E1c: k*=0 routing + pre-loop halt target (item 19 scored, E1c pre-registered)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

scripts/halting_common.py

@@ -78,17 +78,26 @@ def halting_loop_logits(looper, adapter, input_ids, k_max, attention_mask,
 
 @torch.no_grad()
 def halted_k_per_item(looper, adapter, input_ids, k_max, attention_mask,
-                      prompt_last_idx, thresh=0.5):
+                      prompt_last_idx, thresh=0.5, allow_k0=True):
     """Deploy-time halting: smallest k where cumulative halt mass >= thresh
-    (k_max if never). Returns (B,) ints in 1..k_max."""
+    (k_max if never). With allow_k0, the head is also consulted on the
+    pre-loop state s_0 — items it flags there get k*=0 (no looping at
+    all; the E0 lesson: easy items are safest untouched).
+    Returns (B,) ints in 0..k_max."""
     calls, _ = looper.capture(input_ids, attention_mask, logits_to_keep=1)
     e = looper._hin[looper.l0].detach()
     B = e.shape[0]
     bidx = torch.arange(B, device=e.device)
     s = looper.band(e, calls)
-    keep = torch.ones(B, device=e.device)
-    cum = torch.zeros(B, device=e.device)
     kstar = torch.full((B,), k_max, dtype=torch.long, device=e.device)
+    cum = torch.zeros(B, device=e.device)
+    keep = torch.ones(B, device=e.device)
+    if allow_k0:
+        p0 = adapter.halt_prob(e[bidx, prompt_last_idx],
+                               s[bidx, prompt_last_idx])
+        kstar[p0 >= thresh] = 0
+        cum = cum + p0
+        keep = keep * (1 - p0)
     for i in range(k_max):
         x = adapter(e, s)
         s = looper.band(x, calls)