IndisputableMonolith.Acoustics.UltrasoundTherapyThresholdFromJCost
The module instantiates the canonical J-cost band for ultrasound therapy, defining intensity ratios and therapy costs to certify safe mechanical-thermal windows. Acousticians and medical physicists cite it when mapping Recognition Science J-function thresholds to clinical parameters. It follows the six-clause template imported from CanonicalJBand, proving matched-zero at unit ratio and non-negativity across the therapy band.
claimThe module supplies $r = I/I_0$ (intensity ratio) and $J_therapy(r) = J(r)$ (therapy J-cost), together with the certification that the safe window satisfies $J(1)=0$ and $J(r)≥0$ for $r>0$, with mechanical-thermal symmetry and band membership.
background
The module sits in the Acoustics domain and imports the Canonical J-Cost Band template. That template supplies the reusable six-clause structure used across the master cert chain: matched-zero at J(1)=0 and non-negativity J(x)≥0 for x>0. The J function itself is the unique solution to the Recognition Composition Law that is self-similar and non-negative on the positive reals. Local definitions translate these clauses into ultrasound quantities: intensityRatio as the ratio of applied to reference intensity, therapyJCost as J applied to that ratio, and therapy_window_in_band as the interval where the cost remains below the Berry creation threshold.
proof idea
This is a definition module, no proofs. It consists of six sibling declarations that directly instantiate the imported CanonicalJBand template: intensityRatio and therapyJCost as the ratio and cost maps, matched_at_safe and mechanical_thermal_symmetric as the zero and symmetry clauses, therapy_window_in_band as the membership predicate, and cert as the final conjunction of the six clauses.
why it matters in Recognition Science
The module supplies the acoustics-specific case in the Plan v7 domain-cert sequence. It feeds the master cert chain by discharging the J-cost-on-ratio obligations for ultrasound therapy thresholds. The final cert object is the concrete witness that the therapy window lies inside the canonical band, closing one of the forty-something domain openings required for whole-science certification.
scope and limits
- Does not derive numerical intensity values or clinical protocols.
- Does not model tissue-specific absorption or nonlinear propagation.
- Does not address diagnostic or imaging ultrasound regimes.
- Does not incorporate quantum or relativistic corrections.
- Does not prove existence of the J function itself.