The missing term was unary: omit-size solved at its ceiling in 1.4s

Adversarial review of the artifacts found three of my numbers to be
artifacts of my own code. All three reproduced here before acceptance:

- anchor_bound presented probe rows in the same index order on both
  sides, so exact twins had their tie broken onto the diagonal. 0.997 ->
  0.920 on omit-size. Fixed by scrambling the T-side presentation.
- The truth is not a strict local minimum: 51 transpositions have
  exactly zero energy delta. fast_pair_descent only looked stationary
  because its break test treats zero as no-improvement.
- scipy's FAQ takes no n_init, so it was swallowed into unknown_options
  and 'FAQ x30 restarts' computed bit-identically to plain FAQ. Replaced
  with a real restart loop over P0='randomized'.

The blind ceiling for omit-size is 0.836, not 1.0: the text field has 51
exact transposition automorphisms, so T[s,s] is bitwise identical to T
and no objective f(V, P T P^T) can separate an orbit at any order. Every
synthetic accuracy was being divided by the wrong denominator.

The fifteen failed solvers share one property -- all purely quadratic or
purely spectral, none with a node-level term. Eight moments of each
node's own field row, blended with the quadratic term through
Frank-Wolfe, reach 0.837 with an energy gap of exactly zero. The term
must stay in the loop: as a seed for pure-quadratic descent it scores
0.21, pinned through the iterations it scores 0.84 -- which is also why
amplification plateaued, being itself pure-quadratic.

Co-Authored-By: Claude <noreply@anthropic.com>

10 files changed, 551 insertions, 0 deletions

diff --git a/artifacts/spectral_frontier_probe/eval_impure_anchors.log b/artifacts/spectral_frontier_probe/eval_impure_anchors.log
new file mode 100644
index 0000000..a4b957a
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/eval_impure_anchors.log
@@ -0,0 +1,60 @@
+=== (a) PURE random anchors: reproduce the published curve ===
+  K=  12 pure   accuracy 0.589 +- 0.055
+  K=  25 pure   accuracy 0.860 +- 0.058
+  K=  40 pure   accuracy 0.926 +- 0.032
+  K=  50 pure   accuracy 0.949 +- 0.026
+  K=  64 pure   accuracy 0.971 +- 0.017
+  K= 128 pure   accuracy 0.996 +- 0.005
+
+=== (b) IMPURE random anchors: c correct, K-c wrong (wrong = derangement among selected) ===
+  K=  12 prec=1.00 (12/12 right)  accuracy 0.620 +- 0.093
+  K=  12 prec=0.92 (10/12 right)  accuracy 0.390 +- 0.101
+  K=  12 prec=0.88 (10/12 right)  accuracy 0.399 +- 0.109
+  K=  12 prec=0.84 (10/12 right)  accuracy 0.330 +- 0.098
+  K=  12 prec=0.80 (10/12 right)  accuracy 0.408 +- 0.120
+  K=  12 prec=0.72 (9/12 right)  accuracy 0.264 +- 0.068
+  K=  12 prec=0.60 (7/12 right)  accuracy 0.135 +- 0.064
+
+  K=  25 prec=1.00 (25/25 right)  accuracy 0.852 +- 0.049
+  K=  25 prec=0.92 (23/25 right)  accuracy 0.766 +- 0.073
+  K=  25 prec=0.88 (22/25 right)  accuracy 0.746 +- 0.071
+  K=  25 prec=0.84 (21/25 right)  accuracy 0.704 +- 0.079
+  K=  25 prec=0.80 (20/25 right)  accuracy 0.677 +- 0.070
+  K=  25 prec=0.72 (18/25 right)  accuracy 0.527 +- 0.103
+  K=  25 prec=0.60 (15/25 right)  accuracy 0.371 +- 0.091
+
+  K=  40 prec=1.00 (40/40 right)  accuracy 0.933 +- 0.032
+  K=  40 prec=0.92 (37/40 right)  accuracy 0.902 +- 0.038
+  K=  40 prec=0.88 (35/40 right)  accuracy 0.859 +- 0.037
+  K=  40 prec=0.84 (34/40 right)  accuracy 0.835 +- 0.038
+  K=  40 prec=0.80 (32/40 right)  accuracy 0.812 +- 0.047
+  K=  40 prec=0.72 (29/40 right)  accuracy 0.742 +- 0.085
+  K=  40 prec=0.60 (24/40 right)  accuracy 0.574 +- 0.081
+
+  K=  50 prec=1.00 (50/50 right)  accuracy 0.950 +- 0.024
+  K=  50 prec=0.92 (46/50 right)  accuracy 0.920 +- 0.026
+  K=  50 prec=0.88 (44/50 right)  accuracy 0.893 +- 0.033
+  K=  50 prec=0.84 (42/50 right)  accuracy 0.877 +- 0.033
+  K=  50 prec=0.80 (40/50 right)  accuracy 0.855 +- 0.031
+  K=  50 prec=0.72 (36/50 right)  accuracy 0.783 +- 0.055
+  K=  50 prec=0.60 (30/50 right)  accuracy 0.629 +- 0.102
+
+  K= 100 prec=1.00 (100/100 right)  accuracy 0.992 +- 0.009
+  K= 100 prec=0.92 (92/100 right)  accuracy 0.953 +- 0.014
+  K= 100 prec=0.88 (88/100 right)  accuracy 0.933 +- 0.016
+  K= 100 prec=0.84 (84/100 right)  accuracy 0.915 +- 0.018
+  K= 100 prec=0.80 (80/100 right)  accuracy 0.895 +- 0.012
+  K= 100 prec=0.72 (72/100 right)  accuracy 0.852 +- 0.020
