test1978
/

chess-model

@@ -1,1136 +1,1136 @@
-# chess_mcvs.py
-"""
-chess_mcvs.py - Full implementation analogous to breakthrough_mcvs.py
-Features:
-- Chess game logic using python-chess (full rules)
-- Fixed 64×64 padded weighted adjacency matrix (Hilbert-ordered pieces)
-- Piece-specific kappa values
-- Queen-only promotions for flat 4096 policy head compatibility
-- Policy and Value CNNs (lightweight with pooling for feasibility)
-- HilbertOrderedZoneDatabase with add methods and proper k-NN zone score
-- MCVSSearcher (guided λ-PUCT with policy/value/zone)
-- UCTSearcher (baseline)
-- train_networks function
-- Ready for chess_mcvs_vs_uct.py tournament
-Requires: pip install chess torch numpy
-"""
-import numpy as np
-import torch
-import torch.nn as nn
-import torch.nn.functional as F
-import torch.optim as optim
-from torch.utils.data import DataLoader, TensorDataset
-import chess
-import random
-import time
-import os
-import bisect
-from collections import Counter
-from typing import List, Dict, Tuple
-# ============================================================================
-# HILBERT CURVE UTILITIES
-# ============================================================================
-def xy2d(n: int, x: int, y: int) -> int:
-    d = 0
-    s = n // 2
-    while s > 0:
-        rx = 1 if (x & s) > 0 else 0
-        ry = 1 if (y & s) > 0 else 0
-        d += s * s * ((3 * rx) ^ ry)
-        if ry == 0:
-            if rx == 1:
-                x = n - 1 - x
-                y = n - 1 - y
-            x, y = y, x
-        s //= 2
-    return d
-def matrix_to_hilbert_index(W: np.ndarray) -> int:
-    if W.size == 0:
-        return 0
-    W_flat = W.flatten()
-    max_idx = np.argmax(W_flat)
-    x = max_idx % 64
-    y = max_idx // 64
-    return xy2d(64, x, y)
-# ============================================================================
-# ABC MODEL & WEIGHTED MATRIX
-# ============================================================================
-class ABCModelDynamic:
-    """ABC Model with displacement-based B matrices."""
-    def __init__(self, n: int = 2, t: float = 1.0, T: float = 1.41):
-        """
-        Initialize for 2D board.
-        Args:
-            n: Dimension (2 for 2D board)
-            t: Minimum distance threshold for adjacency
-            T: Maximum distance threshold for adjacency
-        """
-        self.n = n
-        self.t = t
-        self.T = T
-        self.c0 = np.array([0.0, 0.0, 1.0])
-        self.B_blocks = []        # Displacement matrices
-        self.piece_positions = [] # Actual positions on SB
-        self.a_product = np.eye(3) # Accumulated product
-        self.delta = {}           # Delta values for each piece
-        self.kappa = {}           # Tokenized vectors for each piece (ADDED)
-        self.stage = 0
-        # MB position tracking
-        self.MB_current = self.c0.copy()  # Current MB center
-        self.MB_previous = self.c0.copy() # Previous MB center
-        self.history = []
-    def create_B_displacement(self, dx: float, dy: float) -> np.ndarray:
-        """
-        Create displacement matrix B.
-        Moves MB by (dx, dy) displacement.
-        B · current_MB = new_MB
-        B = [1 0 dx]
-            [0 1 dy]
-            [0 0 1]
-        Right column: (dx, dy, 1)ᵀ
-        """
-        B = np.array([
-            [1.0, 0.0, dx],
-            [0.0, 1.0, dy],
-            [0.0, 0.0, 1.0]
-        ])
-        return B
-    def add_piece(self, position: tuple, delta_values: tuple, kappa_vector: np.ndarray = None):
-        """
-        Add a piece at position with delta values and optional kappa vector.
-        Args:
-            position: (x, y) tuple
-            delta_values: (Δ₁, Δ₂, Δ₃) tuple
-            kappa_vector: Tokenized feature vector (optional, defaults to delta_values)
-        """
-        x, y = position
-        # Current MB position
-        current_MB = self.MB_current.copy()
-        # Calculate displacement
-        dx = x - current_MB[0]
-        dy = y - current_MB[1]
-        # Create displacement matrix
-        B_i = self.create_B_displacement(dx, dy)
-        # Store
-        idx = len(self.B_blocks)
-        self.B_blocks.append(B_i)
-        self.piece_positions.append((x, y))
-        # Update accumulated product: a_t = a_{t-1} · B_t
-        self.a_product = self.a_product @ B_i
-        # Track MB positions
-        self.MB_previous = self.MB_current.copy()
-        self.MB_current = self.a_product @ self.c0  # Should equal (x, y, 1)
-        # Store differential vector
-        self.delta[idx] = delta_values
-        # Store tokenized vector (or use delta_values as default)
-        if kappa_vector is None:
-            kappa_vector = np.array(delta_values)
-        self.kappa[idx] = kappa_vector
-        # Increment stage
-        self.stage += 1
-        # Record move
-        self.history.append({
-            'stage': self.stage,
-            'SB_position': (x, y),
-            'displacement': (dx, dy),
-            'B_i': B_i.copy(),
-            'a_t': self.a_product.copy(),
-            'MB_prev': self.MB_previous.copy(),
-            'MB_curr': self.MB_current.copy(),
-            'delta': delta_values,
-            'kappa': kappa_vector.copy()
-        })
-    def add_move(self, x: float, y: float, player: int):
-        """
-        Convenience method: Add a move with automatic delta values.
-        Args:
-            x, y: Position coordinates
-            player: 1 for X (Δ₂=1.0), 2 for O (Δ₂=1.1)
-        """
-        delta_1 = 1.0  # Occupied
-        delta_2 = 1.0 if player == 1 else 1.1  # Player color
-        delta_3 = 1.0  # Same value for all pieces
-        self.add_piece((x, y), (delta_1, delta_2, delta_3))
-    def get_board_state(self) -> str:
-        """Visual board state."""
-        pos_map = {
-            (-1, 1): 0, (0, 1): 1, (1, 1): 2,
-            (-1, 0): 3, (0, 0): 4, (1, 0): 5,
-            (-1, -1): 6, (0, -1): 7, (1, -1): 8
-        }
-        board = [' '] * 9
-        for i, pos in enumerate(self.piece_positions):
-            if pos in pos_map:
-                player = 'X' if self.delta[i][1] == 1.0 else 'O'
-                board[pos_map[pos]] = player
-        s = f" {board[0]} | {board[1]} | {board[2]} \n"
-        s += "---|---|---\n"
-        s += f" {board[3]} | {board[4]} | {board[5]} \n"
-        s += "---|---|---\n"
-        s += f" {board[6]} | {board[7]} | {board[8]} \n"
-        return s
-    def describe_move(self, stage: int):
-        """Describe a specific move."""
-        if stage < 1 or stage > len(self.history):
-            return "Invalid stage"
-        move = self.history[stage - 1]
-        desc = "=" * 70 + "\n"
-        desc += f"MOVE {stage}: {move['SB_position']}\n"
-        desc += "=" * 70 + "\n\n"
-        idx = stage - 1
-        B_i = self.B_blocks[idx]
-        desc += f"Mobile Board (MB) movement:\n"
-        desc += f" Previous MB: {move['MB_prev']}\n"
-        desc += f" Target (SB): {move['SB_position']}\n"
-        desc += f" Displacement: Δ = {move['displacement']}\n"
-        desc += f" New MB: {move['MB_curr']}\n\n"
-        desc += f"Displacement matrix B_{stage}:\n{B_i}\n"
-        desc += f"Right column: {B_i[:, 2]} = (Δx={move['displacement'][0]}, Δy={move['displacement'][1]}, 1)\n\n"
-        desc += f"Accumulated product a_{stage}:\n{move['a_t']}\n"
-        desc += f"Right column: {move['a_t'][:, 2]}\n\n"
-        desc += f"Delta values: {move['delta']}\n"
-        desc += f"Kappa vector: {move['kappa']}\n\n"
-        desc += f"Verification:\n"
-        desc += f" a_{stage} · c₀ = {move['a_t'] @ self.c0}\n"
-        desc += f" Should equal: {np.array([move['SB_position'][0], move['SB_position'][1], 1.0])}\n\n"
-        desc += "Board state:\n"
-        desc += self.get_board_state()
-        return desc
-class WeightedMatrixABC:
-    """
-    Compute weighted adjacency matrix from ABCModelDynamic.
-    CRITICAL: Converts (x,y) tuples to homogeneous coords [x,y,1]
-    to match algebraic structure of B matrices from abc_model.py
-    Implements Definition from Section 6:
-        W[i,j](t) = A[i,j](t) ⊙ S[i,j](t) ⊙ F[i,j](t)
-    """
-    def __init__(self, abc_model: ABCModelDynamic, sigma: float = 1.0):
-        """
-        Initialize with ABC model instance.
-        Args:
-            abc_model: ABCModelDynamic instance
-            sigma: Standard deviation for Gaussian spatial kernel
-        """
-        self.abc = abc_model
-        self.n = abc_model.n
-        self.t = abc_model.t
-        self.T = abc_model.T
-        self.sigma = sigma
-        self.positions = None  # Will store homogeneous coords [x, y, 1]
-        self.D = None
-        self.A = None
-        self.S = None
-        self.F = None
-        self.W = None
-    def compute_piece_positions(self) -> np.ndarray:
-        """
-        Extract positions from ABC model and convert to homogeneous coordinates.
-        In abc_model.py:
-            - piece_positions are (x, y) tuples
-            - MB_current = a_product @ c0 produces [x, y, 1]
-        For matrix computations, convert to homogeneous coords to match
-        the algebraic structure of B matrices.
