IndisputableMonolith.Information.RecognitionEntropy
This module supplies local definitions for the golden ratio phi and derived information measures such as phiBit and recognitionEntropy. It supports self-contained calculations in Recognition Science information theory without external dependencies beyond the imported J-cost core and constants. Researchers working on entropy bounds or capacity in the RS framework cite these primitives when deriving results from the J-cost function. The module consists entirely of definitions and elementary properties with no theorem proofs.
claim$phi = (1 + sqrt(5))/2$, $phiBit = log_2(phi)$, $recognitionEntropy(x) = -x log_2(x) - (1-x) log_2(1-x)$ (binary entropy scaled by phi), together with related capacity and efficiency statements.
background
The module operates in the information domain of Recognition Science, importing the fundamental time quantum tau_0 = 1 tick from Constants and the J-cost machinery from JcostCore. It introduces a local definition of the golden ratio phi for self-containment, along with phiBit (information per recognition event) and recognitionEntropy (entropy associated with recognition events). Sibling definitions establish basic inequalities such as phi > 1, phi < 2, and comparisons showing phi-bit efficiency relative to other bases.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module provides the information-theoretic building blocks that feed into Recognition Science results on recognition events, capacity limits, and entropy maximization under uniform distributions. It supplies the phi-based measures used when connecting J-cost to information capacity and when establishing that uniform distributions maximize entropy in the RS setting.
scope and limits
- Does not derive any entropy bounds from first principles.
- Does not link recognitionEntropy to physical observables beyond imported constants.
- Does not contain proofs of capacity theorems.
- Does not address multi-dimensional or continuous extensions.