ResultDepth-4 sibling-value panel, linear Q fit, and pruned-search regret on held-out roots

A sibling-complete panel of 5,398 roots from 48 fair-d4s7 games on already-read training seeds (mean 390,143 points, 112.5 moves, no game censored) was split 32 games for fitting and 16 held out (2,060 roots). The linear action value over 32 one-ply features, fitted by ridge regression to the exact depth-4 sibling values (lambda 0.001 at the grid edge for both the raw and the per-root-centred fit; held-out R^2 0.725 raw, 0.539 within root), is a WORSE ranker of depth-4's choice than the exact one-ply value it can represent: top-1 0.308 against 0.524 (paired difference -0.216, one-sided 95% bound -0.233 over games) and recall@3 0.604 against 0.809, so clauses (a) and (b) fail. A post-hoc check shows why: the features rebuild the exact one-ply value to 6e-11, and least squares halves the held-out error (7.0e9 against 1.4e10 for an affine map of the one-ply value) by predicting deaths within four plies, which cost a million points each, while ranking live siblings worse; refitting on per-root-centred targets clipped at -50,000 recovers exactly the one-ply value's ranking (top-1 0.535, recall@3 0.809) and nothing more. Depth-three exact values rank depth-4's choice into the top three on 95.0% of roots, depth-two on 90.0%, the six-feature CEM policy on 70.1%, centre order on 40.0%. Pruning the depth-4 search at interior max nodes with the exact one-ply value as prior at width three (both interior layers) reproduces the full-width decision on 92.3% of held-out roots (lower bound 91.8%) with mean normalised regret 0.0087 (upper bound 0.0098) and mean raw regret 74 points at 26.4% of the full-width logical work (prior calls included, 5.9% of it) and 3.8x faster wall time; width four gives 93.8% / 0.0059 at 40.9% work, width two 89.3% / 0.0145 at 13.8%. The six-feature prior, which costs no engine calls, reaches 88.4% / 0.0147 at width four (34.6% work); the fitted Q prunes worst (78.8% / 0.037 at width three); centre order is useless (69.1%). Every pruned root value was at or below the full-width value on every root (0 violations of the lower-bound property), and the width-seven searcher reproduced drop7-rs values, actions and work bit for bit. Clause (c) is inconclusive by the preregistered rule: the best configuration at or under 35% work passes the regret threshold (0.0087 <= 0.02) but its agreement of 92.3% sits between the 0.90 fail line and the 0.95 pass line. On the 128-root sub-panel with exact depth-5 values (mean 1.9e8 work per root, 37x depth 4), full-width depth 4 agrees with depth 5 on 79.7% of roots with normalised regret 0.0285 and raw regret 146 points per decision; pruned depth 5 with the one-ply prior at width two on all three interior layers (1.68x the depth-4 work) agrees on 80.5% with normalised regret 0.0174 (paired reduction +0.011, bound -0.0004) but HIGHER raw regret, 189 points (paired change -43, bound -207), so clause (d) is inconclusive at best and unfavourable in points: pruning three interior layers loses the high-stakes continuations that the extra ply was supposed to find. Wider depth-5 pruning (3,3,3 at 4.5x work) reaches only 82.8%. The theory's learned-prior claim is not supported; its mechanism claim is supported for the search's own one-ply value at depth 4 and not at depth 5. Pilot tier, training-role and held-out panel data, no new seeds.