Chance-node decorrelation and search depth compound rather than substitute

Chance-node decorrelation and search depth do not compound; they substitute. The primary arm is complete at 64 of 64 games: depth 4 with seven disc samples and two reveal samples scores 356,548 against the 398,498 of the same search with one reveal sample, a paired -41,950 with a one-sided 95% whole-game bootstrap lower bound of -100,137 and W-T-L 28-0-36, for 4.07x the logical work per move. The gate asked for a lower bound above zero and got a negative point estimate, so the compounding theory is rejected as tested. STATE THE DOSE WHEN QUOTING THIS: two reveal samples raises joint (disc, reveal) coverage from 14.3% to 28.6%, which is a smaller increment than the six samples (85.7%) that first cleared noise at depth 3; at depth 3 the three-sample dose (42.9%) was also not significant (+24,980, lower bound -23,451). This result therefore rejects a doubling of reveal samples on top of the fourth ply, and does not establish that a wide reveal estimator at depth 4 would fail - that arm was never affordable. What the arm does establish is that the depth-4 search is not starved for the thing the extra samples supply. The striking positive finding is an equivalence at near-equal work: depth 3 with six reveal samples costs 4,244,020 work per move and scores 376,442, while depth 4 with one reveal sample costs 4,956,614 and scores 398,498, and the paired delta between them is -22,056 with a lower bound of -89,867 and W-T-L 30-0-34 - two different ways of spending the same budget landing in the same place, which is the same exchangeability the depth factorial shows from the other side. The new arm is not worthless: against the frozen five-stratum depth-4 reference it is +59,221 with a lower bound of +9,134 and W-T-L 37-0-27, so the gain comes from the seven disc samples, not from the reveal samples. Second arm, partial at 32 of 64 games and still running: depth 3 with twelve reveal samples takes joint coverage to 100% and scores -4,495 against the six-sample arm on the 32 shared seeds (lower bound -91,425, W-T-L 15-0-17) and +31,413 against the one-sample arm (lower bound -70,729), so the ladder that ordered with coverage from M=1 to M=6 stops ordering at M=12. Every arm audited 0 decisions below target depth, 0 work-limit events, 0 censored games and 0 score-decomposition identity failures, and the chunk-pooling used to survive interruption was verified to reproduce a single 64-game run field-for-field with identical summed logical work.

SUPERSEDES RS-20260821T181918Z-ea7076a3, which assessed the same experiment while its second arm held 32 of 64 games. Both arms are now complete at 64 of 64 and the run validity rises from partial to valid. The old record remains as committed history and is not edited; this record carries the completed figures and everything below replaces the partial ones. Nothing in arm 1 changed and the direction of arm 2 did not change; only its magnitude did, by about 6x. ARM 1, unchanged and complete: depth 4 with seven disc samples and two reveal samples scores 356,548 against the 398,498 of the same search with one reveal sample - a paired -41,950 with a one-sided 95% bootstrap interval of (-100,137, +17,541) and W-T-L 28-0-36, for 4.07x the logical work per move. The gate required a lower bound above zero, so the compounding theory is rejected as tested. The sign is stable across both cohort halves (-11,082 on seeds 0xa51d1000-0xa51d101f and -72,818 on 0xa51d1020-0xa51d103f), independently confirmed by the agent that completed the runs. The +17,541 ceiling is the load-bearing number: had the axes compounded even at a quarter of the +64,116 the same knob is worth at depth 3, the data would have had to show it. The axes substitute in the strong sense. ARM 2, now complete: depth 3 with twelve reveal samples - the configuration at which (disc, reveal) joint coverage reaches 100% - scores 349,345, not the 356,890 its first 32 games suggested. Against the six-sample arm it is -27,097 with an interval of (-83,807, +31,209) and W-T-L 28-0-36; against the one-sample arm +37,019 (-25,076, +102,426), 30-0-34. THE REVEAL AXIS SATURATES AT M ABOUT 6 AND DOES NOT IMPROVE TO FULL COVERAGE. Read this as saturation, not as a demonstrated regression: the M=6 to M=12 step does not clear zero in either direction, so the data are consistent with the curve being flat from M=6 onward and are not consistent with it continuing to climb at the rate M=1 to M=6 showed. Score, moves, numbered clears and covered reveals all peak at M=6 (85.7% coverage) and fall back at M=12 (100%); only mean occupancy improves monotonically across all four points (23.88, 23.81, 23.49, 23.39). This weakens two SUPPORTING arguments in finding-09 without touching its headline, which rests on its own paired tests and stands: the dose-response is no longer monotone once the fourth point is added, with four of five tracked quantities reversing, and section 2's attribution of strength to joint coverage fails exactly at the 100% endpoint that attribution predicts should be best. finding-09 section 5 should now be read as 'M=6 is a local optimum', not 'more M is better'. Validity controls all pass: 0 decisions below target depth, 0 work-limit events, 0 censored games and 0 score-decomposition identity failures in both arms, and the chunk-and-pool procedure on which every cohort in this family depends was verified end to end by running depth 3 (N=5, M=1) as four 16-game chunks at 1 thread and reproducing the existing 64-game 12-thread artifact field-for-field - 0 mismatches, identical summed logical work of 312,966,881, only per-game wallSeconds differing, which also re-confirms worker-count independence.