estimator forensics closed: cos ceiling = adjoint TRUNCATION + SEMI-CONVERGENCE (not r, not anchor, not transients)

Refutation chain: r-sweep flat (0.02-0.4); deep anchor (res 100x tighter) no
gain; kappa brake monotonically harmful. t2sel window sweep at s2000:
40->80 lifts ALL batches (mean 0.889->0.936, truncation confirmed); past 80
SEMI-CONVERGENT (batch-dependent optimum; the inc-argmin t_best rule fails on
rotating slow modes -> batch2 degrades 0.956->0.875 at 320). Early stopping
IS the regularizer; iteration count = reg parameter.

Shipping insight: holofast + sdpa + t2sel80 ~= old default wall-clock with
cos 0.89->0.94. warm_fast (record) already ran t2sel=80 vs proven-scratch 40
— a real +0.05-cos hidden difference in the lineage table.
Next lever: trend-aware stopping / t_best-neighborhood averaging.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 26 insertions, 0 deletions

diff --git a/ep_run/t2_probe.py b/ep_run/t2_probe.py
new file mode 100644
index 0000000..9463ba0
--- /dev/null
+++ b/ep_run/t2_probe.py
@@ -0,0 +1,26 @@
+"""Adjoint-truncation hypothesis: the cos(EP,BPTT) ceiling at near-edge operators is the finite-T2
+window (adjoint needs ~1/|Re mu| ~ 50-500 steps there; deep-contraction ops converge fast -> 0.98).
+Sweep the tracking window t2sel in {40, 80, 160, 320} at s2000, everything else fixed (bsub=4, T1=150,
+3 batches). Prediction: cos climbs with window; the climb rate quantifies the truncation bias that the
+2.40-plateau memory called the 'estimator bias-floor'."""
+import torch
+import lt_ep_train as L
+from diag_cos import cos_ep_bptt
+
+torch.manual_seed(0)
+blk = L.EQBlock(512, 16, 256, 256, c=1.0, attn_mode='thick'); blk.qknorm = True
+ck = torch.load('runs/redx_traj/s2000.pt', map_location=L.dev)
+with torch.no_grad():
+    for p, w in zip(blk.allp, ck['allp']):
+        p.copy_(w.to(L.dev))
+blk.track = True
+torch.manual_seed(11)
+batches = [L.get_batch('train', 24, 256) for _ in range(3)]
+
+for w in (40, 80, 160, 320):
+    cs = []
+    for idx, y in batches:
+        c, _ = cos_ep_bptt(blk, idx, y, 150, 20, 0.1, 0.02, holo=2, hr=0.02, t2sel=w, bsub=4)
+        cs.append(c)
+    print(f"t2sel={w:<4} cos={' '.join(f'{c:.4f}' for c in cs)}  mean={sum(cs)/len(cs):.4f}", flush=True)
+print("T2_PROBE_DONE", flush=True)