IndisputableMonolith.Mathematics.InformationTheoryFromRS
The module derives information theory structures such as Shannon axioms and entropy measures from the J-cost in Recognition Science. Researchers linking RS foundations to classical information measures would cite it. The module consists of definitions and certificates built directly on the imported Cost module.
claimDefines $\mathrm{ShannonAxiom}$, $\min entropy$ with the property that minimum entropy satisfies $J=0$ for certain outcomes, $\mathrm{pos\_entropy}$, and $\mathrm{InformationTheoryCert}$.
background
The module resides in the Mathematics domain and imports Mathlib together with IndisputableMonolith.Cost, which supplies the J-cost function. It introduces the sibling definitions ShannonAxiom, shannonAxiomCount, min_entropy, pos_entropy, InformationTheoryCert and informationTheoryCert. The local setting connects the Recognition Composition Law to information quantities, with the supplied doc-comment stating "Minimum entropy: J = 0 (certain outcome)."
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the information-theory layer that supports downstream RS derivations, connecting J-cost to entropy concepts. It fills the step from the forcing chain and RCL to information measures, though no direct used_by edges appear in the supplied data.
scope and limits
- Does not derive numerical entropy values for concrete distributions.
- Does not address continuous or quantum extensions.
- Does not prove Shannon axioms independently of the J-cost.