanOccupancy
- 32.7330
- fracWithEntombed34
- 0.4801
- death16-40
- states
- 18,403
- fracWithEntombedGe3
- 0.1783
- meanEntombedGe3
- 0.2425
- meanOccupancy
- 24.8813
- fracWithEntombed34
- 0.1777
- death>40
- states
- 33,258
- fracWithEntombedGe3
- 0.0763
- meanEntombedGe3
- 0.0941
- meanOccupancy
- 20.0137
- fracWithEntombed34
- 0.0761
- occ12-15
- with
- 513
- without
- 186,855
- meanMovesToDeathWith
- 63.0546
- meanMovesToDeathWithout
- 61.1056
- medianWith
- 57
- medianWithout
- 53
- occ16-19
- with
- 6,583
- without
- 658,931
- meanMovesToDeathWith
- 55.4624
- meanMovesToDeathWithout
- 54.8682
- medianWith
- 48
- medianWithout
- 47
- occ20-23
- with
- 43,236
- without
- 856,842
- meanMovesToDeathWith
- 45.5290
- meanMovesToDeathWithout
- 47.7573
- medianWith
- 38
- medianWithout
- 40
- occ24-27
- with
- 142,959
- without
- 845,929
- meanMovesToDeathWith
- 35.0183
- meanMovesToDeathWithout
- 37.3720
- medianWith
- 28
- medianWithout
- 30
- occ28-31
- with
- 233,244
- without
- 541,605
- meanMovesToDeathWith
- 24.6265
- meanMovesToDeathWithout
- 26.3040
- medianWith
- 18
- medianWithout
- 20
- occ32-35
- with
- 232,362
- without
- 235,132
- meanMovesToDeathWith
- 14.6345
- meanMovesToDeathWithout
- 15.7091
- medianWith
- 11
- medianWithout
- 12
- occ36-39
- with
- 168,268
- without
- 78,623
- meanMovesToDeathWith
- 8.2391
- meanMovesToDeathWithout
- 8.4068
- medianWith
- 7
- medianWithout
- 7
- depth3
- completeGames
- 4,096
- gamesWithEntombedGe3AtDeath
- 3,011
- fracAtDeath
- 0.7351
- leadTimeMoves
- median
- 10
- q25
- 6
- q75
- 15
- mean
- 11.0651
- fracAtLeast10
- 0.5739
- fracAtLeast20
- 0.0973
- meanGameLength
- 75.4805
- depth4
- completeGames
- 768
- gamesWithEntombedGe3AtDeath
- 579
- fracAtDeath
- 0.7539
- leadTimeMoves
- median
- 11
- q25
- 5.5000
- q75
- 15
- mean
- 10.8377
- fracAtLeast10
- 0.5665
- fracAtLeast20
- 0.0794
- meanGameLength
- 84.0182
- leafScalar+occupancy
- heldOutR2
- 0.6593
- heldOutPearson
- 0.8120
- train
- 3,891,854
- test
- 486,819
- leafFeatures18+occupancy
- heldOutR2
- 0.6952
- heldOutPearson
- 0.8338
- train
- 3,891,854
- test
- 486,819
- leafFeatures18+occupancy+entombed
- heldOutR2
- 0.6955
- heldOutPearson
- 0.8340
- train
- 3,891,854
- test
- 486,819
- entombedOnly+occupancy
- heldOutR2
- 0.5588
- heldOutPearson
- 0.7476
- train
- 3,891,854
- test
- 486,819
- depth4only
- leafFeatures18+occupancy
- heldOutR2
- 0.6483
- heldOutPearson
- 0.8062
- train
- 50,003
- test
- 5,528
- leafFeatures18+occupancy+entombed
- heldOutR2
- 0.6488
- heldOutPearson
- 0.8065
- train
- 50,003
- test
- 5,528
- depth3only
- leafFeatures18+occupancy
- heldOutR2
- 0.6657
- heldOutPearson
- 0.8162
- train
- 235,370
- test
- 28,612
- leafFeatures18+occupancy+entombed
- heldOutR2
- 0.6662
- heldOutPearson
- 0.8165
- train
- 235,370
- test
- 28,612
- partialCorrelationHeldOut
- ent_count_ge3
- -0.0234
- ent_mass_ge3
- -0.0156
- ent_covers_ge3
- -0.0162
- ent_top_ge3
- -0.0241
- ent_count_34
- -0.0234
- ent_count_ge3
- 0.3518
- ent_mass_ge3
- 8.1043
- ent_covers_ge3
- 1.1874
- ent_top_ge3
- 0.1959
- ent_count_le2
- 2.3535
- ent_count_34
- 0.3465
- Offline, teacher-labelled diagnostic on already-played behaviour games; says nothing about whether avoiding the entombing move would have extended life (a counterfactual replay is the natural follow-up).
- Linear incremental test: a nonlinear interaction with height could still carry signal a linear leaf cannot use; the NNUE leaf sees cell/pair features and could learn it.
- The structural definition ignores release readiness (whether a neighbouring clear could free the disc); dead_low_numbers discounts by readiness and this feature does not.
- Depth-4 behaviour games are 768 of the corpus's 86,784 games; depth-3 (4,096 games) agrees on every quantity.
- The corpus seeds are training-role data; the numbers are development diagnostics and not strength evidence.
Recorded against Prevalence, lead time and incremental lifetime signal of entombed numbered discs in the existing training corpus.
Agent contextHow to extend this record
To add a reader-facing explanation, write web/content/research/RS-20260822T051732Z-ceb257d7.mdx; it renders above this record on the next request. The recorded metrics, gate checks and limitations are in the technical record above.
Record file: research/results/RS-20260822T051732Z-ceb257d7.json, validated against research/schemas/result-v1.schema.json.
- Run ids
RUN-20260822T051517Z-eecf1098
- Contribution ids
CT-20260822T051732Z-a0507c6bCT-20260822T015730Z-eb02ae84
- Per-game artifact
–- Artifact manifest
runs/RUN-20260822T051517Z-eecf1098/analysis.json- Machine profiles
research/system-profiles/MACH-20260820T080056Z-376ada90.json