+  K= 100 prec=0.60 (60/100 right)  accuracy 0.787 +- 0.021
+
+=== (c) IMPURE with wrong partners drawn from OUTSIDE the anchor set ===
+  K=  25 prec=1.00  accuracy 0.866 +- 0.040
+  K=  25 prec=0.88  accuracy 0.729 +- 0.064
+  K=  25 prec=0.84  accuracy 0.689 +- 0.070
+  K=  25 prec=0.80  accuracy 0.603 +- 0.079
+  K=  25 prec=0.72  accuracy 0.501 +- 0.094
+  K=  50 prec=1.00  accuracy 0.945 +- 0.025
+  K=  50 prec=0.88  accuracy 0.832 +- 0.031
+  K=  50 prec=0.84  accuracy 0.808 +- 0.020
+  K=  50 prec=0.80  accuracy 0.775 +- 0.031
+  K=  50 prec=0.72  accuracy 0.689 +- 0.043
diff --git a/artifacts/spectral_frontier_probe/eval_impure_anchors.py b/artifacts/spectral_frontier_probe/eval_impure_anchors.py
new file mode 100644
index 0000000..f6b4397
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/eval_impure_anchors.py
@@ -0,0 +1,65 @@
+import numpy as np, torch
+from scipy.optimize import linear_sum_assignment
+
+def standardise(M):
+    M = np.asarray(M, dtype=np.float64); mask = ~np.eye(len(M), dtype=bool); v = M[mask]
+    out = (M - v.mean()) / v.std(); np.fill_diagonal(out, 0.0); return out
+
+d = torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt', map_location='cpu', weights_only=False)
+V = standardise(d['visual_field']); T = standardise(d['text_field']); N = len(V)
+truth = np.arange(N)
+
+def expand(anchorL, anchorR):
+    """anchorL: vision indices; anchorR: claimed text partner. Returns full accuracy."""
+    probe = np.setdiff1d(np.arange(N), anchorL)
+    # probe scenes on the text side are whatever is not claimed
+    probeR = np.setdiff1d(np.arange(N), anchorR)
+    L = V[np.ix_(probe, anchorL)]; R = T[np.ix_(probeR, anchorR)]
+    L = (L - L.mean(1, keepdims=True)) / L.std(1, keepdims=True).clip(1e-9)
+    R = (R - R.mean(1, keepdims=True)) / R.std(1, keepdims=True).clip(1e-9)
+    S = L @ R.T / L.shape[1]
+    _, cols = linear_sum_assignment(-S)
+    resolved = probeR[cols]
+    n_ok = int((resolved == probe).sum()) + int((anchorR == anchorL).sum())
+    return n_ok / N
+
+rng = np.random.default_rng(0)
+REP = 20
+print("=== (a) PURE random anchors: reproduce the published curve ===")
+for K in (12, 25, 40, 50, 64, 128):
+    a = [expand(*(lambda s: (s, s))(np.sort(rng.choice(N, K, replace=False)))) for _ in range(REP)]
+    print(f"  K={K:4d} pure   accuracy {np.mean(a):.3f} +- {np.std(a):.3f}")
+
+print("\n=== (b) IMPURE random anchors: c correct, K-c wrong (wrong = derangement among selected) ===")
+for K in (12, 25, 40, 50, 100):
+    for prec in (1.0, 0.92, 0.88, 0.84, 0.80, 0.72, 0.60):
+        nb = int(round(K * (1 - prec)))
+        if nb == 1: nb = 2   # a single wrong pair is impossible inside a bijection
+        accs = []
+        for _ in range(REP):
+            sel = np.sort(rng.choice(N, K, replace=False))
+            right = sel.copy()
+            if nb >= 2:
+                bad = rng.choice(K, nb, replace=False)
+                sh = right[bad].copy()
+                while True:
+                    perm = rng.permutation(nb)
+                    if not (perm == np.arange(nb)).any(): break
+                right[bad] = sh[perm]
+            accs.append(expand(sel, right))
+        print(f"  K={K:4d} prec={prec:.2f} ({K-nb}/{K} right)  accuracy {np.mean(accs):.3f} +- {np.std(accs):.3f}")
+    print()
+
+print("=== (c) IMPURE with wrong partners drawn from OUTSIDE the anchor set ===")
+for K in (25, 50):
+    for prec in (1.0, 0.88, 0.84, 0.80, 0.72):
+        nb = int(round(K * (1 - prec))); accs = []
+        for _ in range(REP):
+            sel = np.sort(rng.choice(N, K, replace=False))
+            right = sel.copy()
+            if nb:
+                bad = rng.choice(K, nb, replace=False)
+                outside = np.setdiff1d(np.arange(N), sel)
+                right[bad] = rng.choice(outside, nb, replace=False)
+            accs.append(expand(sel, right))
+        print(f"  K={K:4d} prec={prec:.2f}  accuracy {np.mean(accs):.3f} +- {np.std(accs):.3f}")
diff --git a/artifacts/spectral_frontier_probe/eval_voteanchor_seed7.log b/artifacts/spectral_frontier_probe/eval_voteanchor_seed7.log
new file mode 100644
index 0000000..8852244
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/eval_voteanchor_seed7.log
@@ -0,0 +1,23 @@
+150 ICP solutions in 222s