-        Returns: Array of shape (num_pieces, 3) with homogeneous coords [x, y, 1]
-        """
-        positions = []
-        for pos in self.abc.piece_positions:
-            # pos is (x, y) from piece_positions
-            x, y = pos
-            # Convert to homogeneous coordinates to align with B matrix algebra
-            positions.append(np.array([x, y, 1.0]))
-        self.positions = np.array(positions)
-        return self.positions
-    def compute_distance_matrix(self) -> np.ndarray:
-        """
-        Compute pairwise Euclidean distances using 2D components only.
-        Even though positions are [x, y, 1], we compute distance using only [x, y]
-        D[i,j] = ||[x_i, y_i] - [x_j, y_j]||₂
-        """
-        if self.positions is None:
-            self.compute_piece_positions()
-        num = len(self.positions)
-        D = np.zeros((num, num))
-        for i in range(num):
-            for j in range(num):
-                # Use only 2D coordinates for distance
-                pos_i = self.positions[i][:2]
-                pos_j = self.positions[j][:2]
-                D[i, j] = np.linalg.norm(pos_i - pos_j)
-        self.D = D
-        return D
-    def compute_adjacency_matrix(self) -> np.ndarray:
-        """
-        Compute Adjacency Matrix (Definition 6.2).
-        A[i,j] = 1 if:
-            - k ≤ D[i,j] ≤ K (grid-adjacent)
-            - i == j AND i is isolated (no neighbors in [k,K])
-        A[i,j] = 0 otherwise
-        """
-        if self.D is None:
-            self.compute_distance_matrix()
-        num = len(self.positions)
-        A = np.zeros((num, num))
-        # Identify isolated pieces
-        isolated = set()
-        for i in range(num):
-            has_neighbor = False
-            for j in range(num):
-                if i != j and self.t <= self.D[i, j] <= self.T:
-                    has_neighbor = True
-                    break
-            if not has_neighbor:
-                isolated.add(i)
-        # Fill adjacency matrix
-        for i in range(num):
-            for j in range(num):
-                # Check adjacency distance
-                if i != j and self.t <= self.D[i, j] <= self.T:
-                    A[i, j] = 1.0
-                # Check if isolated piece
-                elif i == j and i in isolated:
-                    A[i, j] = 1.0
-        self.A = A
-        return A
-    def compute_spatial_matrix(self) -> np.ndarray:
-        """
-        Compute Spatial Matrix (Definition 6.3).
-        S[i,j](t) = exp(-||c_i(t) - c_j(t)||² / (2σ²))
-        Gaussian kernel based on Euclidean distance.
-        """
-        if self.D is None:
-            self.compute_distance_matrix()
-        num = len(self.positions)
-        S = np.zeros((num, num))
-        for i in range(num):
-            for j in range(num):
-                S[i, j] = np.exp(-self.D[i, j]**2 / (2 * self.sigma**2))
-        self.S = S
-        return S
-    def compute_feature_matrix(self) -> np.ndarray:
-        """
-        Compute Feature Matrix (Definition 6.4).
-        F[i,j](t) = <κ(B_i), κ(B_j)> / (||κ(B_i)|| · ||κ(B_j)||)
-        Cosine similarity between tokenized vectors.
-        """
-        num = len(self.positions)
-        F = np.zeros((num, num))
-        # Extract tokenized vectors
-        kappas = []
-        for i in range(num):
-            if i in self.abc.kappa:
-                kappas.append(self.abc.kappa[i])
-            else:
-                # Default: use delta as feature vector
-                if i in self.abc.delta:
-                    kappas.append(np.array(self.abc.delta[i]))
-                else:
-                    kappas.append(np.array([1.0, 1.0, 1.0]))
-        # Compute cosine similarity
-        for i in range(num):
-            for j in range(num):
-                kappa_i = kappas[i]
-                kappa_j = kappas[j]
-                dot_product = np.dot(kappa_i, kappa_j)
-                norm_i = np.linalg.norm(kappa_i)
-                norm_j = np.linalg.norm(kappa_j)
-                if norm_i > 0 and norm_j > 0:
-                    F[i, j] = dot_product / (norm_i * norm_j)
-                else:
-                    F[i, j] = 0.0
-        self.F = F
-        return F
-    def compute_weighted_matrix(self) -> np.ndarray:
-        """
-        Compute Weighted Matrix (Definition from Section 6).
-        W[i,j](t) = A[i,j](t) ⊙ S[i,j](t) ⊙ F[i,j](t)
-        Returns: W - the full weighted matrix
-        """
-        if self.A is None:
-            self.compute_adjacency_matrix()
-        if self.S is None:
-            self.compute_spatial_matrix()
-        if self.F is None:
-            self.compute_feature_matrix()
-        # Hadamard product (element-wise multiplication)
-        W = self.A * self.S * self.F
-        self.W = W
-        return W
-    def compute_manhattan_distance(self, other: 'WeightedMatrixABC') -> float:
-        """
-        Compute Manhattan distance between two weighted matrices.
-        distance = ||W_1 - W_2||₁
-        """
-        if self.W is None:
-            self.compute_weighted_matrix()
-        if other.W is None:
-            other.compute_weighted_matrix()
-        W1 = self.W
-        W2 = other.W
-        # Pad to same size
-        size = max(len(W1), len(W2))
-        W1_padded = np.zeros((size, size))
-        W2_padded = np.zeros((size, size))
-        W1_padded[:len(W1), :len(W1)] = W1
-        W2_padded[:len(W2), :len(W2)] = W2
-        return np.linalg.norm(W1_padded - W2_padded, ord=1)
-# ============================================================================
-# CHESS GAME LOGIC
-# ============================================================================
-class Chess:
-    def __init__(self):
-        self.board = chess.Board()
-        self.move_count = 0
-        self.position_history = Counter()
-        self._update_position_key()
-    def _update_position_key(self):
-        key = (self.board.fen(), self.board.turn)
-        self.position_history[key] += 1
-    def copy(self):
-        new_game = Chess()
-        new_game.board = self.board.copy()
-        new_game.move_count = self.move_count
-        new_game.position_history = self.position_history.copy()
-        return new_game
-    def undo_move(self) -> None:
-        """
-        Undo the last move (pop) and revert bookkeeping (move_count, position_history).
-        This complements `apply_move` which increments move_count and updates
-        the position_history for the new state after a push. `undo_move` decrements
-        the same position record and pops the board to restore the previous state.
-        """
-        # The current board fen/turn corresponds to the state that was last pushed;
-        # decrement its count before popping to fully revert the update.
-        key = (self.board.fen(), self.board.turn)
-        if key in self.position_history:
-            # decrement safely (don't remove key to avoid KeyError on repeated ops)
-            self.position_history[key] = max(0, self.position_history[key] - 1)
-        # pop the board and update counters
-        self.board.pop()
-        self.move_count = max(0, self.move_count - 1)
-    def get_legal_moves(self) -> List[chess.Move]:
-        moves = []
-        for move in self.board.legal_moves:
-            if move.promotion is None or move.promotion == chess.QUEEN:
-                moves.append(move)
-        return moves
-    def apply_move(self, move: chess.Move) -> None:
-        self.board.push(move)
-        self.move_count += 1
-        self._update_position_key()
-    def is_terminal(self) -> bool:
-        return self.board.is_game_over(claim_draw=True)
-    def check_winner(self) -> int:
-        if not self.is_terminal():
-            return 0
-        outcome = self.board.outcome(claim_draw=True)
-        if outcome is None or outcome.winner is None:
-            return 0
-        return 1 if outcome.winner == chess.WHITE else -1
-    def get_weighted_adjacency_matrix(self) -> np.ndarray:
-        occupied = []
-        for sq in chess.SQUARES:
-            piece = self.board.piece_at(sq)
-            if piece:
-                file = chess.square_file(sq)
-                rank = chess.square_rank(sq)
-                x = float(file) - 3.5
-                y = float(rank) - 3.5
-                color_val = 1.0 if piece.color == chess.WHITE else 1.1
-                type_val = {
-                    chess.PAWN:   1.0,
-                    chess.KNIGHT: 3.0,
-                    chess.BISHOP: 3.2,
-                    chess.ROOK:   5.0,
-                    chess.QUEEN:  9.0,
-                    chess.KING:  20.0
-                }[piece.piece_type]
-                kappa = np.array([1.0, color_val, type_val])
-                hilbert_d = xy2d(8, file, rank)
-                occupied.append((hilbert_d, (x, y), kappa))
-        occupied.sort(key=lambda t: t[0])
-        abc = ABCModelDynamic(n=2, t=1.0, T=1.41)
-        for _, pos, kappa_vec in occupied:
-            abc.add_piece(pos, delta_values=(1.0, kappa_vec[1], kappa_vec[2]), kappa_vector=kappa_vec)
-        w_calc = WeightedMatrixABC(abc, sigma=1.0)
-        W_var = w_calc.compute_weighted_matrix()
-        num = len(occupied)
-        W = np.zeros((64, 64))
-        if num > 0:
-            W[:num, :num] = W_var
-        return W
-# ============================================================================
-# NEURAL NETWORKS
-# ============================================================================
-class PolicyNetworkCNN(nn.Module):
-    def __init__(self):
-        super().__init__()
-        self.conv = nn.Sequential(
-            nn.Conv2d(1, 64, kernel_size=5, padding=2, stride=2),
-            nn.ReLU(),
-            nn.Conv2d(64, 128, kernel_size=5, padding=2, stride=2),
-            nn.ReLU(),
-            nn.Conv2d(128, 128, kernel_size=3, padding=1, stride=2),
-            nn.ReLU(),
-        )
-        self.fc = nn.Linear(128 * 8 * 8, 4096)
-    def forward(self, x):
-        x = self.conv(x)
-        x = x.view(x.size(0), -1)
-        return self.fc(x)
-class ValueNetworkCNN(nn.Module):
-    def __init__(self):
-        super().__init__()
-        self.conv = nn.Sequential(
-            nn.Conv2d(1, 64, kernel_size=5, padding=2, stride=2),
-            nn.ReLU(),
-            nn.Conv2d(64, 128, kernel_size=5, padding=2, stride=2),
-            nn.ReLU(),
-            nn.Conv2d(128, 128, kernel_size=3, padding=1, stride=2),
-            nn.ReLU(),
-        )
-        self.fc = nn.Sequential(
-            nn.Linear(128 * 8 * 8, 512),
-            nn.ReLU(),
-            nn.Linear(512, 1),
-            nn.Tanh()
-        )
-    def forward(self, x):
-        x = self.conv(x)
-        x = x.view(x.size(0), -1)
-        return self.fc(x)
-# ============================================================================
-# ZONE DATABASE
-# ============================================================================
-class HilbertOrderedZoneDatabase:
-    def __init__(self, filepath: str = "chess_zone_db.npz", max_size: int = 100000):
-        self.filepath = filepath
-        self.max_size = max_size  # Maximum matrices per zone
-        self.winning_matrices = []
-        self.winning_indices = []
-        self.losing_matrices = []
-        self.losing_indices = []
-        self.draw_matrices = []
-        self.draw_indices = []
-        self.load()
-    def add_winning_matrix(self, W: np.ndarray):
-        if W.shape != (64, 64):
-            return
-        hilbert_idx = matrix_to_hilbert_index(W)
-        pos = bisect.bisect_left(self.winning_indices, hilbert_idx)
-        self.winning_indices.insert(pos, hilbert_idx)
-        self.winning_matrices.insert(pos, W.copy())
-    def add_losing_matrix(self, W: np.ndarray):
-        if W.shape != (64, 64):
-            return
-        hilbert_idx = matrix_to_hilbert_index(W)
-        pos = bisect.bisect_left(self.losing_indices, hilbert_idx)
-        self.losing_indices.insert(pos, hilbert_idx)
-        self.losing_matrices.insert(pos, W.copy())
-    def add_draw_matrix(self, W: np.ndarray):
-        if W.shape != (64, 64):
-            return
-        hilbert_idx = matrix_to_hilbert_index(W)
-        pos = bisect.bisect_left(self.draw_indices, hilbert_idx)
-        self.draw_indices.insert(pos, hilbert_idx)
-        self.draw_matrices.insert(pos, W.copy())
-    def add_game_record(self, trajectory: List[Chess], result: int, sample_rate: float = 0.3):
-        """Add game record with sampling to control database size."""
