Scalar Radiance Law

Abstract

The Scalar Radiance Law (SRL) is introduced as a sovereign, first-principles framework for universal radiance scaling. Built entirely from native operators-thermal kernel, geometry, gate, coherence, and collapse-SRL achieves closure without reliance on legacy constants or distributions. The law is expressed as where defines the radiance ceiling and the remaining operators are dimensionless multipliers encoding geometry, threshold activation, coherence, and bounded contraction. Its proof structure-factorization, conservation, entropy monotonicity, and discrete continuityculminates in the universal scaling identity with δ the coherence exponent, η the gate exponent, and q the geometry index. These parameters are experimentally measurable under declared protocols, ensuring transparency and falsifiability. SRL classifies radiance behavior into three universal regimes: low-band (bandwidth-driven scaling), saturation (ceiling-limited scaling), and crossover (matched asymptotics). Bounded corrections-including reinjection and infrared refinement-act only as stabilizers, never altering the leading identity. The law applies across domains: astrophysics and cosmology, condensed matter and nano science, plasma physics, climate and atmospheric science, biophysics, high-energy physics, geophysics, and quantum information. Governance protocols-pre-registration of operator definitions, declaration of expected exponents, error budget propagation, falsifiability conditions, and replication across laboratories-secure SRL's legitimacy as a universal law.