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@@ -568,6 +568,23 @@ direction), not training-under-fault; wave-2 = co-training with faults injected
+### RESULT 48b (2026-07-18): GENERALIZED BBP (amp semantics, measured-spectrum, no iid
+assumption; user-directed): R = spike/edge > 1 EVERYWHERE down to beta=1e-4 — EP's extra noise
+sits 5-50x BELOW the signal spike in bf16-amp too. The digital floor is NOT a detectability
+transition; the binding single-step detection limit is BATCH noise (shared with BP).
+probe_bbp2 @s150000, 8 layers x 8 batches x beta {1e-4..1e-2}: R@1e-4 = 8.7-46.8 per layer,
+FLAT toward low beta (no 1/beta bulk: our theta-read never differences energies numerically —
+beta enters via state displacement, so bf16 bites as an all-or-nothing ROUNDING CLIFF at
+beta*||d|| ~ ulp(z) [RESULT 11's death], not as a noise bulk). u1-overlap ~0.37 (b0-b8) /
+0.66-0.80 (b11) beta-INDEPENDENT => dominated by batch sampling noise (missing control column:
+per-batch BP u1 vs mean-BP u1 — same-batch cos(EP,BP)~0.99 implies EP u1 ~ BP u1, so 0.37 is
+the batch-noise number, not an EP defect). WHERE the sharp BBP transition genuinely lives:
+(a) ANALOG readout (ENOB additive bulk -> T64 design equation stands), (b) aggressive weight/
+compute QUANTIZATION — qb6 beta-buyback is an in-hand crossing of the edge; controlled demo =
+rerun bbp2 with 6-bit qcomp, expect R to cross 1 and overlap to jump with beta. (c) bf16 cliff
+as the degenerate case. beta_floor's empirical benefit now fully attributed to window geometry
+(distance from cliff + T2-sensitivity), NOT detectability.
+
### RESULT 48 (2026-07-18): BBP FLOOR AUDIT — the fp32 SIMULATOR has NO additive detectability floor (a=0 all layers, top-direction overlap 1.000 down to beta=3e-4); BBP becomes a HARDWARE design equation.
probe_bbp @plain s150000, 24 layers (qkv+w2 x12), 6 batches x beta {3e-4,1e-3,3e-3,1e-2}:
additive coefficient a = 0 within fit resolution EVERYWHERE; residual error is beta-independent