halting probe: output-stable orbit, not state fixed point; no free ACT at state level; paper claims softened

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

results-loop/PROTOCOL_UNIFIED.md

@@ -230,3 +230,17 @@ training depth) and no capability; map-sharing is load-bearing for the
 anytime-usable gain. Depth-4 adapter overfit visible in val (hard k4 CE
 0.188@99 -> 0.371@599) — LTV concentrates small-pool overfitting into
 single depths.
+
+--- Outcome, item 13b (scored 2026-07-15): accuracy prediction CONFIRMED
+(k=8 halt run 52.0/90.2/42.9 = plateau level); convergence predictions
+REFUTED. Per-item state-cosine (thresh 0.9995, k=8 cap): k_conv
+distribution 4:3, 5:57, 6:47, 7:17, never-within-8:126 — mean ~7, and NO
+difficulty gradient (easy 7.01 vs hard 7.00). The earlier "bit-exact by
+k~3-4" was the single dynamics-probe example, not the population: outputs
+plateau by k~2-4 while the state keeps drifting at 1e-3..1e-4 cosine
+scale; the fixed point is an OUTPUT-stable orbit (suffix layers + decode
+wash out residual state motion), not a literal state fixed point for most
+prompts. Free-ACT via state-cosine therefore yields no early exit at this
+threshold, and no ACT-like difficulty allocation falls out for free —
+output-level halting signals would be needed. Paper's dynamics claims
+softened accordingly.