IndisputableMonolith.Mathematics.InformationTheoryFromRS
This module derives information theory objects from the Recognition Science J-cost by importing the Cost module. It defines ShannonAxiom, min_entropy at J=0 for certain outcomes, pos_entropy, and InformationTheoryCert. Researchers connecting RS to classical information theory would cite these. The module consists entirely of definitions and axioms with no proofs.
claimThe module defines the Shannon axiom, the minimum entropy condition $J=0$ for certain outcomes, positive entropy, and an information theory certificate built on the J-cost functional.
background
The module imports Mathlib and IndisputableMonolith.Cost, which supplies the J-cost. It introduces sibling definitions including ShannonAxiom, min_entropy (the case of minimum entropy where J equals zero for certain outcomes), pos_entropy, and InformationTheoryCert. The local setting is the formalization of information theory inside the Recognition Science framework using the J-uniqueness from the forcing chain.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies foundational definitions that support the derivation of information theory from RS, including the Shannon axiom and entropy minima tied to J. It feeds the broader development of information-theoretic results in the Recognition framework, though no specific downstream theorems are listed.
scope and limits
- Does not derive the Shannon entropy formula from the RCL.
- Does not compute numerical values or bounds for entropy.
- Does not connect entropy to the phi-ladder or physical constants.
- Does not address quantum information or measurement.