Oracle-visited public states carry transferable fair value (stage D0): the fair-relabelled lifetime of oracle-visited states exceeds that of matched fair-D4 states by a transferable fraction tau >= 0.25
web/content/research/TH-20260823-hpool-optimistic-states-fair-labels-bb707bc9.mdx and it will appear here. The registered record is shown below.The registered record
Claim
Public board states visited by the perfect-information oracle after move 50 have a higher expected remaining lifetime under FAIR, public-randomness continuation than fair-D4-visited states matched on rise phase, occupancy and maximum height. Defining R_fair(O) and R_fair(F) as the mean remaining moves over K independent public futures under a fixed public continuation policy, and R_tape(O), R_real(F) as the realised remaining moves on the states' own trajectories, the transferable fraction tau = (R_fair(O) - R_fair(F)) / (R_tape(O) - R_real(F)) is at least 0.25, with the same sign in both split halves of the O pool, and the oracle's column at oracle-visited roots is fair-top-1 under common public futures at least as often as fair D4's column is.
Mechanism
docs/exploratory/audit-05-optimistic-curriculum.md sections 4-7 classify every oracle-target failure as class (i) information gap and argue the removable cause is optimism in the LABEL (a function of the realised tape). The salvageable core, H-pool, is optimism in the STATE DISTRIBUTION with fair labels: oracle-visited states are publicly distinguishable (manifold classifier held-out AUC 0.925/0.915) and survival-type targets are the only targets this corpus ever fitted well. The crux number - the fair-relabelled value of an oracle-visited state - was computed by approaches/oracle-curriculum/state-curriculum/oracle-curriculum.cpp (7 public-derived H25 restarts per state, domain-separated streams, privilege terminated at the PublicState constructor) but never reported. This theory is a measurement, not a model: if tau is small, the oracle reaches its long lifetimes by knowing the tape, not by standing on better boards, and no student can inherit that by training on those boards. Design: runs/RUN-20260823T191900Z-b9f8f80d/kimi-k3-open-items.md (K4-B, Kimi K3).
What would prove it wrong
- tau < 0.25 on the pooled O set (K >= 32 public futures per state, fixed public D1 continuation, horizon 25, as in the curriculum code) refuses H-pool.
- Split halves of the O pool (by origin game) disagree in the sign of R_fair(O) - R_fair(F).
- At oracle-visited roots the oracle's column is fair-top-1 under common public futures less often than fair D4's column.
- Any one refusal ends the optimistic-teacher program; no follow-on student is trained. A pass licenses exactly one follow-on (pool comparison A1 fair / A2 optimistic / A3 mixed with fair labels), registered separately.
Experiments that test it
- Stage D0: fair relabelling of oracle-visited vs matched fair-D4 public statesoracle-curriculum state pool relabelled under public randomness vs fair-d4 matched state pool · CHECK · completed
Results recorded against it
Stage D0 refuses the H-pool theory on two of its three preregistered criteria. Pool O was 1,984 public states sampled from 64 oracle games (depth 4, beam 128; 63 of 64 games reached the 500-move cap); 1,271 were matched 1:1 to fair-D4 states on exact (rise phase, occupancy/4, max-height/2) buckets over all 256 comparator seeds (match rate 0.641; 713 O states dropped and counted). Under 32 common public futures with fair D1 continuation at horizon 25, oracle-visited boards are only marginally better than matched fair boards: R_fair(O) = 24.783 vs R_fair(F) = 24.520 (difference +0.263 moves, cluster bootstrap 95% [+0.156, +0.367], same positive sign in both origin-game halves). The preregistered transferable fraction is negative, tau = -0.959 (95% cluster interval [-3.069, -0.390]), because its denominator degenerates at this horizon: R_tape(O) = 24.338 vs R_real(F) = 24.611 (94-95% of both realised remainders were capped at 25), so the realised-lifetime gap the fraction was defined against is -0.274 moves rather than positive. Independently of that degeneracy, the action-quality criterion fails outright: the oracle's own column is fair-top-1 at its own roots less often than fair D4's column at the same roots (0.766 vs 0.814 over 1,271 roots, difference -0.049, 95% [-0.069, -0.029]; on the 194 unique-maximum roots 0.268 vs 0.387). Blocked-flow-band fraction over matched O states is 0.0047 (F: 0.026). Per the preregistration the theory is assessed not-supported-as-tested, the pool-comparison follow-on is not registered, and audit-05's H-pool program closes.