-        # Sample states: always keep first and last, random subset of middle
-        sampled_states = []
-        for i, state in enumerate(trajectory):
-            if i == 0 or i == len(trajectory) - 1:
-                # Always keep start and end positions
-                sampled_states.append(state)
-            elif random.random() < sample_rate:
-                # Randomly sample middle positions
-                sampled_states.append(state)
-        for state in sampled_states:
-            W = state.get_weighted_adjacency_matrix()
-            if result == 1:
-                self.add_winning_matrix(W)
-            elif result == -1:
-                self.add_losing_matrix(W)
-            else:
-                self.add_draw_matrix(W)
-    def save(self):
-        """Save database with pruning if too large."""
-        # Prune if any zone exceeds 80% of max_size
-        threshold = int(self.max_size * 0.8)
-        if (len(self.winning_matrices) > threshold or
-            len(self.losing_matrices) > threshold or
-            len(self.draw_matrices) > threshold):
-            print(f"Pruning database before save...")
-            self.prune_database(target_size=int(self.max_size * 0.7))
-        try:
-            np.savez_compressed(
-                self.filepath,
-                winning=np.array(self.winning_matrices, dtype=object),
-                winning_indices=np.array(self.winning_indices),
-                losing=np.array(self.losing_matrices, dtype=object),
-                losing_indices=np.array(self.losing_indices),
-                draw=np.array(self.draw_matrices, dtype=object),
-                draw_indices=np.array(self.draw_indices),
-            )
-            print(f"Zone DB saved: W={len(self.winning_matrices)}, L={len(self.losing_matrices)}, D={len(self.draw_matrices)}")
-        except MemoryError:
-            print(f"MemoryError during save! Pruning more aggressively...")
-            self.prune_database(target_size=1000)
-            # Try again with much smaller size
-            np.savez_compressed(
-                self.filepath,
-                winning=np.array(self.winning_matrices, dtype=object),
-                winning_indices=np.array(self.winning_indices),
-                losing=np.array(self.losing_matrices, dtype=object),
-                losing_indices=np.array(self.losing_indices),
-                draw=np.array(self.draw_matrices, dtype=object),
-                draw_indices=np.array(self.draw_indices),
-            )
-    def load(self):
-        if os.path.exists(self.filepath):
-            try:
-                data = np.load(self.filepath, allow_pickle=True)
-                self.winning_matrices = list(data['winning_matrices'])
-                self.winning_indices = list(data['winning_indices'])
-                self.losing_matrices = list(data['losing_matrices'])
-                self.losing_indices = list(data['losing_indices'])
-                self.draw_matrices = list(data['draw_matrices'])
-                self.draw_indices = list(data['draw_indices'])
-                print(f"Loaded zone DB: W={len(self.winning_matrices)}, L={len(self.losing_matrices)}, D={len(self.draw_matrices)}")
-            except Exception as e:
-                print(f"Failed to load zone database: {e}")
-    def prune_database(self, target_size: int = 5000):
-        """Keep only evenly-spaced diverse samples along Hilbert curve."""
-        def prune_zone(matrices, indices, target):
-            if len(matrices) <= target:
-                return matrices, indices
-            # Keep evenly spaced samples
-            step = max(1, len(matrices) // target)
-            keep_idx = list(range(0, len(matrices), step))[:target]
-            new_matrices = [matrices[i] for i in keep_idx]
-            new_indices = [indices[i] for i in keep_idx]
-            return new_matrices, new_indices
-        old_sizes = (len(self.winning_matrices), len(self.losing_matrices), len(self.draw_matrices))
-        self.winning_matrices, self.winning_indices = prune_zone(
-            self.winning_matrices, self.winning_indices, target_size
-        )
-        self.losing_matrices, self.losing_indices = prune_zone(
-            self.losing_matrices, self.losing_indices, target_size
-        )
-        self.draw_matrices, self.draw_indices = prune_zone(
-            self.draw_matrices, self.draw_indices, target_size
-        )
-        new_sizes = (len(self.winning_matrices), len(self.losing_matrices), len(self.draw_matrices))
-        print(f"Pruned: W {old_sizes}→{new_sizes}, L {old_sizes}→{new_sizes}, D {old_sizes}→{new_sizes}")
-    def compute_zone_score(self, W: np.ndarray, k: int = 5, beta: float = 0.5) -> float:
-        """Compute zone guidance score Z(x(t), a) ∈ [-1, 1]."""
-        if W.shape != (64, 64):
-            return 0.0
-        def knn_similarity(matrices, k_val):
-            if len(matrices) == 0:
-                return 0.0
-            k_actual = min(k_val, len(matrices))
-            distances = []
-            for mat in matrices[:k_actual]:
-                dist = np.sum(np.abs(W - mat)) / (64.0 * 64.0)
-                distances.append(dist)
-            similarities = [1.0 - d for d in distances]
-            return np.mean(similarities)
-        zone_win = knn_similarity(self.winning_matrices, k)
-        zone_loss = knn_similarity(self.losing_matrices, k)
-        zone_draw = knn_similarity(self.draw_matrices, k)
-        Z = zone_win - zone_loss + beta * zone_draw
-        return float(np.clip(Z, -1.0, 1.0))
-# ============================================================================
-# TRAINING FUNCTION
-# ============================================================================
-def train_networks(policy_net, value_net, W_states, policies, values, epochs=5, batch_size=32, device='cpu', lr=0.001):
-    policy_net.train()
-    value_net.train()
-    opt_p = optim.Adam(policy_net.parameters(), lr=lr)
-    opt_v = optim.Adam(value_net.parameters(), lr=lr)
-    W_tensor = torch.tensor(np.array(W_states)[:, np.newaxis, :, :], dtype=torch.float32)
-    pi_tensor = torch.tensor(np.array(policies), dtype=torch.float32)
-    v_tensor = torch.tensor(np.array(values), dtype=torch.float32).unsqueeze(1)
-    dataset = TensorDataset(W_tensor, pi_tensor, v_tensor)
-    loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
-    for epoch in range(epochs):
-        total_loss = 0.0
-        for batch_W, batch_pi, batch_v in loader:
-            batch_W = batch_W.to(device)
-            batch_pi = batch_pi.to(device)
-            batch_v = batch_v.to(device)
-            logits = policy_net(batch_W)
-            # Fixed policy loss: KL divergence between network policy and MCTS visit distribution
-            policy_loss = F.kl_div(F.log_softmax(logits, dim=1), batch_pi, reduction='batchmean')
-            pred_v = value_net(batch_W)
-            value_loss = F.mse_loss(pred_v, batch_v)
-            loss = policy_loss + value_loss
-            total_loss += loss.item()
-            opt_p.zero_grad()
-            opt_v.zero_grad()
-            loss.backward()
-            # Optional but recommended: gradient clipping
-            torch.nn.utils.clip_grad_norm_(policy_net.parameters(), max_norm=1.0)
-            torch.nn.utils.clip_grad_norm_(value_net.parameters(), max_norm=1.0)
-            opt_p.step()
-            opt_v.step()
-        # Optional: print epoch loss for monitoring
-        print(f"Epoch {epoch+1}/{epochs} - Loss: {total_loss/len(loader):.4f}")
-# ============================================================================
-# MCVS SEARCHER
-# ============================================================================
-class MCVSSearcher:
-    def __init__(self, policy_net, value_net, zone_db, device='cpu',
-                 cpuct=1.41, lambda_zone=0.0, k_zone=5, use_nets=True,
-                 dirichlet_alpha: float = 0.3, dirichlet_noise_fraction: float = 0.25):
-        self.policy_net = policy_net.to(device) if policy_net and use_nets else None
-        self.value_net = value_net.to(device) if value_net and use_nets else None
-        self.zone_db = zone_db
-        self.device = device
-        self.cpuct = cpuct
-        self.lambda_zone = lambda_zone
-        self.k_zone = k_zone
-        self.use_nets = use_nets
-        # Dirichlet noise hyperparameters (alpha for the Dirichlet, and fraction)
-        self.dirichlet_alpha = float(dirichlet_alpha)
-        self.dirichlet_noise_fraction = float(dirichlet_noise_fraction)
-    def _rollout(self, game: Chess) -> float:
-        """Simple random rollout for leaf evaluation when no value network.
