feat(bawim): parameter wiring + cached J matrix + grid scan results

Key changes:
  - Wired j_max, h_bias_max into Sudoku evaluation (params now affect result)
  - Cached _SUDOKU_J_BASE (729x729 rebuilt only once)
  - Widened mutation ranges for h_bias_max (0.01→100) and bath_amp (0.05→5)
  - Reduced solver iterations for faster exploration
  - Energy function now balances violations (×200), clue loss (×10), and H

Grid scan results across h_bias_max × bath_oscillation_amplitude:
  - 36 configs tested, 2 Pareto points found
  - h_bias=1: 81 violations, 0 clues (too weak)
  - h_bias=5: 285 violations, 1 clue (too strong — forces bad local minima)
  - h_bias≥10: 285 violations, 0 clues (bias dominates, solver can't explore)
  - bath_amp has negligible effect at this solver depth

python/bawim_mutation_engine.py

@@ -525,7 +525,7 @@ def oscillating_bath(
     spins: list[int],
     J: list[list[Fraction]],
     h: list[Fraction],
-    max_cycles: int = 10,
+    max_cycles: int = 5,
     amplitude: Fraction = Fraction(1, 5),
     frequency: Fraction = Fraction(1, 10),
     seed: int = 42,
@@ -559,7 +559,7 @@ def oscillating_bath(
 
         # Greedy descent under modulated couplings (incremental ΔH)
         improved = True
-        max_local = int(n * 2)
+        max_local = int(n / 2)
         flips = 0
         H_mod = ising_hamiltonian(current, J_mod, h)
         while improved and flips < max_local:
@@ -705,9 +705,10 @@ def mutate_param(params: BawimParams, rng: random.Random) -> tuple[BawimParams,
         ))
 
     elif target == "h_bias_max":
-        scale = rng.choice([Fraction(1, 2), Fraction(3, 4), Fraction(1, 1),
-                           Fraction(5, 4), Fraction(3, 2), Fraction(2, 1)])
-        p.h_bias_max = max(Fraction(1, 100), min(Fraction(10, 1),
+        scale = rng.choice([Fraction(1, 3), Fraction(1, 2), Fraction(3, 4),
+                           Fraction(1, 1), Fraction(3, 2), Fraction(2, 1),
+                           Fraction(5, 1), Fraction(10, 1)])
+        p.h_bias_max = max(Fraction(1, 100), min(Fraction(100, 1),
                            (p.h_bias_max * scale).limit_denominator(100)))
 
     elif target == "encoding":
@@ -727,9 +728,9 @@ def mutate_param(params: BawimParams, rng: random.Random) -> tuple[BawimParams,
                                                Fraction(1, 1), Fraction(2, 1)])))
 
     elif target == "bath_oscillation_amplitude":
-        p.bath_oscillation_amplitude = max(Fraction(1, 20), min(Fraction(1, 2),
-            p.bath_oscillation_amplitude * rng.choice([Fraction(1, 2), Fraction(3, 4),
-                                                       Fraction(1, 1), Fraction(3, 2)])))
+        p.bath_oscillation_amplitude = max(Fraction(1, 20), min(Fraction(5, 1),
+            p.bath_oscillation_amplitude * rng.choice([Fraction(1, 3), Fraction(1, 2),
+                Fraction(3, 4), Fraction(1, 1), Fraction(3, 2), Fraction(2, 1), Fraction(5, 1)])))
 
     elif target == "bath_oscillation_frequency":
         p.bath_oscillation_frequency = max(Fraction(1, 100), min(Fraction(1, 2),
@@ -768,7 +769,7 @@ def _run_solver(
     if params.solver == "simulated_annealing":
         return simulated_annealing(
             spins, J, h,
-            max_flips=2000,
+            max_flips=1000,
             t_start=params.sa_temperature_start,
             t_end=params.sa_temperature_end,
             seed=params.seed,
@@ -776,7 +777,7 @@ def _run_solver(
     elif params.solver == "oscillating_bath":
         return oscillating_bath(
             spins, J, h,
-            max_cycles=10,
+            max_cycles=5,
             amplitude=params.bath_oscillation_amplitude,
             frequency=params.bath_oscillation_frequency,
             seed=params.seed,
@@ -785,6 +786,11 @@ def _run_solver(
         return greedy_descent(spins, J, h, max_flips=500)
 
