IndisputableMonolith.Acoustics.SpeechIntelligibilityFromJCost
This module defines the speech-recognition J-cost applied to the SNR ratio together with supporting predicates for intelligibility. Acoustics researchers working in the Recognition Science program cite these objects when constructing auditory threshold models. The module consists of a sequence of definitions and elementary properties with no complex proofs.
claimDefine $\mathrm{srCost}(\rho) = J(\rho)$ for SNR ratio $\rho$, together with the zero-at-threshold lemma, reciprocal symmetry, non-negativity, the hearing-loss penalty term, and the predicate $\mathrm{SpeechIntelligibilityCert}$ that certifies intelligibility when the cost lies below a fixed bound.
background
Recognition Science obtains all physical quantities from the single functional equation whose solution yields the J-cost $J(x) = (x + x^{-1})/2 - 1$. The imported Cost module supplies this J function and the Recognition Composition Law; the Constants module fixes the native time quantum $\tau_0 = 1$ tick. The present acoustics module specializes J to the SNR ratio to obtain a cost measure for speech recognition.
The module introduces the concrete objects srCost, hearingLossPenalty, and the certification predicate SpeechIntelligibilityCert, together with their immediate algebraic properties.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the base definitions that populate the acoustics domain of Recognition Science. It feeds the speech-intelligibility certificate and its cost function into any later model that derives auditory performance from the J-cost and the phi-ladder. No downstream users are recorded yet.
scope and limits
- Does not incorporate frequency-dependent auditory filters.
- Does not treat reverberation or multi-talker interference.
- Does not derive numerical intelligibility scores from the cost function.