PerDepthAdapter (Bae-style per-iteration merges) + convergence-halting probe (free ACT); pre-registration item 13

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

results-loop/PROTOCOL_UNIFIED.md

@@ -133,3 +133,19 @@ number for the unified adapter exists at time of writing.
     stability is where genuine iteration must live. Either outcome
     formalizes "the anchor coefficient is the stability dial" as
     "the anchor coefficient is the spectral radius".
+
+13. **Per-depth adapter arm + free-ACT probe (pre-registered 2026-07-15,
+    before training).** (a) PerDepthAdapter: one merge adapter per
+    iteration (n=4, Bae-style depth-wise relaxation at the entrance;
+    breaks time-invariance — LTV, no fixed-point guarantee), standard
+    curriculum, e400, eval ks 0,2,4,8. Prediction: lands at or below the
+    distill/rung-2 amortization ceiling (~46% hard) because depth-indexed
+    weights add content, not state-evolution; exceeding it would show
+    per-iteration expressivity was binding and amend the deflationary
+    claim. Depths >4 reuse adapter 4 (stated: k=8 cell is then
+    fixed-point-like by construction). (b) Free-ACT probe on the standard
+    merge arm: record per-item convergence depth (cos>0.9995) at k=8 cap.
+    Predictions: accuracy unchanged vs fixed k (post-convergence no-ops);
+    mean k_conv ≈ 3; hard-labeled items converge SLOWER than easy ones
+    (adaptive compute allocates like ACT without any learned halting
+    parameter).