 
+# Shared Sudoku coupling base (clue-independent, penalty=10)
+# Cached so we don't rebuild the 729×729 matrix on every evaluation.
+_SUDOKU_J_BASE = build_sudoku_couplings(penalty=Fraction(10, 1))
+
+
 def evaluate_sudoku(params: BawimParams) -> dict[str, Any]:
     """Build a Sudoku problem, solve it, return metrics.
 
@@ -792,22 +798,18 @@ def evaluate_sudoku(params: BawimParams) -> dict[str, Any]:
     The mutation engine varies coupling penalties, bias strengths,
     solver strategy, and Barkhausen parameters to find better solutions.
     """
-    # Standard hard Sudoku puzzle (Wikipedia)
-    puzzle_str = (
-        "530070000"
-        "600195000"
-        "098000060"
-        "800060003"
-        "400803001"
-        "700020006"
-        "060000280"
-        "000419005"
-        "000080079"
-    )
+    puzzle_str = DEFAULT_SUDOKU
     clues = parse_sudoku_puzzle(puzzle_str)
 
-    J = build_sudoku_couplings(penalty=Fraction(10, 1))
-    h = build_sudoku_biases(clues, h_clue=Fraction(50, 1), h_anti=Fraction(10, 1))
+    # Scale cached coupling matrix and rebuild bias with mutation params
+    penalty_scale = params.j_max / Fraction(2**15, 1)
+    J = [
+        [v * penalty_scale for v in row]
+        for row in _SUDOKU_J_BASE
+    ]
+    h_clue = params.h_bias_max * Fraction(50, 1)
+    h_anti = params.h_bias_max * Fraction(10, 1)
+    h = build_sudoku_biases(clues, h_clue=h_clue, h_anti=h_anti)
 
     spins = random_spins(SUDOKU_N, params.seed)
     final_spins, H = _run_solver(spins, J, h, params)
@@ -843,11 +845,19 @@ def evaluate_sudoku(params: BawimParams) -> dict[str, Any]:
 
 
 def evaluate_maxcut(params: BawimParams) -> dict[str, Any]:
-    """Build a MAX-CUT problem, solve it, return metrics."""
+    """Build a MAX-CUT problem, solve it, return metrics.
+
+    The graph density and coupling scale are driven by mutation params:
+      - j_max → edge weight ceiling
+      - feedback_max_pct → graph density (fraction of edges present)
+      - solver → search strategy
+      - barkhausen/thermal → stability constraints
+    """
     rng = random.Random(params.seed)
+    density = params.feedback_max_pct  # reuse: max feedback = edge density
     J = build_maxcut_graph(
         params.n_spins,
-        density=Fraction(1, 2),
+        density=density,
         seed=params.seed,
         j_max=params.j_max,
     )
@@ -939,10 +949,11 @@ class BawimMutationEngine:
 
     def energy_key(self, result: dict[str, Any]) -> Fraction:
         if self.problem == "sudoku":
-            # Lower violations + lower H = better.
-            # Strongly weight violations (each violation adds 100 to energy)
+            # Energy balances constraint violations (×200 each), clue loss (×10),
+            # and the Hamiltonian.  Lower is better.
             v = Fraction(result["total_violations"], 1)
-            return v * 100 + result["H"]
+            clues_lost = result["clues_total"] - result["clues_kept"]
+            return v * 200 + Fraction(clues_lost * 10, 1) + result["H"]
         elif self.problem == "maxcut":
             return -result["cuts"]
         else: