FINDINGS: K3 sealed — matched-tuning parity n=3 (EP 2.0500+-0.015 vs BP 2.0530+-0.004), the three-act retraction arc documented

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

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diff --git a/docs/campaign/FINDINGS.md b/docs/campaign/FINDINGS.md
index d3da6bb..4b78f78 100644
--- a/docs/campaign/FINDINGS.md
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@@ -737,3 +737,26 @@ docs/campaign/CASCADE_ABLATION_PLAN.md. Scripts: cascade_probe.py (schemes incl.
 casc_eq_train.py (v5: adaptive β via σ̂_tok, quality-governed K, cos telemetry). Negative results
 recorded: govfloor rr_floor 2/3 lethal at C512 (free phase must stay resreg-free); governor
 certification needs a ρ>0.95 lower bound (certified a ρ=0.80 corpse).
+
+## 2026-07-11 — K3 SEALED: matched-tuning PARITY (n=3), and the honest arc that got there
+
+**Final table (C256 L6 T256, TinyStories, 4k steps, both at tuned lr 1e-3, tok_init 0.02):**
+- equilibrium fb-EP EXACT mode (dtop_every=1, fixed β 0.003): 2.0481 / 2.0687 / 2.0331 → **2.0500 ± 0.015**
+- BP: 2.0503 / 2.0580 / 2.0506 → **2.0530 ± 0.004**
+- ⟹ **statistically indistinguishable. "Standard transformer, no backprop, equilibrium-EP training
+  = BP quality at matched tuning."** cos(EP,BP) telemetry ≥0.9998 throughout all arms.
+
+**The three-act arc (all pre-registered readouts, no post-hoc stories):**
+1. "EP beats BP by 0.074" (first C1) → KILLED by BP lr-sweep (BP@1e-3 → 2.0855; both had sat at
+   BP-suboptimal 3e-4). β-sweep showed NO β-growing dividend ⟹ prospective-configuration
+   regularization hypothesis not supported (β sweet zone 0.003–0.03; 0.1 breaks fb, 0.001 amplifies
+   /β noise).
+2. "EP pays a ~4% tax" (3-seed matrix, v7 fast mode: 2.144 vs 2.053) → KILLED by the bisection arm:
+   the tax was ENTIRELY the v7 dedups (stale d_top at high lr). Exact mode restored parity.
+3. Parity, n=3, sealed. Fast mode retained as a documented ~20%-compute/−4%-CE dial (exact = default).
+
+**Cost ledger (1080, C256 L6):** BP 8.8 it/s; EP exact ≈ 2.3–2.5 it/s (~3.6× BP); fast mode 2.68 it/s
+(3.28×). Optimization headroom (compile on A-cards, ±-phase batching, bf16-relax pending A0.4) mapped.
+
+**Next: D-tier** — L12×C512 (~45M standard GPT-small) EP-vs-BP flagship + Muon arm (OmniOpt sweet
+spot 60–350M; Muon = digital-side, free on GPU, EP-interaction unmeasured).