feat: add numeric and symbolic scripts

scripts/subblock.py

@@ -0,0 +1,25 @@
+"""subblock.py -- extract the "fully active" 9x9 sub-block M_{S->S^c} (both source and
+target sectors fully active, i.e. every party involved) from the full bigraduated
+cluster map. This is Corollary "sub-block witnesses" specialized to V=S, T=S^c."""
+import numpy as np
+
+
+def fully_active_block(C, s0, s1):
+    others = [k for k in range(4) if k not in (s0, s1)]
+    c0, c1 = others
+    M = np.zeros((9, 9))
+    rows = [(i, j) for i in [1, 2, 3] for j in [1, 2, 3]]
+    cols = [(i, j) for i in [1, 2, 3] for j in [1, 2, 3]]
+    for ri, (ia, ib) in enumerate(rows):
+        for ci, (ic, idd) in enumerate(cols):
+            idx = [0, 0, 0, 0]
+            idx[s0] = ia
+            idx[s1] = ib
+            idx[c0] = ic
+            idx[c1] = idd
+            M[ri, ci] = C[tuple(idx)]
+    return M / 3.0  # same normalization convention as cluster.cluster_map
+
+
+def nuc(M):
+    return np.linalg.svd(M, compute_uv=False).sum()