- ✓CHECK gates before any seed is read: privilege boundary (relabel binary links no oracle tape accessor), determinism of R_fair across two runs and thread counts, domain separation of restart streams, mirror invariance of R_fair — observed: ALL GATES PASS in runs/RUN-20260823T191900Z-b9f8f80d/d0/gates.log on probe seeds 0xa5278000-0xa527810f: 0 oracle symbols in d0-relabel, generate byte-identical at 16 vs 4 threads, relabel byte-identical at 1 vs 8 threads across two runs, 0 mirror/metadata/sibling/stream failures on 47 probe states (mirror invariance is exact: the restart plays in the canonical frame), label edits changed no relabel byte
- ✕tau >= 0.25 pooled — observed: tau = -0.9590, 95% cluster interval [-3.0691, -0.3897]; denominator R_tape(O)-R_real(F) = -0.274 moves is degenerate at horizon 25 (94-95% of both realised remainders capped) while the numerator R_fair(O)-R_fair(F) = +0.263 [+0.156, +0.367]
- ✓sign of R_fair(O) - R_fair(F) agrees in both origin-game halves — observed: half 0 (games 0-31): +0.2319; half 1 (games 32-63): +0.3146; both positive
- ✕oracle-column fair-top-1 rate at O roots >= fair-D4-column fair-top-1 rate at the same roots — observed: oracle 0.7655 vs fair D4 0.8143 over all 1,271 matched O roots under the same 32 common futures (no subsampling; ties count for every tied column); difference -0.0488, 95% cluster interval [-0.0691, -0.0288]; strict-maximum roots only: 0.268 vs 0.387
Recorded metrics
- -3.0691
- -0.3897
- half0
- -0.8357
- half1
- -1.1761
- mean
- 24.7826
- seStates
- 0.0365
- seOriginGames
- 0.0633
- mean
- 24.5201
- seStates
- 0.0491
- seOriginGames
- 0.1772
- mean
- 24.3375
- seStates
- 0.0904
- seOriginGames
- 0.0827
- mean
- 24.6113
- seStates
- 0.0525
- seOriginGames
- 0.2163
- 0.1561
- 0.3670
- half0
- 0.2319
- half1
- 0.3146
- oStates
- 1,984
- oMatched
- 1,271
- oUnmatched
- 713
- matchRate
- 0.6406
- fStates
- 1,271
- oOriginGames
- 64
- fOriginGames
- 101
- bucketsMatched
- 63
- R_tape_O_cappedAt25Fraction
- 0.9473
- R_real_F_cappedAt25Fraction
- 0.9426
- R_fair_O_survivedHorizonFraction
- 0.9624
- R_fair_F_survivedHorizonFraction
- 0.9167
- oracleGamesCensoredAt500
- 63
- oracleOriginCensoredStates
- 62
- O_matched_blocked
- 0.0047
- O_all_blocked
- 0.0030
- F_blocked
- 0.0260
- roots
- 1,271
- subsampled
- false
- oracleColumnTop1Rate
- 0.7655
- fairD4ColumnTop1Rate
- 0.8143
- difference
- -0.0488
- difference95ClusterBootstrap
- -0.0691
- -0.0288
- oracleEqualsD4ColumnRate
- 0.3895
- uniqueMaximumRoots
- 194
- oracleColumnTop1RateStrictRoots
- 0.2680
- fairD4ColumnTop1RateStrictRoots
- 0.3866
- method
- cluster bootstrap over O origin games carrying matched F partners
- resamples
- 10,000
- seed
- 0xb0071eaf
- clusters
- 64
- sensitivityIndependentClustersTau95
- -9.3496
- 5.1228
- The preregistered tau is ill-conditioned as measured: with 63 of 64 oracle games censored at the 500-move cap and comparator states drawn from the same shape buckets, both realised remainders sit at the 25-move horizon cap (R_tape(O) 24.34, R_real(F) 24.61, 94-95% capped), so the denominator is -0.274 moves instead of the large positive gap the definition assumed. The tau < 0.25 refusal is therefore driven by a degenerate denominator, not by a negative numerator; the numerator (the fair-value advantage of oracle boards) is positive but small, +0.263 moves on a 25-move horizon.
- The fair-top-1 criterion is unaffected by that degeneracy and fails on its own: the oracle's action is fair-best at its own roots significantly less often than fair D4's action at the same roots.
- Match rate 0.641: the 713 dropped O states skew toward buckets fair D4 rarely visits (matched O states are shape-matched by construction), so the numerator is a lower bound on the raw O-vs-F fair-value difference over all oracle states, and the comparison is conditional on shape overlap as preregistered.
- R_fair uses a fixed public D1 continuation and horizon 25 with 32 futures; 92-96% of futures survive the horizon, so both pools are near the measurement ceiling and the +0.263 difference is compressed by censoring at both ends.
- F origin games contribute clustered states (mean 12.6 matched states over 101 of 256 games); uncertainty uses cluster bootstrap over O origin games carrying matched partners, with the independent-clusters sensitivity interval also recorded (it is much wider: [-9.35, +5.12]).
- Diagnostic tier (CHECK): no gameplay evidence and no policy claim; training-role seeds only, opened once.