K refuted as L12 lever (cos K-invariant K3==K8); BP 3-seed sealed 1.919; mechanism = finite-beta SNR collapse; add --beta_floor/--beta_fixed + launch floor sweep

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

2 files changed, 21 insertions, 0 deletions

diff --git a/docs/campaign/CASCADE_ABLATION_PLAN.md b/docs/campaign/CASCADE_ABLATION_PLAN.md
index 34d16d5..76cf71d 100644
--- a/docs/campaign/CASCADE_ABLATION_PLAN.md
+++ b/docs/campaign/CASCADE_ABLATION_PLAN.md
@@ -59,6 +59,23 @@ under-convergence, fix = scale K with depth, then relaunch full 3-seed at min-su
 verdict. If K8 does NOT close it -> genuine estimator depth-tax; next arm = beta-floor (needs a code
 flag) and/or lambda_l per-layer energy weighting (B4). Follow-on (not yet launched): Muon-on-EP arm.
 
+### RESULT 1 (2026-07-10 00:40): K REFUTED as the lever; BP 3-seed sealed.
+- BP 3-seed reference SEALED: 1.9169 / 1.9194 / 1.9214 = **1.9192 +/- 0.0019** (L12 C512 H8).
+- **cos is K-INVARIANT.** K3 and K8 track to 4 decimals through step 1200 (both 1.0->0.9997->0.9991)
+  AND give identical val CE at every matched step (900: 2.545 vs 2.548; 1100: 2.399 vs 2.404).
+  More relaxation rounds do NOTHING -> the cos erosion is NOT fb under-convergence. K8 killed (redundant).
+- **Real mechanism = finite-beta SNR collapse.** beta_t = beta0*bscale*(SIG0/sig)^2 collapses ~120x
+  (3e-3 -> 2.5e-5) as sig_tok grows 1.6->17.8. The estimator computes E/(NBT*beta_t) from residuals
+  (z-o) that are O(beta_t*sig) ~ 4e-4 obtained by subtracting two O(17) states -> catastrophic
+  cancellation as beta shrinks AND sig grows. Both worsen with depth. cos erodes 1.0 -> 0.997 (@2000)
+  -> 0.98 (@2800 in the dead run). This is a beta-SCHEDULE problem, not a relaxation-depth problem.
+- **Fix under test:** added `--beta_floor` / `--beta_fixed` flags. Launched paired arms seed 1
+  (control = K3 floor=0, still running): `d1b_ep_bf1e4_s1` (floor 1e-4), `d1b_ep_bf3e4_s1` (floor 3e-4).
+  Decision rule: if floored cos stays high through step 2000-2800 and CE drops toward BP 1.919 ->
+  beta-floor is the depth fix; pick min-sufficient floor, run 3-seed K4 verdict. Watch drift guard at
+  the higher floor (larger nudge). If floors DON'T help -> escalate to double-sided estimator (cancels
+  O(beta) Taylor bias, allows large beta, 2x cost) or lambda_l energy weighting.
+
 ## STATUS 2026-07-09 (same day): Tier 0 CLOSED GREEN via the zil scheme; C1 running
 
 - **Naive relaxation FAILS at depth** (the B1-lite sweep): jacobi K=40·L → cos 0.82 (L6) / 0.67 (L12)
diff --git a/ep_run/casc_eq_train.py b/ep_run/casc_eq_train.py
index f1f26a4..67ee98f 100644
--- a/ep_run/casc_eq_train.py
+++ b/ep_run/casc_eq_train.py
@@ -26,6 +26,8 @@ ap.add_argument('--muon_lr', type=float, default=0.02)
 ap.add_argument('--tok_init', type=float, default=0.0)  # >0: init tok/pos with this std (GPT-standard 0.02)
 ap.add_argument('--compile', action='store_true')       # torch.compile each block (free speed where supported)
 ap.add_argument('--sig_every', type=int, default=25)    # tok-sigma refresh interval (amortized)
+ap.add_argument('--beta_floor', type=float, default=0.0) # >0: floor beta_t (anti finite-beta SNR collapse at depth)
+ap.add_argument('--beta_fixed', action='store_true')     # disable sig^2 schedule, hold beta_t = args.beta constant
 ap.add_argument('--dtop_every', type=int, default=1)    # 1 = exact (DEFAULT, BP-parity); 2 = fast mode (~20% cheaper, ~4% CE tax at high lr)
 ap.add_argument('--gate_every', type=int, default=200)  # in-training cos(EP,BP) telemetry; <=0 = fully BP-free (no bp_gate at all)
 ap.add_argument('--gate_govern', action='store_true')   # let gate cos adjust K/bscale (default: observe-only => training control is BP-free)
@@ -157,6 +159,8 @@ def ep_step(x, y):
     sig = GOV['sig']
     if SIG0 is None: SIG0 = sig
     beta_t = args.beta * GOV['bscale'] * (SIG0 * SIG0) / max(sig * sig, 1e-9)
+    if args.beta_fixed: beta_t = args.beta * GOV['bscale']
+    if args.beta_floor > 0.0: beta_t = max(beta_t, args.beta_floor)
     z0, zs, ins, outs = free_states_graphed(x)
     zs_free = [z.clone() for z in zs]
     free_ce = F.cross_entropy(readout(zs_free[-1]).reshape(-1, vocab), y.reshape(-1)).item()