+lowest-8 (E, acc, r): [(0.6733, 0.008, 8), (0.6824, 0.027, 10), (0.6956, 0.031, 10), (0.6988, 0.016, 8), (0.7011, 0.074, 12), (0.7026, 0.023, 10), (0.7052, 0.004, 10), (0.7052, 0.012, 8)]
+mean pairwise agreement among top-30: 0.046
+
+--- ROUTE A (free readout of the same ensemble) ---
+  best-E member acc 0.008 -> after exact descent acc 0.012  E=0.6565  [5s]
+  descend 5 lowest-E, pick by energy: acc 0.043  E=0.6316
+
+--- ROUTE B (the proposal) ---
+  m= 5 K= 12 kept= 12 precision=0.167 -> expansion acc 0.039 -> after descent 0.039
+  m= 5 K= 25 kept= 25 precision=0.080 -> expansion acc 0.031 -> after descent 0.051
+  m= 5 K= 50 kept= 47 precision=0.064 -> expansion acc 0.031 -> after descent 0.023
+  m= 5 K=100 kept= 91 precision=0.044 -> expansion acc 0.031 -> after descent 0.023
+  m=10 K= 12 kept= 12 precision=0.250 -> expansion acc 0.043 -> after descent 0.074
+  m=10 K= 25 kept= 23 precision=0.130 -> expansion acc 0.035 -> after descent 0.043
+  m=10 K= 50 kept= 48 precision=0.104 -> expansion acc 0.059 -> after descent 0.066
+  m=10 K=100 kept= 87 precision=0.069 -> expansion acc 0.035 -> after descent 0.035
+  m=30 K= 12 kept= 12 precision=0.417 -> expansion acc 0.094 -> after descent 0.180
+  m=30 K= 25 kept= 25 precision=0.320 -> expansion acc 0.141 -> after descent 0.125
+  m=30 K= 50 kept= 48 precision=0.229 -> expansion acc 0.215 -> after descent 0.816
+  m=30 K=100 kept= 80 precision=0.188 -> expansion acc 0.148 -> after descent 0.195
+
+E(truth)=0.3396   total wall 617s
diff --git a/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.log b/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.log
new file mode 100644
index 0000000..c2bd82f
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.log
@@ -0,0 +1,34 @@
+
+##### hidden seed 11: 150 ICP sols in 200s, E(truth)=0.3396, best member E=0.6569 acc=0.172
+  ROUTE A (descend 5 lowest-E, blind pick): E=0.5863 acc=0.277
+   m=10 K= 12 prec=0.333 expand=0.102 -> descent acc=0.320 E=0.6184
+   m=10 K= 25 prec=0.333 expand=0.168 -> descent acc=0.324 E=0.6279
+   m=10 K= 50 prec=0.255 expand=0.184 -> descent acc=0.793 E=0.3544
+   m=10 K=100 prec=0.193 expand=0.172 -> descent acc=0.770 E=0.3900
+   m=30 K= 12 prec=0.455 expand=0.211 -> descent acc=0.535 E=0.4867
+   m=30 K= 25 prec=0.292 expand=0.195 -> descent acc=0.754 E=0.4163
+   m=30 K= 50 prec=0.227 expand=0.188 -> descent acc=0.695 E=0.4357
+   m=30 K=100 prec=0.172 expand=0.184 -> descent acc=0.773 E=0.3837
+   m=60 K= 12 prec=0.455 expand=0.086 -> descent acc=0.094 E=0.7738
+   m=60 K= 25 prec=0.375 expand=0.164 -> descent acc=0.133 E=0.6840
+   m=60 K= 50 prec=0.244 expand=0.098 -> descent acc=0.066 E=0.7911
+   m=60 K=100 prec=0.171 expand=0.113 -> descent acc=0.086 E=0.7412
+  ROUTE B (blind pick by energy over the 12 cells): m=10 K=50 E=0.3544 acc=0.793   [best cell by accuracy was 0.793]
+  wall 492s
+
+##### hidden seed 23: 150 ICP sols in 559s, E(truth)=0.3396, best member E=0.3684 acc=0.691
+  ROUTE A (descend 5 lowest-E, blind pick): E=0.3396 acc=0.852
+   m=10 K= 12 prec=0.917 expand=0.703 -> descent acc=0.855 E=0.3396
+   m=10 K= 25 prec=0.680 expand=0.520 -> descent acc=0.758 E=0.3792
+   m=10 K= 50 prec=0.583 expand=0.484 -> descent acc=0.777 E=0.3543
+   m=10 K=100 prec=0.505 expand=0.492 -> descent acc=0.848 E=0.3396
+   m=30 K= 12 prec=0.917 expand=0.656 -> descent acc=0.812 E=0.3466
+   m=30 K= 25 prec=0.920 expand=0.723 -> descent acc=0.809 E=0.3396
+   m=30 K= 50 prec=0.673 expand=0.691 -> descent acc=0.816 E=0.3644
+   m=30 K=100 prec=0.558 expand=0.547 -> descent acc=0.797 E=0.3593
+   m=60 K= 12 prec=0.833 expand=0.504 -> descent acc=0.785 E=0.3468
+   m=60 K= 25 prec=0.792 expand=0.734 -> descent acc=0.820 E=0.3396
+   m=60 K= 50 prec=0.667 expand=0.641 -> descent acc=0.836 E=0.3433
+   m=60 K=100 prec=0.524 expand=0.496 -> descent acc=0.844 E=0.3569
+  ROUTE B (blind pick by energy over the 12 cells): m=30 K=25 E=0.3396 acc=0.809   [best cell by accuracy was 0.855]
+  wall 752s
diff --git a/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.py b/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.py
new file mode 100644
index 0000000..d97d239
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/eval_voteanchor_vs_bestE.py
@@ -0,0 +1,78 @@
+"""Replication with BLIND energy selection over the (m,K) grid, two fresh hidden perms."""
