RESULT 54: 上界∝1/σ²下沉(σ242→473翻倍,β*从0.12跌到<0.03),固定β=停滞非安全(plain2收官89%skip,best其实是200k成绩); K=30密探针推翻Codex的β*=0.7(K=8误判慢发散为收敛); σ-scaling原设计对但被floor钉死+早期σ暴涨张力; --beta_cos_min实装(按进程cosine降β跟踪下沉上界); betacos王冠2e-2→8e-4在飞

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

1 files changed, 24 insertions, 0 deletions

diff --git a/docs/campaign/CASCADE_ABLATION_PLAN.md b/docs/campaign/CASCADE_ABLATION_PLAN.md
index f0a82be..6dd93e5 100644
--- a/docs/campaign/CASCADE_ABLATION_PLAN.md
+++ b/docs/campaign/CASCADE_ABLATION_PLAN.md
@@ -568,6 +568,30 @@ direction), not training-under-fault; wave-2 = co-training with faults injected
 
 
 
+### RESULT 54 (2026-07-20): THE CEILING SINKS ∝1/σ² AS TRAINING SHARPENS — no fixed β survives;
+"fixed β never explodes" was FALSE (it STALLS: endgame skip-storm = frozen training). β must DESCEND.
+User caught it: "固定β永不炸个屁！你一直skip还训不训了？" — dead right.
+EVIDENCE: plain2 fixed-3e-3 full run — best 3.3437 hit at step 199800, then skip rate SURGES:
+84%/step @224k, 89%/step @231k. Endgame (200-234k) = 34k steps of ~zero effective updates;
+the "234k crown 3.3437" is really a 200k result. skip ≠ safe, skip = STALL.
+DENSE ρ-PROBE (probe_cx3_rhogrid, K=30 asymptotic — corrects Codex's K=8 β*=0.7 which mistook
+slow divergence for convergence): true ceiling β* (max β whose resK reaches the fp floor) SINKS:
+  s35000  β*≈0.12 (σ242) | s95000 β*≈0.12 | s150000 β*≈0.08 (σ443) | s230000 β*<0.03 (σ473).
+MECHANISM: training sharpens the model (σ 242→473, ~2×); a sharper block Jacobian makes the nudge
+relaxation harder to converge → ceiling drops. It's ∝1/σ^~2. The sunk endgame ceiling (<0.03,
+approaching the 3e-3 training β) is WHY fixed 3e-3 skip-storms late.
+CODE: σ-scaling EXISTS (line 473: β=β0·SIG0²/σ²) — the ORIGINAL wall-1 design already tracks σ —
+but line 477 floor=3e-3 PINS it (plain2 wanted β↓1.94e-3 @σ473, floor forced 3e-3). My beta_simple
+"full ownership" that DELETED σ-scaling was exactly backwards. But naive un-flooring fails too:
+early σ 3.9→242 (62×, network growing structure NOT sharpening) would crush β∝1/σ² to 8e-7 and
+starve training — which is WHY the floor existed. The real tension: early σ-growth (structure,
+don't cut β) vs late σ-growth (sharpening, DO cut β); σ magnitude can't separate them.
+FIX (least-assumption): SCHEDULE β descent by progress like LR — --beta_cos_min added (cosine
+β from --beta to min, bypasses σ-scaling+floor). Calibrated to the measured ceiling: early 2e-2
+(<0.12), endgame 8e-4 (<sunk ceiling). Conservative=safe (CE flat in-corridor → undershoot free,
+overshoot skips). fw72m_betacos (2e-2→8e-4, 234k, guards silent) IN FLIGHT vs plain2 3.3437 —
+decisive test = does endgame KEEP LEARNING instead of skip-stalling.
+
 ### RESULT 53 (2026-07-20): THE β DOGMA REBUILT — ceiling is REAL (β*≈0.7 @s35000) but the v1
 collapse did NOT cross it; fixed β never explodes (only the controller does); policy = FIXED SMALL β.
 Codex ρ-probe (probe_cx2_rho, s35000, one relax, no training): ρ = res_k/res_{k-1} vs β: