UltrasoundModality
plain-language theorem explainer
UltrasoundModality enumerates five standard therapeutic ultrasound modalities as an inductive type equipped with decidable equality and finite cardinality. Acoustics researchers cite it when establishing the configuration dimension for therapy protocols or verifying modality counts against the J-cost band. The definition proceeds by direct enumeration of the five constructors with automatic derivation of the required type classes.
Claim. Let $U$ be the inductive type of ultrasound modalities with five constructors: HIFU, low-intensity pulsed ultrasound, diagnostic ultrasound, lithotripsy, and sonoporation, equipped with decidable equality and finite type structure.
background
In the Recognition Science treatment of acoustics, therapeutic ultrasound operates via thermal heating at J(temperature ratio) and mechanical cavitation at J(pressure ratio), both thresholds lying in the canonical J(φ) band. The module sets the number of modalities equal to configDim D = 5. This inductive definition supplies the finite set whose cardinality is later used in certification structures.
proof idea
The declaration is a direct inductive definition that lists the five modalities explicitly, with the deriving clause automatically generating instances for DecidableEq, Repr, BEq, and Fintype.
why it matters
This definition supplies the base type for the modality count theorem proving cardinality five and for the UltrasoundTherapyCert structure that pairs the count with CanonicalCert. It realizes configDim D = 5 for ultrasound therapy, connecting to the J-cost mechanism and phi-ladder thresholds in the Recognition framework.
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