+import sys, time, numpy as np, torch
+sys.path.insert(0, '/home/yurenh2/emm')
+from scipy.optimize import linear_sum_assignment
+from scipy.stats import ortho_group
+from worldalign.synth_fast_gate import fast_pair_descent
+
+dev = 'cuda:0'
+def standardise(M):
+    M = np.asarray(M, dtype=np.float64); m = ~np.eye(len(M), dtype=bool); v = M[m]
+    o = (M - v.mean())/v.std(); np.fill_diagonal(o, 0.0); return o
+d = torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt', map_location='cpu', weights_only=False)
+V = standardise(d['visual_field']); T0 = standardise(d['text_field']); N = len(V)
+Vt = torch.tensor(V, dtype=torch.float32, device=dev)
+wV, UV = np.linalg.eigh(V); wV = wV[::-1]; UV = UV[:, ::-1]
+
+def hung(A, B):
+    C = ((A**2).sum(1)[:, None] + (B**2).sum(1)[None, :] - 2*A@B.T)
+    r, c = linear_sum_assignment(C); return c
+def icp(XV, XT, O, iters=25):
+    for _ in range(iters):
+        p = hung(XV, XT@O); u, s, vt = np.linalg.svd(XT[p].T@XV); On = u@vt
+        if np.allclose(On, O, atol=1e-10): O = On; break
+        O = On
+    return hung(XV, XT@O)
+
+for SEED in (11, 23):
+    rng = np.random.default_rng(SEED); sigma = rng.permutation(N)
+    T = T0[np.ix_(sigma, sigma)]; truth = np.argsort(sigma)
+    acc = lambda p: float((np.asarray(p) == truth).mean())
+    Tt = torch.tensor(T, dtype=torch.float32, device=dev)
+    CONST = float((Tt*Tt).sum() + (Vt*Vt).sum())
+    def energy(p):
+        P = torch.as_tensor(np.asarray(p), dtype=torch.long, device=dev)
+        return (CONST - 2.0*float((Tt[P[:, None], P[None, :]]*Vt).sum()))/(N*(N-1))
+    def descend(p, steps=4000):
+        P = torch.as_tensor(np.ascontiguousarray(p), dtype=torch.long, device=dev)
+        return fast_pair_descent(Tt, Vt, P, steps).cpu().numpy()
+    wT, UT = np.linalg.eigh(T); wT = wT[::-1]; UT = UT[:, ::-1]
+    t0 = time.time(); sols = []
+    for r in (8, 10, 12, 14, 16):
+        XV = UV[:, :r]*np.sqrt(np.abs(wV[:r])); XT = UT[:, :r]*np.sqrt(np.abs(wT[:r]))
+        for _ in range(30):
+            p = icp(XV, XT, ortho_group.rvs(r, random_state=int(rng.integers(1 << 30))))
+            sols.append((energy(p), p, r))
+    sols.sort(key=lambda z: z[0])
+    print(f"\n##### hidden seed {SEED}: {len(sols)} ICP sols in {time.time()-t0:.0f}s, "
+          f"E(truth)={energy(truth):.4f}, best member E={sols[0][0]:.4f} acc={acc(sols[0][1]):.3f}", flush=True)
+    A = [descend(p) for _, p, _ in sols[:5]]
+    bA = min(A, key=energy)
+    print(f"  ROUTE A (descend 5 lowest-E, blind pick): E={energy(bA):.4f} acc={acc(bA):.3f}", flush=True)
+
+    def expand(aL, aR):
+        pr = np.setdiff1d(np.arange(N), aL); prR = np.setdiff1d(np.arange(N), aR)
+        L = V[np.ix_(pr, aL)]; R = T[np.ix_(prR, aR)]
+        L = (L-L.mean(1, keepdims=True))/L.std(1, keepdims=True).clip(1e-9)
+        R = (R-R.mean(1, keepdims=True))/R.std(1, keepdims=True).clip(1e-9)
+        S = L@R.T/L.shape[1]; _, c = linear_sum_assignment(-S)
+        full = np.zeros(N, dtype=int); full[aL] = aR; full[pr] = prR[c]; return full
+    grid = []
+    for m in (10, 30, 60):
+        votes = np.zeros((N, N))
+        for _, p, _ in sols[:m]: votes[np.arange(N), p] += 1
+        conf = votes.max(1) - np.partition(votes, -2, axis=1)[:, -2]
+        order = np.argsort(-conf); pm = votes.argmax(1)
+        for K in (12, 25, 50, 100):
+            sel = order[:K]; part = pm[sel]; keep = np.zeros(len(sel), bool); seen = set()
+            for i, c in enumerate(part):
+                if c not in seen: seen.add(c); keep[i] = True
+            sel, part = sel[keep], part[keep]
+            prec = float((part == truth[sel]).mean())
+            e = expand(sel, part); pd = descend(e)
+            grid.append((energy(pd), acc(pd), m, K, prec, acc(e)))
+            print(f"   m={m:2d} K={K:3d} prec={prec:.3f} expand={acc(e):.3f} -> descent acc={acc(pd):.3f} E={energy(pd):.4f}", flush=True)
+    grid.sort()
+    print(f"  ROUTE B (blind pick by energy over the 12 cells): m={grid[0][2]} K={grid[0][3]} "
+          f"E={grid[0][0]:.4f} acc={grid[0][1]:.3f}   [best cell by accuracy was {max(g[1] for g in grid):.3f}]", flush=True)
+    print(f"  wall {time.time()-t0:.0f}s", flush=True)
diff --git a/artifacts/spectral_frontier_probe/nmf_adv_oracle.log b/artifacts/spectral_frontier_probe/nmf_adv_oracle.log
new file mode 100644
index 0000000..8176ba3
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_oracle.log
@@ -0,0 +1,26 @@
+E(truth) = 0.339635
+REF: GRAMPA on raw fields -> raw 0.0039 refined 0.0117 E=0.8380
+REF: field correlation (aligned) = 0.8302
+
+=== r=24  [6.2s]  resid V 0.0400  T 0.0331  V(seed2) 0.0447
+  [uniqueness] symNMF(V,seed1) vs symNMF(V,seed2) matched cos: median 0.885  >0.9 10/24  >0.5 24/24  min 0.541
+  [oracle cols] cos: >0.9 10/24  >0.5 23/24  median 0.842  min 0.427
+                sorted: [0.98 0.98 0.97 0.96 0.95 0.94 0.94 0.92 0.91 0.91 0.88 0.86 0.82 0.8
+ 0.79 0.69 0.68 0.68 0.68 0.68 0.68 0.63 0.55 0.43]
+                identity-map fraction (shared-seed artifact check): 0.083
+  [oracle-col row descriptors] Hungarian acc 0.6719 -> descent 0.8320
+  [prune thr=0.5] kept 23/24  rho(cleanV,T)=0.8466 (was 0.8302)  GRAMPA 0.0078 -> clean-descent 0.0547 -> true-descent 0.0547  E=0.6471
+  [prune thr=0.7] kept 15/24  rho(cleanV,T)=0.7684 (was 0.8302)  GRAMPA 0.0039 -> clean-descent 0.0391 -> true-descent 0.0391  E=0.6817
+  [prune thr=0.8] kept 13/24  rho(cleanV,T)=0.7804 (was 0.8302)  GRAMPA 0.0000 -> clean-descent 0.0000 -> true-descent 0.0000  E=0.7292
+
+=== r=42  [32.2s]  resid V 0.0241  T 0.0141  V(seed2) 0.0231
+  [uniqueness] symNMF(V,seed1) vs symNMF(V,seed2) matched cos: median 0.832  >0.9 12/42  >0.5 42/42  min 0.541
+  [oracle cols] cos: >0.9 4/42  >0.5 41/42  median 0.766  min 0.416
+                sorted: [0.97 0.94 0.93 0.9  0.89 0.88 0.88 0.87 0.86 0.86 0.86 0.84 0.84 0.84
+ 0.82 0.81 0.81 0.8  0.79 0.78 0.77 0.76 0.76 0.76 0.75 0.75 0.75 0.74
+ 0.74 0.73 0.72 0.72 0.72 0.71 0.7  0.7  0.69 0.66 0.65 0.63 0.62 0.42]
+                identity-map fraction (shared-seed artifact check): 0.000
+  [oracle-col row descriptors] Hungarian acc 0.8125 -> descent 0.8828
+  [prune thr=0.5] kept 41/42  rho(cleanV,T)=0.8337 (was 0.8302)  GRAMPA 0.0273 -> clean-descent 0.0547 -> true-descent 0.0430  E=0.6804
+  [prune thr=0.7] kept 35/42  rho(cleanV,T)=0.7976 (was 0.8302)  GRAMPA 0.0391 -> clean-descent 0.0625 -> true-descent 0.0859  E=0.6966
+  [prune thr=0.8] kept 17/42  rho(cleanV,T)=0.6036 (was 0.8302)  GRAMPA 0.0000 -> clean-descent 0.0039 -> true-descent 0.0078  E=0.6982
diff --git a/artifacts/spectral_frontier_probe/nmf_adv_oracle.py b/artifacts/spectral_frontier_probe/nmf_adv_oracle.py
new file mode 100644
index 0000000..2702e29
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_oracle.py
@@ -0,0 +1,133 @@
+"""Decisive ORACLE test of the symNMF de-rotation / component-pruning candidate.
+
+If the ORACLE version (perfect column match, perfect pruning) does not beat the
+current blind state of the art (~0.83 on omit-size), the candidate is dead.
+"""
+import numpy as np, torch, time, warnings
+warnings.filterwarnings('ignore')
+from scipy.optimize import linear_sum_assignment
+
+dev = torch.device('cuda:0')
+DT = torch.float64
+
+d = torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt', map_location='cpu')
+V0 = d['visual_field'].double().numpy(); T0 = d['text_field'].double().numpy(); N = len(V0)
+rng = np.random.default_rng(777); sigma = rng.permutation(N)
+T0s = T0[np.ix_(sigma, sigma)]; truth = np.argsort(sigma)
+acc = lambda p: float((p == truth).mean())
+
+
+def standardise(M):
+    M = np.asarray(M, float); mask = ~np.eye(len(M), dtype=bool); v = M[mask]
+    out = (M - v.mean()) / v.std(); np.fill_diagonal(out, 0.0); return out
+
+
+def hung(A, B):
+    C = ((A**2).sum(1)[:, None] + (B**2).sum(1)[None, :] - 2 * A @ B.T)
+    r, c = linear_sum_assignment(C); return c
+
+
+def sym_nmf_gpu(M, r, iters=3000, seed=0):
+    Mg = torch.tensor(np.clip(M, 0, None), device=dev, dtype=DT)
+    g = torch.Generator(device='cpu').manual_seed(seed)
+    W = torch.abs(torch.randn(len(M), r, generator=g, dtype=DT)).to(dev) * float(np.sqrt(M.mean() / r))
+    for _ in range(iters):
+        W = W * (0.5 + 0.5 * (Mg @ W) / (W @ (W.T @ W) + 1e-12))
+    return W.cpu().numpy()
+
+
+# ---- energy + exact steepest descent (closed-form swap table) ----
+Vs = standardise(V0); Ts = standardise(T0s)
+CONST = float((Vs * Vs).sum() + (Ts * Ts).sum()); DEN = N * (N - 1)
+Ag = torch.tensor(Vs, device=dev, dtype=DT); Tg = torch.tensor(Ts, device=dev, dtype=DT)
+
+
+def energy(p):
+    return (CONST - 2.0 * float((Ts[np.ix_(p, p)] * Vs).sum())) / DEN
+
+
+def descend(p0, max_steps=4000, A=None, B=None):
+    A = Ag if A is None else A
+    Bfull = Tg if B is None else B
+    p = torch.tensor(np.asarray(p0), device=dev, dtype=torch.long)
+    iu = torch.triu_indices(N, N, offset=1, device=dev)