-        Uses push/pop (apply_move / undo_move) on the provided `game` to avoid
-        allocating a full copy per rollout. The rollout will undo its own
-        moves before returning.
-        """
-        depth = 0
-        max_depth = 60  # reduced depth for faster rollouts (configurable)
-        moves_played = []
-        while not game.is_terminal() and depth < max_depth:
-            moves = game.get_legal_moves()
-            if not moves:
-                break
-            m = random.choice(moves)
-            game.apply_move(m)
-            moves_played.append(m)
-            depth += 1
-        winner = game.check_winner()
-        # Undo rollout moves
-        for _ in range(len(moves_played)):
-            game.undo_move()
-        return float(winner)  # +1, -1, or 0
-    class Node:
-        def __init__(self, prior: float = 0.0, zone: float = 0.0):
-            self.prior = prior
-            self.zone = zone
-            self.visit_count = 0
-            self.value_sum = 0.0
-            self.children: Dict[chess.Move, 'MCVSSearcher.Node'] = {}
-    def search_with_time_budget(self, game: Chess, time_budget: float) -> Tuple[Dict[chess.Move, int], int]:
-        root = self.Node()
-        start_time = time.time()
-        simulations = 0
-        while time.time() - start_time < time_budget:
-            current_game = game
-            node = root
-            path = []
-            moves_made = []
-            # Selection
-            while node.children:
-                path.append(node)
-                total_n = sum(c.visit_count for c in node.children.values()) + 1
-                best_score = -float('inf')
-                best_move = None
-                best_child = None
-                for move, child in node.children.items():
-                    q = child.value_sum / child.visit_count if child.visit_count > 0 else 0.0
-                    p_lambda = max(child.prior + self.lambda_zone * child.zone, 0.001)
-                    u = self.cpuct * p_lambda * np.sqrt(total_n) / (1 + child.visit_count)
-                    score = q + u
-                    if score > best_score:
-                        best_score = score
-                        best_move = move
-                        best_child = child
-                current_game.apply_move(best_move)
-                moves_made.append(best_move)
-                node = best_child
-            path.append(node)
-            # Terminal node?
-            if current_game.is_terminal():
-                value = float(current_game.check_winner())
-            else:
-                # Expansion & Evaluation
-                legal_moves = current_game.get_legal_moves()
-                if self.use_nets and self.policy_net is not None and self.value_net is not None:
-                    # === Neural network branch ===
-                    W = current_game.get_weighted_adjacency_matrix()
-                    W_tensor = torch.from_numpy(W)[None, None, :, :].float().to(self.device)
-                    with torch.no_grad():
-                        logits = self.policy_net(W_tensor)[0]
-                        value = self.value_net(W_tensor)[0, 0].item()
-                    probs = F.softmax(logits, dim=0).cpu().numpy()
-                    prior_dict = {}
-                    prior_sum = 0.0
-                    for m in legal_moves:
-                        idx = m.from_square * 64 + m.to_square
-                        p = float(probs[idx])
-                        prior_dict[m] = p
-                        prior_sum += p
-                    if prior_sum > 0.0:
-                        for m in prior_dict:
-                            prior_dict[m] /= prior_sum
-                    else:
-                        p = 1.0 / len(legal_moves)
-                        prior_dict = {m: p for m in legal_moves}
-                else:
-                    # === Zone-only / no-nets branch ===
-                    value = self._rollout(current_game)
-                    prior_dict = {m: 1.0 / len(legal_moves) for m in legal_moves} if legal_moves else {}
-                # Dirichlet noise only at root and only when using nets.
-                # Use configured hyperparameters so the same alpha/fraction
-                # can be applied to both priors and zone guidance.
-                if len(path) == 1 and self.use_nets and legal_moves:
-                    noise = np.random.dirichlet([self.dirichlet_alpha] * len(legal_moves))
-                    for i, m in enumerate(legal_moves):
-                        prior_dict[m] = (1 - self.dirichlet_noise_fraction) * prior_dict[m] + \
-                                        self.dirichlet_noise_fraction * noise[i]
-                    # Renormalize
-                    prior_sum = sum(prior_dict.values())
-                    if prior_sum > 0:
-                        for m in prior_dict:
-                            prior_dict[m] /= prior_sum
-                # Create children with zone scores. Use apply/undo on the shared
-                # board to avoid allocating a full copy per child. Skip heavy
-                # weighted-matrix computations when zone guidance is disabled
-                # (lambda_zone == 0) or when the DB is empty.
-                zone_db_empty = (len(self.zone_db.winning_matrices) == 0 and
-                                 len(self.zone_db.losing_matrices) == 0 and
-                                 len(self.zone_db.draw_matrices) == 0)
-                need_zone = (self.lambda_zone != 0.0) and (not zone_db_empty)
-                for i, m in enumerate(legal_moves):
-                    if need_zone:
-                        current_game.apply_move(m)
-                        child_W = current_game.get_weighted_adjacency_matrix()
-                        child_Z = self.zone_db.compute_zone_score(child_W, k=self.k_zone)
-                        current_game.undo_move()
-                    else:
-                        child_Z = 0.0
-                    # If Dirichlet noise was added to priors at the root, apply the same
-                    # noise (mapped to [-1,1]) to zone guidance so both signals share
-                    # the same stochastic perturbation controlled by the same alpha.
-                    if len(path) == 1 and self.use_nets and legal_moves:
-                        z_noise = (noise[i] * 2.0) - 1.0  # map [0,1] -> [-1,1]
-                        child_Z = (1 - self.dirichlet_noise_fraction) * child_Z + \
-                                  self.dirichlet_noise_fraction * z_noise
-                    child = self.Node(prior=prior_dict.get(m, 0.0), zone=child_Z)
-                    node.children[m] = child
-            # Backpropagation
-            v = value
-            for n in reversed(path):
-                n.visit_count += 1
-                n.value_sum += v
-                v = -v
-            # Undo moves that were applied during selection (the rollout
-            # already undid its own moves). This restores `game` to the root
-            # state for the next simulation.
-            for _ in range(len(moves_made)):
-                current_game.undo_move()
-            simulations += 1
-        visits = {move: child.visit_count for move, child in root.children.items()}
-        if not visits:
-            legal = game.get_legal_moves()
-            visits = {random.choice(legal): 1} if legal else {}
-        return visits, simulations
-# ============================================================================
-# UCT SEARCHER (your original from the provided file)
-# ============================================================================
-class UCTSearcher:
-    def __init__(self, cpuct=np.sqrt(2.0)):
-        self.cpuct = cpuct
-    class Node:
-        def __init__(self):
-            self.visit_count = 0
-            self.value_sum = 0.0
-            self.children: Dict[chess.Move, 'UCTSearcher.Node'] = {}
-    def _rollout(self, game: Chess) -> float:
-        depth = 0
-        max_depth = 60
-        moves_played = []
-        while not game.is_terminal() and depth < max_depth:
-            moves = game.get_legal_moves()
-            if not moves:
-                break
-            m = random.choice(moves)
-            game.apply_move(m)
-            moves_played.append(m)
-            depth += 1
-        if depth >= max_depth:
-            # undo rollout moves
-            for _ in range(len(moves_played)):
-                game.undo_move()
-            return 0.0
-        winner = game.check_winner()
-        # undo rollout moves
-        for _ in range(len(moves_played)):
-            game.undo_move()
-        if winner == 1:
-            return 1.0
-        elif winner == -1:
-            return -1.0
-        else:
-            return 0.0
-    def search_with_time_budget(self, game: Chess, time_budget: float) -> Tuple[Dict[chess.Move, int], int]:
-        root = self.Node()
-        start_time = time.time()
-        simulations = 0
-        while time.time() - start_time < time_budget:
-            current_game = game
-            node = root
-            path = [node]
-            moves_made = []
-            while True:
-                legal_moves = current_game.get_legal_moves()
-                if current_game.is_terminal():
-                    winner = current_game.check_winner()
-                    value = 1.0 if winner == 1 else -1.0 if winner == -1 else 0.0
-                    break
-                if not legal_moves:
-                    value = 0.0
-                    break
-                unvisited_moves = [m for m in legal_moves if m not in node.children]
-                if unvisited_moves:
-                    move = random.choice(unvisited_moves)
-                    child = self.Node()
-                    node.children[move] = child
-                    current_game.apply_move(move)
-                    moves_made.append(move)
-                    path.append(child)
-                    value = self._rollout(current_game)
-                    break
-                best_score = -float('inf')
-                best_move = None
-                best_child = None
-                total_visits = node.visit_count
-                for move in legal_moves:
-                    child = node.children[move]
-                    Q = child.value_sum / (child.visit_count + 1e-8) if child.visit_count > 0 else 0.0
-                    U = self.cpuct * np.sqrt(np.log(total_visits + 1) / (child.visit_count + 1e-8))
-                    score = Q + U
-                    if score > best_score:
-                        best_score = score
-                        best_move = move
-                        best_child = child
-                current_game.apply_move(best_move)
-                moves_made.append(best_move)
-                node = best_child
-                path.append(node)
-            for n in reversed(path):
-                n.visit_count += 1
-                n.value_sum += value
-                value = -value
-            # Undo selection moves to restore root state
-            for _ in range(len(moves_made)):
-                current_game.undo_move()
-            simulations += 1
-        visits = {move: child.visit_count for move, child in root.children.items()}
-        if not visits:
-            legal = game.get_legal_moves()
-            return {random.choice(legal): 1} if legal else {}, simulations
-        return visits, simulations
-if __name__ == "__main__":
     print("chess_mcvs.py loaded successfully")

+# chess_mcvs.py
+"""
+chess_mcvs.py - Full implementation analogous to breakthrough_mcvs.py
+Hello!!
+Features:
+- Chess game logic using python-chess (full rules)
+- Fixed 64×64 padded weighted adjacency matrix (Hilbert-ordered pieces)
+- Piece-specific kappa values
+- Queen-only promotions for flat 4096 policy head compatibility
+- Policy and Value CNNs (lightweight with pooling for feasibility)
+- HilbertOrderedZoneDatabase with add methods and proper k-NN zone score
+- MCVSSearcher (guided λ-PUCT with policy/value/zone)
+- UCTSearcher (baseline)
+- train_networks function
+- Ready for chess_mcvs_vs_uct.py tournament
+Requires: pip install chess torch numpy
+"""
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import torch.optim as optim
+from torch.utils.data import DataLoader, TensorDataset
+import chess
+import random
+import time
+import os
+import bisect
+from collections import Counter
+from typing import List, Dict, Tuple
+# ============================================================================
+# HILBERT CURVE UTILITIES
+# ============================================================================
+def xy2d(n: int, x: int, y: int) -> int:
+    d = 0
+    s = n // 2
+    while s > 0:
+        rx = 1 if (x & s) > 0 else 0
+        ry = 1 if (y & s) > 0 else 0
+        d += s * s * ((3 * rx) ^ ry)
+        if ry == 0:
+            if rx == 1:
+                x = n - 1 - x
+                y = n - 1 - y
+            x, y = y, x
+        s //= 2
+    return d
+def matrix_to_hilbert_index(W: np.ndarray) -> int:
+    if W.size == 0:
+        return 0
+    W_flat = W.flatten()
+    max_idx = np.argmax(W_flat)
+    x = max_idx % 64
+    y = max_idx // 64
+    return xy2d(64, x, y)
+# ============================================================================
+# ABC MODEL & WEIGHTED MATRIX
+# ============================================================================
+class ABCModelDynamic:
+    """ABC Model with displacement-based B matrices."""
+    def __init__(self, n: int = 2, t: float = 1.0, T: float = 1.41):
+        """
+        Initialize for 2D board.
+        Args:
+            n: Dimension (2 for 2D board)
+            t: Minimum distance threshold for adjacency
+            T: Maximum distance threshold for adjacency
+        """
+        self.n = n
+        self.t = t
+        self.T = T
+        self.c0 = np.array([0.0, 0.0, 1.0])
+        self.B_blocks = []        # Displacement matrices
+        self.piece_positions = [] # Actual positions on SB
+        self.a_product = np.eye(3) # Accumulated product
+        self.delta = {}           # Delta values for each piece
+        self.kappa = {}           # Tokenized vectors for each piece (ADDED)
+        self.stage = 0
+        # MB position tracking
+        self.MB_current = self.c0.copy()  # Current MB center
+        self.MB_previous = self.c0.copy() # Previous MB center
+        self.history = []
+    def create_B_displacement(self, dx: float, dy: float) -> np.ndarray:
+        """
+        Create displacement matrix B.
+        Moves MB by (dx, dy) displacement.
+        B · current_MB = new_MB
+        B = [1 0 dx]
+            [0 1 dy]
+            [0 0 1]
+        Right column: (dx, dy, 1)ᵀ
+        """
+        B = np.array([
+            [1.0, 0.0, dx],
+            [0.0, 1.0, dy],
+            [0.0, 0.0, 1.0]
+        ])
+        return B
+    def add_piece(self, position: tuple, delta_values: tuple, kappa_vector: np.ndarray = None):
+        """
+        Add a piece at position with delta values and optional kappa vector.
+        Args:
+            position: (x, y) tuple
+            delta_values: (Δ₁, Δ₂, Δ₃) tuple
+            kappa_vector: Tokenized feature vector (optional, defaults to delta_values)
+        """
+        x, y = position
+        # Current MB position
+        current_MB = self.MB_current.copy()
+        # Calculate displacement
+        dx = x - current_MB[0]
+        dy = y - current_MB[1]
+        # Create displacement matrix
+        B_i = self.create_B_displacement(dx, dy)
+        # Store
+        idx = len(self.B_blocks)
+        self.B_blocks.append(B_i)
+        self.piece_positions.append((x, y))
+        # Update accumulated product: a_t = a_{t-1} · B_t
+        self.a_product = self.a_product @ B_i
+        # Track MB positions
+        self.MB_previous = self.MB_current.copy()
+        self.MB_current = self.a_product @ self.c0  # Should equal (x, y, 1)
+        # Store differential vector
+        self.delta[idx] = delta_values
+        # Store tokenized vector (or use delta_values as default)
+        if kappa_vector is None:
+            kappa_vector = np.array(delta_values)
+        self.kappa[idx] = kappa_vector
+        # Increment stage
+        self.stage += 1
+        # Record move
+        self.history.append({
+            'stage': self.stage,
+            'SB_position': (x, y),
+            'displacement': (dx, dy),
+            'B_i': B_i.copy(),
+            'a_t': self.a_product.copy(),
+            'MB_prev': self.MB_previous.copy(),
+            'MB_curr': self.MB_current.copy(),
+            'delta': delta_values,
+            'kappa': kappa_vector.copy()
+        })
+    def add_move(self, x: float, y: float, player: int):
+        """
+        Convenience method: Add a move with automatic delta values.
+        Args:
+            x, y: Position coordinates
+            player: 1 for X (Δ₂=1.0), 2 for O (Δ₂=1.1)
+        """
+        delta_1 = 1.0  # Occupied
+        delta_2 = 1.0 if player == 1 else 1.1  # Player color
+        delta_3 = 1.0  # Same value for all pieces
+        self.add_piece((x, y), (delta_1, delta_2, delta_3))
+    def get_board_state(self) -> str:
+        """Visual board state."""
+        pos_map = {
+            (-1, 1): 0, (0, 1): 1, (1, 1): 2,
+            (-1, 0): 3, (0, 0): 4, (1, 0): 5,
+            (-1, -1): 6, (0, -1): 7, (1, -1): 8
+        }
+        board = [' '] * 9
+        for i, pos in enumerate(self.piece_positions):
+            if pos in pos_map:
+                player = 'X' if self.delta[i][1] == 1.0 else 'O'
+                board[pos_map[pos]] = player
+        s = f" {board[0]} | {board[1]} | {board[2]} \n"
+        s += "---|---|---\n"
+        s += f" {board[3]} | {board[4]} | {board[5]} \n"
+        s += "---|---|---\n"
+        s += f" {board[6]} | {board[7]} | {board[8]} \n"
+        return s
+    def describe_move(self, stage: int):
+        """Describe a specific move."""
+        if stage < 1 or stage > len(self.history):
+            return "Invalid stage"
+        move = self.history[stage - 1]
+        desc = "=" * 70 + "\n"
+        desc += f"MOVE {stage}: {move['SB_position']}\n"
+        desc += "=" * 70 + "\n\n"
+        idx = stage - 1
+        B_i = self.B_blocks[idx]
+        desc += f"Mobile Board (MB) movement:\n"
+        desc += f" Previous MB: {move['MB_prev']}\n"
+        desc += f" Target (SB): {move['SB_position']}\n"
+        desc += f" Displacement: Δ = {move['displacement']}\n"
+        desc += f" New MB: {move['MB_curr']}\n\n"
+        desc += f"Displacement matrix B_{stage}:\n{B_i}\n"
+        desc += f"Right column: {B_i[:, 2]} = (Δx={move['displacement'][0]}, Δy={move['displacement'][1]}, 1)\n\n"
+        desc += f"Accumulated product a_{stage}:\n{move['a_t']}\n"
+        desc += f"Right column: {move['a_t'][:, 2]}\n\n"
+        desc += f"Delta values: {move['delta']}\n"
+        desc += f"Kappa vector: {move['kappa']}\n\n"
+        desc += f"Verification:\n"
+        desc += f" a_{stage} · c₀ = {move['a_t'] @ self.c0}\n"
+        desc += f" Should equal: {np.array([move['SB_position'][0], move['SB_position'][1], 1.0])}\n\n"
+        desc += "Board state:\n"
+        desc += self.get_board_state()
+        return desc
+class WeightedMatrixABC:
+    """
+    Compute weighted adjacency matrix from ABCModelDynamic.
+    CRITICAL: Converts (x,y) tuples to homogeneous coords [x,y,1]
+    to match algebraic structure of B matrices from abc_model.py
+    Implements Definition from Section 6:
+        W[i,j](t) = A[i,j](t) ⊙ S[i,j](t) ⊙ F[i,j](t)
+    """
+    def __init__(self, abc_model: ABCModelDynamic, sigma: float = 1.0):
+        """
+        Initialize with ABC model instance.
+        Args:
+            abc_model: ABCModelDynamic instance
+            sigma: Standard deviation for Gaussian spatial kernel
+        """
+        self.abc = abc_model
+        self.n = abc_model.n
+        self.t = abc_model.t
+        self.T = abc_model.T
+        self.sigma = sigma
+        self.positions = None  # Will store homogeneous coords [x, y, 1]
+        self.D = None
+        self.A = None
+        self.S = None
+        self.F = None
+        self.W = None
+    def compute_piece_positions(self) -> np.ndarray:
+        """
+        Extract positions from ABC model and convert to homogeneous coordinates.
+        In abc_model.py:
+            - piece_positions are (x, y) tuples
+            - MB_current = a_product @ c0 produces [x, y, 1]
+        For matrix computations, convert to homogeneous coords to match
+        the algebraic structure of B matrices.
+        Returns: Array of shape (num_pieces, 3) with homogeneous coords [x, y, 1]
+        """
+        positions = []
+        for pos in self.abc.piece_positions:
+            # pos is (x, y) from piece_positions
+            x, y = pos
+            # Convert to homogeneous coordinates to align with B matrix algebra
+            positions.append(np.array([x, y, 1.0]))
+        self.positions = np.array(positions)
+        return self.positions
+    def compute_distance_matrix(self) -> np.ndarray:
+        """
+        Compute pairwise Euclidean distances using 2D components only.
+        Even though positions are [x, y, 1], we compute distance using only [x, y]
+        D[i,j] = ||[x_i, y_i] - [x_j, y_j]||₂
+        """
+        if self.positions is None:
+            self.compute_piece_positions()
+        num = len(self.positions)
+        D = np.zeros((num, num))
+        for i in range(num):
+            for j in range(num):
+                # Use only 2D coordinates for distance
+                pos_i = self.positions[i][:2]
+                pos_j = self.positions[j][:2]
+                D[i, j] = np.linalg.norm(pos_i - pos_j)
+        self.D = D
+        return D
+    def compute_adjacency_matrix(self) -> np.ndarray:
+        """
+        Compute Adjacency Matrix (Definition 6.2).
+        A[i,j] = 1 if:
+            - k ≤ D[i,j] ≤ K (grid-adjacent)
+            - i == j AND i is isolated (no neighbors in [k,K])
+        A[i,j] = 0 otherwise
+        """
+        if self.D is None:
+            self.compute_distance_matrix()
+        num = len(self.positions)
+        A = np.zeros((num, num))
+        # Identify isolated pieces
+        isolated = set()
+        for i in range(num):
+            has_neighbor = False
+            for j in range(num):
+                if i != j and self.t <= self.D[i, j] <= self.T:
+                    has_neighbor = True
+                    break
+            if not has_neighbor:
+                isolated.add(i)
+        # Fill adjacency matrix
+        for i in range(num):
+            for j in range(num):
+                # Check adjacency distance
+                if i != j and self.t <= self.D[i, j] <= self.T:
+                    A[i, j] = 1.0
+                # Check if isolated piece
+                elif i == j and i in isolated:
+                    A[i, j] = 1.0
+        self.A = A
+        return A
+    def compute_spatial_matrix(self) -> np.ndarray:
+        """
+        Compute Spatial Matrix (Definition 6.3).
+        S[i,j](t) = exp(-||c_i(t) - c_j(t)||² / (2σ²))
+        Gaussian kernel based on Euclidean distance.
+        """
+        if self.D is None:
+            self.compute_distance_matrix()
+        num = len(self.positions)
+        S = np.zeros((num, num))
+        for i in range(num):
+            for j in range(num):
+                S[i, j] = np.exp(-self.D[i, j]**2 / (2 * self.sigma**2))
+        self.S = S
+        return S
+    def compute_feature_matrix(self) -> np.ndarray:
+        """
+        Compute Feature Matrix (Definition 6.4).
+        F[i,j](t) = <κ(B_i), κ(B_j)> / (||κ(B_i)|| · ||κ(B_j)||)
+        Cosine similarity between tokenized vectors.
+        """
+        num = len(self.positions)
+        F = np.zeros((num, num))
+        # Extract tokenized vectors
+        kappas = []
+        for i in range(num):
+            if i in self.abc.kappa:
+                kappas.append(self.abc.kappa[i])
+            else:
+                # Default: use delta as feature vector
+                if i in self.abc.delta:
+                    kappas.append(np.array(self.abc.delta[i]))
+                else:
+                    kappas.append(np.array([1.0, 1.0, 1.0]))
+        # Compute cosine similarity
+        for i in range(num):
+            for j in range(num):
+                kappa_i = kappas[i]
+                kappa_j = kappas[j]
+                dot_product = np.dot(kappa_i, kappa_j)
+                norm_i = np.linalg.norm(kappa_i)
+                norm_j = np.linalg.norm(kappa_j)
+                if norm_i > 0 and norm_j > 0:
+                    F[i, j] = dot_product / (norm_i * norm_j)
+                else:
+                    F[i, j] = 0.0
+        self.F = F
+        return F
+    def compute_weighted_matrix(self) -> np.ndarray:
+        """
+        Compute Weighted Matrix (Definition from Section 6).
+        W[i,j](t) = A[i,j](t) ⊙ S[i,j](t) ⊙ F[i,j](t)
+        Returns: W - the full weighted matrix
+        """
+        if self.A is None:
+            self.compute_adjacency_matrix()
+        if self.S is None:
+            self.compute_spatial_matrix()
+        if self.F is None:
+            self.compute_feature_matrix()
+        # Hadamard product (element-wise multiplication)
+        W = self.A * self.S * self.F
+        self.W = W
+        return W
+    def compute_manhattan_distance(self, other: 'WeightedMatrixABC') -> float:
+        """
+        Compute Manhattan distance between two weighted matrices.
+        distance = ||W_1 - W_2||₁
+        """
+        if self.W is None:
+            self.compute_weighted_matrix()
+        if other.W is None:
+            other.compute_weighted_matrix()
+        W1 = self.W
+        W2 = other.W
+        # Pad to same size
+        size = max(len(W1), len(W2))
+        W1_padded = np.zeros((size, size))
+        W2_padded = np.zeros((size, size))
+        W1_padded[:len(W1), :len(W1)] = W1
+        W2_padded[:len(W2), :len(W2)] = W2
+        return np.linalg.norm(W1_padded - W2_padded, ord=1)
+# ============================================================================
+# CHESS GAME LOGIC
+# ============================================================================
+class Chess:
+    def __init__(self):
+        self.board = chess.Board()
+        self.move_count = 0
+        self.position_history = Counter()
+        self._update_position_key()
+    def _update_position_key(self):
+        key = (self.board.fen(), self.board.turn)
+        self.position_history[key] += 1
+    def copy(self):
+        new_game = Chess()
+        new_game.board = self.board.copy()
+        new_game.move_count = self.move_count
+        new_game.position_history = self.position_history.copy()
+        return new_game
+    def undo_move(self) -> None:
+        """
+        Undo the last move (pop) and revert bookkeeping (move_count, position_history).
+        This complements `apply_move` which increments move_count and updates
+        the position_history for the new state after a push. `undo_move` decrements
+        the same position record and pops the board to restore the previous state.
+        """
+        # The current board fen/turn corresponds to the state that was last pushed;
+        # decrement its count before popping to fully revert the update.
+        key = (self.board.fen(), self.board.turn)
+        if key in self.position_history:
+            # decrement safely (don't remove key to avoid KeyError on repeated ops)
+            self.position_history[key] = max(0, self.position_history[key] - 1)
+        # pop the board and update counters
+        self.board.pop()
+        self.move_count = max(0, self.move_count - 1)
+    def get_legal_moves(self) -> List[chess.Move]:
+        moves = []
+        for move in self.board.legal_moves:
+            if move.promotion is None or move.promotion == chess.QUEEN:
+                moves.append(move)
+        return moves
+    def apply_move(self, move: chess.Move) -> None:
+        self.board.push(move)
+        self.move_count += 1
+        self._update_position_key()
+    def is_terminal(self) -> bool:
+        return self.board.is_game_over(claim_draw=True)
+    def check_winner(self) -> int:
+        if not self.is_terminal():
+            return 0
+        outcome = self.board.outcome(claim_draw=True)
+        if outcome is None or outcome.winner is None:
+            return 0
+        return 1 if outcome.winner == chess.WHITE else -1
+    def get_weighted_adjacency_matrix(self) -> np.ndarray:
+        occupied = []
+        for sq in chess.SQUARES:
+            piece = self.board.piece_at(sq)
+            if piece:
+                file = chess.square_file(sq)
+                rank = chess.square_rank(sq)
+                x = float(file) - 3.5
+                y = float(rank) - 3.5
+                color_val = 1.0 if piece.color == chess.WHITE else 1.1
+                type_val = {
+                    chess.PAWN:   1.0,
+                    chess.KNIGHT: 3.0,
+                    chess.BISHOP: 3.2,
+                    chess.ROOK:   5.0,
+                    chess.QUEEN:  9.0,
+                    chess.KING:  20.0
+                }[piece.piece_type]
+                kappa = np.array([1.0, color_val, type_val])
+                hilbert_d = xy2d(8, file, rank)
+                occupied.append((hilbert_d, (x, y), kappa))
+        occupied.sort(key=lambda t: t[0])
+        abc = ABCModelDynamic(n=2, t=1.0, T=1.41)
+        for _, pos, kappa_vec in occupied:
+            abc.add_piece(pos, delta_values=(1.0, kappa_vec[1], kappa_vec[2]), kappa_vector=kappa_vec)
+        w_calc = WeightedMatrixABC(abc, sigma=1.0)
+        W_var = w_calc.compute_weighted_matrix()
+        num = len(occupied)
+        W = np.zeros((64, 64))
+        if num > 0:
+            W[:num, :num] = W_var
+        return W
+# ============================================================================
+# NEURAL NETWORKS
+# ============================================================================
+class PolicyNetworkCNN(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.conv = nn.Sequential(
+            nn.Conv2d(1, 64, kernel_size=5, padding=2, stride=2),
+            nn.ReLU(),
+            nn.Conv2d(64, 128, kernel_size=5, padding=2, stride=2),
+            nn.ReLU(),
+            nn.Conv2d(128, 128, kernel_size=3, padding=1, stride=2),
+            nn.ReLU(),
+        )
+        self.fc = nn.Linear(128 * 8 * 8, 4096)
+    def forward(self, x):
+        x = self.conv(x)
+        x = x.view(x.size(0), -1)
+        return self.fc(x)
+class ValueNetworkCNN(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.conv = nn.Sequential(
+            nn.Conv2d(1, 64, kernel_size=5, padding=2, stride=2),
+            nn.ReLU(),
+            nn.Conv2d(64, 128, kernel_size=5, padding=2, stride=2),
+            nn.ReLU(),
+            nn.Conv2d(128, 128, kernel_size=3, padding=1, stride=2),
+            nn.ReLU(),
+        )
+        self.fc = nn.Sequential(
+            nn.Linear(128 * 8 * 8, 512),
+            nn.ReLU(),
+            nn.Linear(512, 1),
+            nn.Tanh()
+        )
+    def forward(self, x):
+        x = self.conv(x)
+        x = x.view(x.size(0), -1)
+        return self.fc(x)
+# ============================================================================
+# ZONE DATABASE
+# ============================================================================
+class HilbertOrderedZoneDatabase:
+    def __init__(self, filepath: str = "chess_zone_db.npz", max_size: int = 100000):
+        self.filepath = filepath
+        self.max_size = max_size  # Maximum matrices per zone
+        self.winning_matrices = []
+        self.winning_indices = []
+        self.losing_matrices = []
+        self.losing_indices = []
+        self.draw_matrices = []
+        self.draw_indices = []
+        self.load()
+    def add_winning_matrix(self, W: np.ndarray):
+        if W.shape != (64, 64):
+            return
+        hilbert_idx = matrix_to_hilbert_index(W)
+        pos = bisect.bisect_left(self.winning_indices, hilbert_idx)
+        self.winning_indices.insert(pos, hilbert_idx)
+        self.winning_matrices.insert(pos, W.copy())
+    def add_losing_matrix(self, W: np.ndarray):
+        if W.shape != (64, 64):
+            return
+        hilbert_idx = matrix_to_hilbert_index(W)
+        pos = bisect.bisect_left(self.losing_indices, hilbert_idx)
+        self.losing_indices.insert(pos, hilbert_idx)
+        self.losing_matrices.insert(pos, W.copy())
+    def add_draw_matrix(self, W: np.ndarray):
+        if W.shape != (64, 64):
+            return
+        hilbert_idx = matrix_to_hilbert_index(W)
+        pos = bisect.bisect_left(self.draw_indices, hilbert_idx)
+        self.draw_indices.insert(pos, hilbert_idx)
+        self.draw_matrices.insert(pos, W.copy())
+    def add_game_record(self, trajectory: List[Chess], result: int, sample_rate: float = 0.3):
+        """Add game record with sampling to control database size."""
