CAT-v3-wall-shape.md

CAT v3 - Cross-gap wall shape attention

Episode hook: Search was pruning useful corridor walls, but the first shape pass over-credited useless T-junctions far from the race.

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Problem

1. Opening MCTS loved e5v after e3v d4h because rollouts saw +1 on Black while ignoring that White's own path also lengthened.
2. The first geometry pass treated any perpendicular-at-chain-end as "half protrusion". That revived futile T-walls on the opposite side of the board and polluted ordering.

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Correct geometry

Cross-gap (tiny ordering nudge only)

Perpendicular wall placed through the one-row/col gap between two parallel walls:

• V(r-1,c) + V(r+1,c) -> candidate H(r,c)
• H(r,c-1) + H(r,c+1) -> candidate V(r,c)

Adjacent chain ends (V(r,c)+V(r+1,c) with H at the junction) are not cross-gap walls.

Cross-gap block

Shifted placement beside the door slot that would become a cross-gap:

• vertical gap at col c -> H(r,c-1) or H(r,c+1)
• horizontal gap at row r -> V(r-1,c) or V(r+1,c)

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Search integration

Mechanism	Effect
wall_shape_attention_bonus	+40 cm cross / +35 cm block in move ordering only
Gating	max(edge heat, touched heat) >= CAT_HOT_CM (160)
Pruning	Shape bonus does not rescue otherwise dead walls

Static eval is unchanged.

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Opening fix

Hybrid switches to minimax once walls_placed >= 2, so ply 9 after e3v d4h no longer uses opening MCTS.

MCTS expansion now drops walls with non-positive net race value (opp_gain - our_loss <= 0, or net < 2 when tied/behind).