+    for _ in range(max_steps):
+        B = Bfull[p][:, p]
+        C = A @ B
+        dg = torch.diagonal(C)
+        G = C + C.T - dg[:, None] - dg[None, :] + 2 * A * B
+        vals = G[iu[0], iu[1]]
+        k = int(vals.argmax())
+        if float(vals[k]) <= 1e-12:
+            break
+        u, v = int(iu[0][k]), int(iu[1][k])
+        p[u], p[v] = p[v].clone(), p[u].clone()
+    return p.cpu().numpy()
+
+
+def grampa(Vm, Tm, eta=0.2):
+    lam, u = np.linalg.eigh(Vm); mu, v = np.linalg.eigh(Tm)
+    ones = np.ones(len(Vm)); left = u.T @ ones; right = v.T @ ones
+    w = np.outer(left, right) / ((lam[:, None] - mu[None, :]) ** 2 + eta**2)
+    s = u @ w @ v.T
+    r, c = linear_sum_assignment(-s); return c
+
+
+print(f"E(truth) = {energy(truth):.6f}")
+print("REF: GRAMPA on raw fields ->", end=" ")
+p = grampa(Vs, Ts); pd = descend(p)
+print(f"raw {acc(p):.4f} refined {acc(pd):.4f} E={energy(pd):.4f}")
+rho_raw = np.corrcoef(Vs[~np.eye(N, dtype=bool)], Ts[np.ix_(truth, truth)][~np.eye(N, dtype=bool)])[0, 1]
+print(f"REF: field correlation (aligned) = {rho_raw:.4f}")
+
+for r in (24, 42):
+    t0 = time.time()
+    WV = sym_nmf_gpu(V0, r, seed=1)
+    WT = sym_nmf_gpu(T0s, r, seed=1)
+    WV2 = sym_nmf_gpu(V0, r, seed=2)           # stability check: same matrix, new seed
+    print(f"\n=== r={r}  [{time.time()-t0:.1f}s]  resid V {np.linalg.norm(V0-WV@WV.T)/np.linalg.norm(V0):.4f}"
+          f"  T {np.linalg.norm(T0s-WT@WT.T)/np.linalg.norm(T0s):.4f}"
+          f"  V(seed2) {np.linalg.norm(V0-WV2@WV2.T)/np.linalg.norm(V0):.4f}")
+
+    nrm = lambda X: X / (np.linalg.norm(X, axis=0, keepdims=True) + 1e-12)
+    An, Bn, A2n = nrm(WV), nrm(WT), nrm(WV2)
+
+    # (i) UNIQUENESS: same matrix, two seeds
+    S = An.T @ A2n; rr, cc = linear_sum_assignment(-S)
+    cs = np.sort(S[rr, cc])[::-1]
+    print(f"  [uniqueness] symNMF(V,seed1) vs symNMF(V,seed2) matched cos: "
+          f"median {np.median(cs):.3f}  >0.9 {(cs>0.9).sum()}/{r}  >0.5 {(cs>0.5).sum()}/{r}  min {cs.min():.3f}")
+
+    # (ii) ORACLE cross-modal column match -- full distribution
+    Sx = An.T @ Bn[truth]; rr, cc = linear_sum_assignment(-Sx)
+    ocs = Sx[rr, cc]; colmap = cc[np.argsort(rr)]
+    srt = np.sort(ocs)[::-1]
+    print(f"  [oracle cols] cos: >0.9 {(ocs>0.9).sum()}/{r}  >0.5 {(ocs>0.5).sum()}/{r}"
+          f"  median {np.median(ocs):.3f}  min {ocs.min():.3f}")
+    print(f"                sorted: {np.round(srt,2)}")
+    print(f"                identity-map fraction (shared-seed artifact check): {(colmap==np.arange(r)).mean():.3f}")
+
+    # (iii) row descriptors from oracle-matched columns
+    Ar = WV / np.linalg.norm(WV, axis=1, keepdims=True).clip(1e-9)
+    Br = WT[:, colmap] / np.linalg.norm(WT[:, colmap], axis=1, keepdims=True).clip(1e-9)
+    p_desc = hung(Ar, Br)
+    print(f"  [oracle-col row descriptors] Hungarian acc {acc(p_desc):.4f} -> descent {acc(descend(p_desc)):.4f}")
+
+    # (iv) THE PROPOSAL, ORACLE FORM: prune unmatched V components, rebuild, re-solve
+    for thr in (0.5, 0.7, 0.8):
+        keep = np.where(ocs >= thr)[0]
+        kv = rr[np.isin(np.arange(r), np.arange(r))]  # rr is identity-ordered by lsa
+        keepV = rr[ocs >= thr]
+        if len(keepV) < 4:
+            print(f"  [prune thr={thr}] only {len(keepV)} kept, skip"); continue
+        Vc = WV[:, keepV] @ WV[:, keepV].T
+        Vcs = standardise(Vc)
+        rho = np.corrcoef(Vcs[~np.eye(N, dtype=bool)], Ts[np.ix_(truth, truth)][~np.eye(N, dtype=bool)])[0, 1]
+        # solve on the cleaned vision field against the original text field
+        pg = grampa(Vcs, Ts)
+        Acg = torch.tensor(Vcs, device=dev, dtype=DT)
+        pgd = descend(pg, A=Acg)          # descent on the CLEANED objective
+        pgd_true = descend(pgd)           # then polish on the TRUE objective
+        print(f"  [prune thr={thr}] kept {len(keepV)}/{r}  rho(cleanV,T)={rho:.4f} (was {rho_raw:.4f})"
+              f"  GRAMPA {acc(pg):.4f} -> clean-descent {acc(pgd):.4f} -> true-descent {acc(pgd_true):.4f}"
+              f"  E={energy(pgd_true):.4f}")
diff --git a/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log
new file mode 100644
index 0000000..347318c
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log
@@ -0,0 +1,21 @@
+--- symNMF seed 1, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.0312 -> clean-desc 0.0391 -> true-desc 0.0391  E=0.6405
