srCost
plain-language theorem explainer
srCost defines the J-cost applied directly to the signal-to-noise ratio r for speech intelligibility modeling. Acoustics researchers would cite this when deriving hearing-loss penalties or certifying zero-cost thresholds at r = 1. The definition is a one-line alias to the Jcost operation inside the RS-native Cost structure.
Claim. Define the speech-recognition cost by $srCost(r) := J(r)$ for $r > 0$, where $J$ is the J-cost function satisfying $J(1) = 0$ and $J(r) = J(r^{-1})$.
background
The module models speech intelligibility via recognition cost on the SNR ratio $r :=$ signal power over noise power. The J-cost vanishes at the intelligibility-1 threshold $r = 1$ and rises symmetrically for $r < 1$, matching clinical speech-reception thresholds near $-7$ dB ($r ≈ 0.2$). Cost is the quantity type carrying the Jcost operation, imported from RSNative.Core.
proof idea
One-line definition that directly applies the Jcost operation from the Cost structure.
why it matters
This supplies the base cost for hearingLossPenalty at phi-steps and for the SpeechIntelligibilityCert structure that encodes threshold-zero, reciprocal symmetry, and non-negativity. It places the J-cost inside acoustics, consistent with T5 J-uniqueness and the phi-ladder, enabling downstream certification of intelligibility conditions.
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