IndisputableMonolith.Foundation.BlackBodyRadiationDeep
Module Foundation.BlackBodyRadiationDeep establishes zero recognition cost for the matched configurations under Wien's law and the Stefan-Boltzmann law. Researchers deriving thermodynamic relations from the J-cost functional would cite these results. The module structure consists of targeted zero-cost theorems that reduce expressions to the J fixed point via the upstream Cost module.
claim$J(\text{matched Wien configuration}) = 0$, $J(\text{matched Stefan-Boltzmann configuration}) = 0$
background
The module sits in the foundation layer and imports Constants (where $\tau_0 = 1$ tick) together with the Cost module that supplies the J-cost. It applies the Recognition Composition Law to black-body spectra in RS-native units. The DOC_COMMENT states the central claim: Wien matched configuration has zero cost.
proof idea
The module collects zero-cost theorems (wien_zero_cost, stefan_boltzmann_zero_cost and supporting lemmas). Each reduces the cost expression to the identity element of J by direct substitution of the matched point and application of the composition law from the Cost import.
why it matters in Recognition Science
The module supplies the zero-cost property required for thermodynamic derivations in Recognition Science. It fills the Wien claim noted in the module documentation and prepares the ground for higher-level radiation results, even though no downstream uses are recorded yet.
scope and limits
- Does not derive the full Planck spectrum.
- Does not compute numerical values of radiation constants.
- Does not treat off-match positive-cost configurations.
- Does not address non-equilibrium or time-dependent cases.