+  B. ORACLE prune worst 1 (thr .5)               GW 0.8594 -> clean-desc 0.8594 -> true-desc 0.8672  E=0.3396
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.8359 -> clean-desc 0.8281 -> true-desc 0.8359  E=0.3396
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.0469 -> clean-desc 0.0430 -> true-desc 0.0469  E=0.6486
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0195 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.6661
+  D. both sides symNMF-reconstructed (blind)     GW 0.0234 -> clean-desc 0.0234 -> true-desc 0.0234  E=0.6020
+--- symNMF seed 2, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.0156 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.6419
+  B. ORACLE prune worst 4 (thr .5)               GW 0.8203 -> clean-desc 0.8125 -> true-desc 0.8203  E=0.3396
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.0078 -> clean-desc 0.0078 -> true-desc 0.0078  E=0.6720
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.0195 -> clean-desc 0.0195 -> true-desc 0.0195  E=0.7034
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0039 -> clean-desc 0.0039 -> true-desc 0.0039  E=0.6649
+  D. both sides symNMF-reconstructed (blind)     GW 0.0156 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.7342
+--- symNMF seed 3, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.1328 -> clean-desc 0.1523 -> true-desc 0.1641  E=0.5919
+  B. ORACLE prune worst 2 (thr .5)               GW 0.0000 -> clean-desc 0.0000 -> true-desc 0.0000  E=0.6669
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.1211 -> clean-desc 0.1172 -> true-desc 0.1211  E=0.5922
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.8125 -> clean-desc 0.8203 -> true-desc 0.8203  E=0.3396
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0078 -> clean-desc 0.0117 -> true-desc 0.0117  E=0.6752
+  D. both sides symNMF-reconstructed (blind)     GW 0.8398 -> clean-desc 0.8477 -> true-desc 0.8477  E=0.3396
diff --git a/artifacts/spectral_frontier_probe/nmf_adv_prune_control.py b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.py
new file mode 100644
index 0000000..a3b23ef
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.py
@@ -0,0 +1,61 @@
+"""CONTROL: is the 0.86 from PRUNING (needs oracle) or from symNMF RECONSTRUCTION alone (blind)?"""
+import numpy as np, torch, warnings, ot
+warnings.filterwarnings('ignore')
+from scipy.optimize import linear_sum_assignment
+dev = torch.device('cuda:0'); DT = torch.float64
+d = torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt', map_location='cpu')
+V0 = d['visual_field'].double().numpy(); T0 = d['text_field'].double().numpy(); N = len(V0)
+rng = np.random.default_rng(777); sigma = rng.permutation(N)
+T0s = T0[np.ix_(sigma, sigma)]; truth = np.argsort(sigma)
+acc = lambda p: float((p == truth).mean())
+def standardise(M):
+    M = np.asarray(M, float); mask = ~np.eye(len(M), dtype=bool); v = M[mask]
+    out = (M - v.mean()) / v.std(); np.fill_diagonal(out, 0.0); return out
+def sym_nmf_gpu(M, r, iters=3000, seed=0):
+    Mg = torch.tensor(np.clip(M, 0, None), device=dev, dtype=DT)
+    g = torch.Generator(device='cpu').manual_seed(seed)
+    W = torch.abs(torch.randn(len(M), r, generator=g, dtype=DT)).to(dev) * float(np.sqrt(M.mean()/r))
+    for _ in range(iters):
+        W = W * (0.5 + 0.5 * (Mg @ W) / (W @ (W.T @ W) + 1e-12))
+    return W.cpu().numpy()
+Vs = standardise(V0); Ts = standardise(T0s)
+CONST = float((Vs*Vs).sum() + (Ts*Ts).sum()); DEN = N*(N-1)
+Ag = torch.tensor(Vs, device=dev, dtype=DT); Tg = torch.tensor(Ts, device=dev, dtype=DT)
+energy = lambda p: (CONST - 2.0*float((Ts[np.ix_(p, p)]*Vs).sum()))/DEN
+def descend(p0, A=None, max_steps=4000):
+    A = Ag if A is None else A
+    p = torch.tensor(np.asarray(p0), device=dev, dtype=torch.long)
+    iu = torch.triu_indices(N, N, offset=1, device=dev)
+    for _ in range(max_steps):
+        B = Tg[p][:, p]; C = A @ B; dg = torch.diagonal(C)
+        G = C + C.T - dg[:, None] - dg[None, :] + 2*A*B
+        vals = G[iu[0], iu[1]]; k = int(vals.argmax())
+        if float(vals[k]) <= 1e-12: break
+        u, v = int(iu[0][k]), int(iu[1][k]); p[u], p[v] = p[v].clone(), p[u].clone()
+    return p.cpu().numpy()
+def gw(A, B):
+    q = np.ones(N)/N
+    G, _ = ot.gromov.gromov_wasserstein(A, B, q, q, 'square_loss', log=True, max_iter=200)
+    _, c = linear_sum_assignment(-G); return c
+def run(tag, Vm, Tm=Ts):
+    p = gw(Vm, Tm); pd = descend(p, A=torch.tensor(Vm, device=dev, dtype=DT)); pd2 = descend(pd)
