IndisputableMonolith.Foundation.BlackBodyRadiationDeep
The BlackBodyRadiationDeep module constructs explicit zero-cost matchings for Wien's displacement law and the Stefan-Boltzmann law inside the Recognition Science cost framework. Researchers deriving thermodynamic scaling from the J-functional would reference these base cases. The module proceeds by importing the RS time quantum and cost primitives then defining direct zero-defect configurations for the matched states.
claimThe module supplies $wien_zero_cost$ asserting that the configuration matched to Wien's law has $J$-cost zero, together with the analogous $stefan_boltzmann_zero_cost$ and the certificate $BlackBodyRadiationDeepCert$ witnessing the deep zero-cost embedding.
background
The module sits in the Foundation layer and imports the RS-native time quantum from Constants, where $τ_0 = 1$ tick, together with the J-cost functional from the Cost module. It works inside the Recognition Composition Law and the phi-ladder scaling that converts rung numbers into mass and energy units. The local setting is the deep version of blackbody radiation in which matched configurations are required to incur exactly zero defect cost.
proof idea
This is a definition module. It contains direct constructions of the zero-cost states for the Wien and Stefan-Boltzmann matchings, followed by simple inhabitance proofs for the certificate type; no tactic-heavy reductions or external lemmas beyond the imported constants and cost axioms are required.
why it matters in Recognition Science
The module supplies the zero-cost foundation cases that later derivations of the full blackbody spectrum rely upon. It corresponds to the classical limit step in the T0-T8 forcing chain by exhibiting matched configurations with vanishing J-cost. It leaves open the extension to nonzero-cost quantum corrections at the phi^5 rung.
scope and limits
- Does not derive the Planck spectrum or frequency-dependent intensity.
- Does not prove uniqueness of the zero-cost matching.
- Does not address temperature dependence beyond the classical scaling.
- Does not incorporate gravitational or curved-space corrections.