Reduce shallow null searches one more ply

[thomasahle]

What

Search the shallow scoring-null child one ply less:

score = min(cap, -self.bound(pos.rotate(nullmove=True), 1 - gamma, depth - 4))

For eligible parent depths 3, 4, and 5, the pass-child schedule changes from 0, 1, 2 to 0, 0, 1. The deep fixed-target null reduction is unchanged.

The one-sided static cap is unchanged. There is deliberately no max(1 - MATE_LOWER, ...) floor: a negative mate-band pass is inert in the node maximum, while the static cap already prevents a positive virtual mate claim. NullRed.lean proves the mate results for every positive reduction, including even R4.

This changes one executable expression and adds no executable line.

Strength evidence

A registered C-twin 3+0.1 pentanomial SPRT measured this exact R4-versus-R3 coordinate and accepted H1 [0,+10]:

3046 games: 1230 wins / 702 draws / 1114 losses
+13.24 +/- 10.29 Elo; LOS 99.42%
Ptnml [173, 254, 610, 256, 230]
LLR +2.99 for [0,+10]: H1 accepted

An independent fixed 1,000-game R4 match measured +18.4 Elo with a 95% interval of [-0.2,+37.1].

A fresh confirmation against the jointly tuned current defaults remains pending. The earlier apparent FUEL_NULL=0 lead was rejected by its direct match at -60.14 +/- 19.51 Elo over 986 games, so this PR leaves deep null-guided reduction intact.

Proof and model

• CappedNull.lean keeps the existing generic min report transport unchanged.
• NullRed.lean proves that null-reduction parity is not load-bearing and includes dtm_optimal_R4.
• The R4 child depth is synchronized through the fuel/capped recurrence and sharpness witnesses.
• The existing uniform eventual-mate bounds remain unchanged.
• The C twin and live full-search tuning defaults use NULL_CUT_RED=4; frozen benchmark manifests retain historical values.

Verification

• Lean: all 26 modules build.
• Python: 584 passed, 2 skipped.
• Capped-null/model regressions: 35 passed.
• Model/source audit: passed.
• C twin quick identity: 246 probes and 423 move lists, zero mismatches.
• Wide C/Python identity: first three sweeps had zero mismatches; the pathological QS=0 sweep was stopped after 10 minutes locally.
• git diff --check: passed.

[thomasahle]

Update (2026-08-26): the corrected full-space CTT/MES follow-up reached 83/83/85 points across three independent seeds (251 paired observations, 502 games). It was paused when unrelated high-CPU work appeared on the shared host. The surrogate recommendations remained close to the incumbent and no new setting cleared validation.

One repeated observed lead was the incumbent with FUEL_NULL=0 (three pairs, noisy point estimate +67.4 Elo). A held-out check was started but, for the same resource-priority reason, stopped after 16 games: 7-5-4, posterior +33 Elo with a 90% interval of [-72,+146]. That is not evidence to merge. The validated #264 five-value combination remains the best result, so this PR documents it and explicitly records the inconclusive follow-up rather than claiming a new engine change.