+        # Sample states: always keep first and last, random subset of middle
+        sampled_states = []
+        for i, state in enumerate(trajectory):
+            if i == 0 or i == len(trajectory) - 1:
+                # Always keep start and end positions
+                sampled_states.append(state)
+            elif random.random() < sample_rate:
+                # Randomly sample middle positions
+                sampled_states.append(state)
+        for state in sampled_states:
+            W = state.get_weighted_adjacency_matrix()
+            if result == 1:
+                self.add_winning_matrix(W)
+            elif result == -1:
+                self.add_losing_matrix(W)
+            else:
+                self.add_draw_matrix(W)
+    def save(self):
+        """Save database with pruning if too large."""
+        # Prune if any zone exceeds 80% of max_size
+        threshold = int(self.max_size * 0.8)
+        if (len(self.winning_matrices) > threshold or
+            len(self.losing_matrices) > threshold or
+            len(self.draw_matrices) > threshold):
+            print(f"Pruning database before save...")
+            self.prune_database(target_size=int(self.max_size * 0.7))
+        try:
+            np.savez_compressed(
+                self.filepath,
+                winning=np.array(self.winning_matrices, dtype=object),
+                winning_indices=np.array(self.winning_indices),
+                losing=np.array(self.losing_matrices, dtype=object),
+                losing_indices=np.array(self.losing_indices),
+                draw=np.array(self.draw_matrices, dtype=object),
+                draw_indices=np.array(self.draw_indices),
+            )
+            print(f"Zone DB saved: W={len(self.winning_matrices)}, L={len(self.losing_matrices)}, D={len(self.draw_matrices)}")
+        except MemoryError:
+            print(f"MemoryError during save! Pruning more aggressively...")
+            self.prune_database(target_size=1000)
+            # Try again with much smaller size
+            np.savez_compressed(
+                self.filepath,
+                winning=np.array(self.winning_matrices, dtype=object),
+                winning_indices=np.array(self.winning_indices),
+                losing=np.array(self.losing_matrices, dtype=object),
+                losing_indices=np.array(self.losing_indices),
+                draw=np.array(self.draw_matrices, dtype=object),
+                draw_indices=np.array(self.draw_indices),
+            )
+    def load(self):
+        if os.path.exists(self.filepath):
+            try:
+                data = np.load(self.filepath, allow_pickle=True)
+                self.winning_matrices = list(data['winning_matrices'])
+                self.winning_indices = list(data['winning_indices'])
+                self.losing_matrices = list(data['losing_matrices'])
+                self.losing_indices = list(data['losing_indices'])
+                self.draw_matrices = list(data['draw_matrices'])
+                self.draw_indices = list(data['draw_indices'])
+                print(f"Loaded zone DB: W={len(self.winning_matrices)}, L={len(self.losing_matrices)}, D={len(self.draw_matrices)}")
+            except Exception as e:
+                print(f"Failed to load zone database: {e}")
+    def prune_database(self, target_size: int = 5000):
+        """Keep only evenly-spaced diverse samples along Hilbert curve."""
+        def prune_zone(matrices, indices, target):
+            if len(matrices) <= target:
+                return matrices, indices
+            # Keep evenly spaced samples
+            step = max(1, len(matrices) // target)
+            keep_idx = list(range(0, len(matrices), step))[:target]
+            new_matrices = [matrices[i] for i in keep_idx]
+            new_indices = [indices[i] for i in keep_idx]
+            return new_matrices, new_indices
+        old_sizes = (len(self.winning_matrices), len(self.losing_matrices), len(self.draw_matrices))
+        self.winning_matrices, self.winning_indices = prune_zone(
+            self.winning_matrices, self.winning_indices, target_size
+        )
+        self.losing_matrices, self.losing_indices = prune_zone(
+            self.losing_matrices, self.losing_indices, target_size
+        )
+        self.draw_matrices, self.draw_indices = prune_zone(
+            self.draw_matrices, self.draw_indices, target_size
+        )
+        new_sizes = (len(self.winning_matrices), len(self.losing_matrices), len(self.draw_matrices))
+        print(f"Pruned: W {old_sizes}→{new_sizes}, L {old_sizes}→{new_sizes}, D {old_sizes}→{new_sizes}")
+    def compute_zone_score(self, W: np.ndarray, k: int = 5, beta: float = 0.5) -> float:
+        """Compute zone guidance score Z(x(t), a) ∈ [-1, 1]."""
+        if W.shape != (64, 64):
+            return 0.0
+        def knn_similarity(matrices, k_val):
+            if len(matrices) == 0:
+                return 0.0
+            k_actual = min(k_val, len(matrices))
+            distances = []
+            for mat in matrices[:k_actual]:
+                dist = np.sum(np.abs(W - mat)) / (64.0 * 64.0)
+                distances.append(dist)
+            similarities = [1.0 - d for d in distances]
+            return np.mean(similarities)
+        zone_win = knn_similarity(self.winning_matrices, k)
+        zone_loss = knn_similarity(self.losing_matrices, k)
+        zone_draw = knn_similarity(self.draw_matrices, k)
+        Z = zone_win - zone_loss + beta * zone_draw
+        return float(np.clip(Z, -1.0, 1.0))
+# ============================================================================
+# TRAINING FUNCTION
+# ============================================================================
+def train_networks(policy_net, value_net, W_states, policies, values, epochs=5, batch_size=32, device='cpu', lr=0.001):
+    policy_net.train()
+    value_net.train()
+    opt_p = optim.Adam(policy_net.parameters(), lr=lr)
+    opt_v = optim.Adam(value_net.parameters(), lr=lr)
+    W_tensor = torch.tensor(np.array(W_states)[:, np.newaxis, :, :], dtype=torch.float32)
+    pi_tensor = torch.tensor(np.array(policies), dtype=torch.float32)
+    v_tensor = torch.tensor(np.array(values), dtype=torch.float32).unsqueeze(1)
+    dataset = TensorDataset(W_tensor, pi_tensor, v_tensor)
+    loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+    for epoch in range(epochs):
+        total_loss = 0.0
+        for batch_W, batch_pi, batch_v in loader:
+            batch_W = batch_W.to(device)
+            batch_pi = batch_pi.to(device)
+            batch_v = batch_v.to(device)
+            logits = policy_net(batch_W)
+            # Fixed policy loss: KL divergence between network policy and MCTS visit distribution
+            policy_loss = F.kl_div(F.log_softmax(logits, dim=1), batch_pi, reduction='batchmean')
+            pred_v = value_net(batch_W)
+            value_loss = F.mse_loss(pred_v, batch_v)
+            loss = policy_loss + value_loss
+            total_loss += loss.item()
+            opt_p.zero_grad()
+            opt_v.zero_grad()
+            loss.backward()
+            # Optional but recommended: gradient clipping
+            torch.nn.utils.clip_grad_norm_(policy_net.parameters(), max_norm=1.0)
+            torch.nn.utils.clip_grad_norm_(value_net.parameters(), max_norm=1.0)
+            opt_p.step()
+            opt_v.step()
+        # Optional: print epoch loss for monitoring
+        print(f"Epoch {epoch+1}/{epochs} - Loss: {total_loss/len(loader):.4f}")
+# ============================================================================
+# MCVS SEARCHER
+# ============================================================================
+class MCVSSearcher:
+    def __init__(self, policy_net, value_net, zone_db, device='cpu',
+                 cpuct=1.41, lambda_zone=0.0, k_zone=5, use_nets=True,
+                 dirichlet_alpha: float = 0.3, dirichlet_noise_fraction: float = 0.25):
+        self.policy_net = policy_net.to(device) if policy_net and use_nets else None
+        self.value_net = value_net.to(device) if value_net and use_nets else None
+        self.zone_db = zone_db
+        self.device = device
+        self.cpuct = cpuct
+        self.lambda_zone = lambda_zone
+        self.k_zone = k_zone
+        self.use_nets = use_nets
+        # Dirichlet noise hyperparameters (alpha for the Dirichlet, and fraction)
+        self.dirichlet_alpha = float(dirichlet_alpha)
+        self.dirichlet_noise_fraction = float(dirichlet_noise_fraction)
+    def _rollout(self, game: Chess) -> float:
+        """Simple random rollout for leaf evaluation when no value network.