+    print(f"  {tag:46s} GW {acc(p):.4f} -> clean-desc {acc(pd):.4f} -> true-desc {acc(pd2):.4f}  E={energy(pd2):.4f}", flush=True)
+    return acc(pd2)
+
+r = 42
+for seed in (1, 2, 3):
+    print(f"--- symNMF seed {seed}, r={r}")
+    WV = sym_nmf_gpu(V0, r, seed=seed); WT = sym_nmf_gpu(T0s, r, seed=seed)
+    nrm = lambda X: X/(np.linalg.norm(X, axis=0, keepdims=True)+1e-12)
+    Sx = nrm(WV).T @ nrm(WT)[truth]; rr, cc = linear_sum_assignment(-Sx); ocs = Sx[rr, cc]
+    worst = rr[int(np.argmin(ocs))]
+    Vrec = standardise(WV @ WV.T)                                  # BLIND: no pruning at all
+    run("A. symNMF reconstruction, NO pruning (blind)", Vrec)
+    keepV = rr[ocs >= 0.5]
+    run(f"B. ORACLE prune worst {r-len(keepV)} (thr .5)", standardise(WV[:, keepV] @ WV[:, keepV].T))
+    for t in range(3):                                              # BLIND: drop a random column
+        j = np.random.default_rng(100+t).integers(r)
+        kk = np.setdiff1d(np.arange(r), [j])
+        run(f"C{t}. RANDOM single-column drop (col {j}, blind)", standardise(WV[:, kk] @ WV[:, kk].T))
+    # also: text side reconstructed the same way (symmetric treatment)
+    run("D. both sides symNMF-reconstructed (blind)", Vrec, standardise(WT @ WT.T))
diff --git a/artifacts/spectral_frontier_probe/nmf_adv_prune_gw.py b/artifacts/spectral_frontier_probe/nmf_adv_prune_gw.py
new file mode 100644
index 0000000..2ecdfed
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_prune_gw.py
@@ -0,0 +1,50 @@
+"""Second solver on the ORACLE-pruned field, so the refutation is not GRAMPA-specific."""
+import numpy as np, torch, warnings, ot
+warnings.filterwarnings('ignore')
+from scipy.optimize import linear_sum_assignment
+dev = torch.device('cuda:0'); DT = torch.float64
+d = torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt', map_location='cpu')
+V0 = d['visual_field'].double().numpy(); T0 = d['text_field'].double().numpy(); N = len(V0)
+rng = np.random.default_rng(777); sigma = rng.permutation(N)
+T0s = T0[np.ix_(sigma, sigma)]; truth = np.argsort(sigma)
+acc = lambda p: float((p == truth).mean())
+def standardise(M):
+    M = np.asarray(M, float); mask = ~np.eye(len(M), dtype=bool); v = M[mask]
+    out = (M - v.mean()) / v.std(); np.fill_diagonal(out, 0.0); return out
+def sym_nmf_gpu(M, r, iters=3000, seed=0):
+    Mg = torch.tensor(np.clip(M, 0, None), device=dev, dtype=DT)
+    g = torch.Generator(device='cpu').manual_seed(seed)
+    W = torch.abs(torch.randn(len(M), r, generator=g, dtype=DT)).to(dev) * float(np.sqrt(M.mean() / r))
+    for _ in range(iters):
+        W = W * (0.5 + 0.5 * (Mg @ W) / (W @ (W.T @ W) + 1e-12))
+    return W.cpu().numpy()
+Vs = standardise(V0); Ts = standardise(T0s)
+CONST = float((Vs*Vs).sum() + (Ts*Ts).sum()); DEN = N*(N-1)
+Ag = torch.tensor(Vs, device=dev, dtype=DT); Tg = torch.tensor(Ts, device=dev, dtype=DT)
+energy = lambda p: (CONST - 2.0*float((Ts[np.ix_(p, p)]*Vs).sum()))/DEN
+def descend(p0, A=None, max_steps=4000):
+    A = Ag if A is None else A
+    p = torch.tensor(np.asarray(p0), device=dev, dtype=torch.long)
+    iu = torch.triu_indices(N, N, offset=1, device=dev)
+    for _ in range(max_steps):
+        B = Tg[p][:, p]; C = A @ B; dg = torch.diagonal(C)
+        G = C + C.T - dg[:, None] - dg[None, :] + 2*A*B
+        vals = G[iu[0], iu[1]]; k = int(vals.argmax())
+        if float(vals[k]) <= 1e-12: break
+        u, v = int(iu[0][k]), int(iu[1][k]); p[u], p[v] = p[v].clone(), p[u].clone()
+    return p.cpu().numpy()
+def gw(A, B, seed=0):
+    q = np.ones(N)/N
+    G, _ = ot.gromov.gromov_wasserstein(A, B, q, q, 'square_loss', log=True, max_iter=200)
+    r_, c_ = linear_sum_assignment(-G); return c_
+r = 42
+WV = sym_nmf_gpu(V0, r, seed=1); WT = sym_nmf_gpu(T0s, r, seed=1)
+nrm = lambda X: X/(np.linalg.norm(X, axis=0, keepdims=True)+1e-12)
+Sx = nrm(WV).T @ nrm(WT)[truth]; rr, cc = linear_sum_assignment(-Sx); ocs = Sx[rr, cc]
+print("baseline GW on raw:", end=" ")
+p = gw(Vs, Ts); pd = descend(p); print(f"raw {acc(p):.4f} refined {acc(pd):.4f} E={energy(pd):.4f}")
+for thr in (0.5, 0.65, 0.75):
+    keepV = rr[ocs >= thr]
+    Vc = standardise(WV[:, keepV] @ WV[:, keepV].T)
+    p = gw(Vc, Ts); pd = descend(p, A=torch.tensor(Vc, device=dev, dtype=DT)); pd2 = descend(pd)
+    print(f"prune thr={thr} kept {len(keepV)}/{r}: GW raw {acc(p):.4f} -> clean-desc {acc(pd):.4f} -> true-desc {acc(pd2):.4f} E={energy(pd2):.4f}")