IndisputableMonolith.Physics.PhotoelectricEffectFromJCost
The module formalizes the photoelectric effect threshold via the J-cost function. It defines PhotoelectricMaterial along with predicates and certificates that enforce J(W/hν) = 0 exactly at threshold. The structure is purely definitional, importing the Cost module to supply the underlying J properties and Recognition Composition Law.
claimFor a photoelectric material with work function $W$, the threshold condition is $J(W/hν)=0$ where $J(x)=(x+x^{-1})/2-1$. The module introduces the type PhotoelectricMaterial, the count function photoelectricMaterialCount, the threshold predicate photoelectric_threshold, the below-threshold check below_threshold, and the certificate type PhotoelectricCert with constructor photoelectricCert.
background
Recognition Science obtains all physics from the single functional equation whose solution yields the J-cost $J(x)=(x+x^{-1})/2-1$. The imported Cost module supplies this definition together with the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The present module applies these objects to the photoelectric effect by introducing PhotoelectricMaterial as a structure carrying work function and frequency parameters, then encoding the threshold condition directly as the vanishing of J at $W/hν$.
proof idea
This is a definition module, no proofs. It consists of inductive type declarations for PhotoelectricMaterial and PhotoelectricCert, plus simple function definitions for photoelectric_threshold, below_threshold, and photoelectricCert that directly embed the J-cost zero condition supplied by the Cost import.
why it matters in Recognition Science
The module supplies the basic objects needed to embed the photoelectric threshold inside the Recognition Science framework, directly instantiating the J-uniqueness step (T5) for an observable laboratory effect. It therefore serves as a concrete physics interface that later derivations of mass ladders or forcing-chain results can reference, even though the current dependency graph lists no downstream users.
scope and limits
- Does not compute numerical thresholds for concrete materials.
- Does not address intensity or multi-photon regimes.
- Does not incorporate external fields or relativistic kinematics.