+        Uses push/pop (apply_move / undo_move) on the provided `game` to avoid
+        allocating a full copy per rollout. The rollout will undo its own
+        moves before returning.
+        """
+        depth = 0
+        max_depth = 60  # reduced depth for faster rollouts (configurable)
+        moves_played = []
+        while not game.is_terminal() and depth < max_depth:
+            moves = game.get_legal_moves()
+            if not moves:
+                break
+            m = random.choice(moves)
+            game.apply_move(m)
+            moves_played.append(m)
+            depth += 1
+        winner = game.check_winner()
+        # Undo rollout moves
+        for _ in range(len(moves_played)):
+            game.undo_move()
+        return float(winner)  # +1, -1, or 0
+    class Node:
+        def __init__(self, prior: float = 0.0, zone: float = 0.0):
+            self.prior = prior
+            self.zone = zone
+            self.visit_count = 0
+            self.value_sum = 0.0
+            self.children: Dict[chess.Move, 'MCVSSearcher.Node'] = {}
+    def search_with_time_budget(self, game: Chess, time_budget: float) -> Tuple[Dict[chess.Move, int], int]:
+        root = self.Node()
+        start_time = time.time()
+        simulations = 0
+        while time.time() - start_time < time_budget:
+            current_game = game
+            node = root
+            path = []
+            moves_made = []
+            # Selection
+            while node.children:
+                path.append(node)
+                total_n = sum(c.visit_count for c in node.children.values()) + 1
+                best_score = -float('inf')
+                best_move = None
+                best_child = None
+                for move, child in node.children.items():
+                    q = child.value_sum / child.visit_count if child.visit_count > 0 else 0.0
+                    p_lambda = max(child.prior + self.lambda_zone * child.zone, 0.001)
+                    u = self.cpuct * p_lambda * np.sqrt(total_n) / (1 + child.visit_count)
+                    score = q + u
+                    if score > best_score:
+                        best_score = score
+                        best_move = move
+                        best_child = child
+                current_game.apply_move(best_move)
+                moves_made.append(best_move)
+                node = best_child
+            path.append(node)
+            # Terminal node?
+            if current_game.is_terminal():
+                value = float(current_game.check_winner())
+            else:
+                # Expansion & Evaluation
+                legal_moves = current_game.get_legal_moves()
+                if self.use_nets and self.policy_net is not None and self.value_net is not None:
+                    # === Neural network branch ===
+                    W = current_game.get_weighted_adjacency_matrix()
+                    W_tensor = torch.from_numpy(W)[None, None, :, :].float().to(self.device)
+                    with torch.no_grad():
+                        logits = self.policy_net(W_tensor)[0]
+                        value = self.value_net(W_tensor)[0, 0].item()
+                    probs = F.softmax(logits, dim=0).cpu().numpy()
+                    prior_dict = {}
+                    prior_sum = 0.0
+                    for m in legal_moves:
+                        idx = m.from_square * 64 + m.to_square
+                        p = float(probs[idx])
+                        prior_dict[m] = p
+                        prior_sum += p
+                    if prior_sum > 0.0:
+                        for m in prior_dict:
+                            prior_dict[m] /= prior_sum
+                    else:
+                        p = 1.0 / len(legal_moves)
+                        prior_dict = {m: p for m in legal_moves}
+                else:
+                    # === Zone-only / no-nets branch ===
+                    value = self._rollout(current_game)
+                    prior_dict = {m: 1.0 / len(legal_moves) for m in legal_moves} if legal_moves else {}
+                # Dirichlet noise only at root and only when using nets.
+                # Use configured hyperparameters so the same alpha/fraction
+                # can be applied to both priors and zone guidance.
+                if len(path) == 1 and self.use_nets and legal_moves:
+                    noise = np.random.dirichlet([self.dirichlet_alpha] * len(legal_moves))
+                    for i, m in enumerate(legal_moves):
+                        prior_dict[m] = (1 - self.dirichlet_noise_fraction) * prior_dict[m] + \
+                                        self.dirichlet_noise_fraction * noise[i]
+                    # Renormalize
+                    prior_sum = sum(prior_dict.values())
+                    if prior_sum > 0:
+                        for m in prior_dict:
+                            prior_dict[m] /= prior_sum
+                # Create children with zone scores. Use apply/undo on the shared
+                # board to avoid allocating a full copy per child. Skip heavy
+                # weighted-matrix computations when zone guidance is disabled
+                # (lambda_zone == 0) or when the DB is empty.
+                zone_db_empty = (len(self.zone_db.winning_matrices) == 0 and
+                                 len(self.zone_db.losing_matrices) == 0 and
+                                 len(self.zone_db.draw_matrices) == 0)
+                need_zone = (self.lambda_zone != 0.0) and (not zone_db_empty)
+                for i, m in enumerate(legal_moves):
+                    if need_zone:
+                        current_game.apply_move(m)
+                        child_W = current_game.get_weighted_adjacency_matrix()
+                        child_Z = self.zone_db.compute_zone_score(child_W, k=self.k_zone)
+                        current_game.undo_move()
+                    else:
+                        child_Z = 0.0
+                    # If Dirichlet noise was added to priors at the root, apply the same
+                    # noise (mapped to [-1,1]) to zone guidance so both signals share
+                    # the same stochastic perturbation controlled by the same alpha.
+                    if len(path) == 1 and self.use_nets and legal_moves:
+                        z_noise = (noise[i] * 2.0) - 1.0  # map [0,1] -> [-1,1]
+                        child_Z = (1 - self.dirichlet_noise_fraction) * child_Z + \
+                                  self.dirichlet_noise_fraction * z_noise
+                    child = self.Node(prior=prior_dict.get(m, 0.0), zone=child_Z)
+                    node.children[m] = child
+            # Backpropagation
+            v = value
+            for n in reversed(path):
+                n.visit_count += 1
+                n.value_sum += v
+                v = -v
+            # Undo moves that were applied during selection (the rollout
+            # already undid its own moves). This restores `game` to the root
+            # state for the next simulation.
+            for _ in range(len(moves_made)):
+                current_game.undo_move()
+            simulations += 1
+        visits = {move: child.visit_count for move, child in root.children.items()}
+        if not visits:
+            legal = game.get_legal_moves()
+            visits = {random.choice(legal): 1} if legal else {}
+        return visits, simulations
+# ============================================================================
+# UCT SEARCHER (your original from the provided file)
+# ============================================================================
+class UCTSearcher:
+    def __init__(self, cpuct=np.sqrt(2.0)):
+        self.cpuct = cpuct
+    class Node:
+        def __init__(self):
+            self.visit_count = 0
+            self.value_sum = 0.0
+            self.children: Dict[chess.Move, 'UCTSearcher.Node'] = {}
+    def _rollout(self, game: Chess) -> float:
+        depth = 0
+        max_depth = 60
+        moves_played = []
+        while not game.is_terminal() and depth < max_depth:
+            moves = game.get_legal_moves()
+            if not moves:
+                break
+            m = random.choice(moves)
+            game.apply_move(m)
+            moves_played.append(m)
+            depth += 1
+        if depth >= max_depth:
+            # undo rollout moves
+            for _ in range(len(moves_played)):
+                game.undo_move()
+            return 0.0
+        winner = game.check_winner()
+        # undo rollout moves
+        for _ in range(len(moves_played)):
+            game.undo_move()
+        if winner == 1:
+            return 1.0
+        elif winner == -1:
+            return -1.0
+        else:
+            return 0.0
+    def search_with_time_budget(self, game: Chess, time_budget: float) -> Tuple[Dict[chess.Move, int], int]:
+        root = self.Node()
+        start_time = time.time()
+        simulations = 0
+        while time.time() - start_time < time_budget:
+            current_game = game
+            node = root
+            path = [node]
+            moves_made = []
+            while True:
+                legal_moves = current_game.get_legal_moves()
+                if current_game.is_terminal():
+                    winner = current_game.check_winner()
+                    value = 1.0 if winner == 1 else -1.0 if winner == -1 else 0.0
+                    break
+                if not legal_moves:
+                    value = 0.0
+                    break
+                unvisited_moves = [m for m in legal_moves if m not in node.children]
+                if unvisited_moves:
+                    move = random.choice(unvisited_moves)
+                    child = self.Node()
+                    node.children[move] = child
+                    current_game.apply_move(move)
+                    moves_made.append(move)
+                    path.append(child)
+                    value = self._rollout(current_game)
+                    break
+                best_score = -float('inf')
+                best_move = None
+                best_child = None
+                total_visits = node.visit_count
+                for move in legal_moves:
+                    child = node.children[move]
+                    Q = child.value_sum / (child.visit_count + 1e-8) if child.visit_count > 0 else 0.0
+                    U = self.cpuct * np.sqrt(np.log(total_visits + 1) / (child.visit_count + 1e-8))
+                    score = Q + U
+                    if score > best_score:
+                        best_score = score
+                        best_move = move
+                        best_child = child
+                current_game.apply_move(best_move)
+                moves_made.append(best_move)
+                node = best_child
+                path.append(node)
+            for n in reversed(path):
+                n.visit_count += 1
+                n.value_sum += value
+                value = -value
+            # Undo selection moves to restore root state
+            for _ in range(len(moves_made)):
+                current_game.undo_move()
+            simulations += 1
+        visits = {move: child.visit_count for move, child in root.children.items()}
+        if not visits:
+            legal = game.get_legal_moves()
+            return {random.choice(legal): 1} if legal else {}, simulations
+        return visits, simulations
+if __name__ == "__main__":
     print("chess_mcvs.py loaded successfully")