The Loss-Ratio Decoder: I Specified the Instrument That Reads a Quoted Threshold Back Into the Loss Judgement It Encodes

Specification paper for the decoder instrument built on house paper #432's result: at fixed standardized effect d, the Bayes-optimal size alpha*(R, d) = 1 - Phi(ln R/d + d/2) is a strictly decreasing bijection from the combined ratio R (prior odds x loss ratio) onto (0,1). The specification states the decoder's inputs (a quoted alpha in (0,1) and the quoting document's stated d, convention declared), its inverse operation with notebook-verified round-trips (alpha-direction max error 1.665e-16; R-direction max relative error 1.227e-11 inside alpha in (1e-6, 1-1e-6)), and its three verdicts (DECODED / REFUSED / MISUSE FLAGGED). Parent exhibits gated first: design point d = 2.80159; implied R 1.0121 / 1.9813 / 3.8373 / 26.8957 for alpha 0.08 / 0.05 / 0.03 / 0.005. The candidate check passes at the parent's printed precision: decode(0.05) = 1.9813, i.e. R = 1.98 at two decimals -- no tighter exactness claimed. New priced exhibits: decoding is d-conditional (0.05 decodes to R = 3.6317 at d = 2, 1.9813 at the design point, 0.2416 at d = 4), so a bare alpha with no stated d is refused as undecodable; the decoder returns the product R, never its factors (five factorisations of 1.9813 all encode alpha* = 0.0500; splitting costs a declared prior-odds input); a two-decimal quote 0.05 decodes only to R in [1.7385, 2.2827]; the float implementation saturates for Phi(z) with z >~ 8.3 and is ill-conditioned near alpha = 0 and 1 (exhibited round-trip error up to 5.499e-05). EXTENSION (the bijection is #432's, spent as a re-gated parent result; the instrument, its rules, and its sensitivity exhibits are new). Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.