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@@ -721,8 +721,14 @@ nudge +β·CE at the top, relax states to the nudged equilibrium, ∇θ = local
**Result (diagC, tied + 0.02 init, equilibrium fb-EP, NO regularizers, NO guards triggered):
best val CE 2.9021 in 1500 steps, cos(EP,BP) pinned at 1.0000 throughout, K=3 never raised** —
-already below the bad-init BP twin's 4000-step 2.9746. Final same-init C1 pair (casc_bp6i vs
-casc_eqv5, 4k steps) running.
+already below the bad-init BP twin's 4000-step 2.9746.
+
+**FINAL C1 VERDICT (same-init pair, 4k steps, seed 0): equilibrium fb-EP 2.2949 vs BP 2.3694 —
+EP BEATS BP by 0.074** (cos pinned 1.0000 the whole run, zero skips, K=3 never raised, wall-clock
+3.9× BP: 2.23 vs 8.79 it/s on the same 1080). K1 (exactness-on-trajectory), K2 (GPU cost), and K3
+(training parity, exceeded) are all bought. Same EP>BP flavor as the looped-EP 1.7065-vs-1.7921
+flagship — second independent instance of the pattern. Remaining: K4 depth rungs (L12 C512, D-tier)
+and K5 analog tolerances (E-tier).
**Costs & implications:** equilibrium-mode ≈ 4× BP (fb K3 single-sided) ⟹ $20k AWS ≈ 3–4B-param
Chinchilla run in TRUE-EP mode. Optimization headroom mapped (±phase batching, red-black grouped