Tune shallow search jointly

[thomasahle]

Result

Jointly tunes five existing search constants with no new mechanism and no
Python/C engine line increase:

Parameter	Master	Candidate
QS	40	36
QS_A	140	180
LMR	75	70
LMR_MIN_DEPTH	6	7
FUT_CAP_DEPTH	3	4

The combination searches slightly more around the depth-six LMR boundary,
reduces a slightly broader intrinsic-value tail from depth seven, and keeps
the monotone shallow move cap for one additional finite depth. The changes
were selected jointly; the PR does not claim that any coordinate is valuable
in isolation.

The checked-in C-twin defaults receive the same substitutions. Regenerating
compressed.py is mechanical.

Strength

All matches used the classic C twin at 3+0.1, paired openings, and no engine
failure.

• Pentanomial SPRT [0,+10], alpha/beta 0.05: H1 accepted after 1,314 games.
  Score 559-286-469; pentanomial [71,95,266,123,102]; LLR 2.96 / 2.94.
• Independent fixed 1,000 games: 420-253-327,
  +32.41 +/- 18.52 Elo, pentanomial [55,75,177,108,85], LOS 99.97%.
• Pinned Stockfish-1800 panel arms, 400 opening pairs per configuration:
  candidate-minus-master +16.10 Elo.
• Pinned ChessIdle panel arms, 400 opening pairs per configuration:
  candidate-minus-master +6.96 Elo.
• Frozen 2:1:1 master/Stockfish/ChessIdle panel, paired cluster bootstrap:
  +21.84 Elo, 90% interval [+11.11,+30.22] over 100,000 resamples.

The SPRT decides promotion; the fixed-N match supplies the quoted Elo
magnitude. Both external matchup point estimates are non-negative, and the
weighted panel's lower bound is positive.

Correctness and search model

Extending the static-cap horizon changes the selective recurrence but keeps
the existing monotone-cap proof. The Lean model is updated in the same commit:

• forced mate in k plies is found uniformly by D >= 3k + 2;
• the forced-loss dual is found by D >= 3k + 5;
• a concrete mate-in-three witness still fails at depth 10, proving the first
  bound sharp for this recurrence;
• executable eventual-mate depths move to 5, 11, and 17.

No gamma-dependent semantics or new TT premise is introduced.

Verification

• full Lean build: passed;
• model/source audit: passed;
• Python tests: 576 passed, 2 skipped;
• NNUE-side tests: 28 passed;
• C/Python twin gate: 5,220 bound reports and 1,042 move lists, zero mismatch;
• TT consistency: 48 passed;
• terminal corpus at depth 5: 149 passed;
• deterministic corpora: WAC d8 170/300, Bratko-Kopec d8 11/24,
  Lichess regressions d8 451/1736;
• no added line exceeds 120 characters;
• git diff --check: passed.

The repository diff is net -23 lines because the generalized mate-depth proof
is shorter; executable engine line count is unchanged.