IndisputableMonolith.Information.CompressionPrior
The CompressionPrior module establishes that the φ-prior is the unique minimum description length prior derived from T5 J-uniqueness. Researchers grounding information measures in Recognition Science cite it to connect J-cost to coding lengths. The argument reduces the MDL condition to the Recognition Composition Law through the phi-ladder.
claimThe $\phi$-prior is the unique minimum description length (MDL) prior obtained from J-uniqueness (T5), where $J(x) = \frac{x + x^{-1}}{2} - 1$.
background
This module sits in the Information domain and imports the Cost module, which supplies the J-cost function. It introduces sibling objects mdl_prior, coding_length, and prior_holds to formalize MDL grounded in J-cost. The setting forms part of the information-theoretic foundation that bridges to thermodynamic results, with the central claim that the φ-prior holds uniquely from T5.
proof idea
This is a definition module whose central theorem follows directly from the J-uniqueness property in the upstream Cost import; supporting definitions for coding length and prior are assembled around the Recognition Composition Law and phi-ladder.
why it matters in Recognition Science
The module feeds the parent Information aggregator, which collects the information-theoretic and thermodynamic foundation of Recognition Science. It realizes the step from T5 J-uniqueness to the MDL prior, advancing the bridge that links J-cost to the full information structure. It touches the Recognition Composition Law and phi-ladder landmarks.
scope and limits
- Does not derive numerical values for constants such as alpha.
- Does not address thermodynamic interpretations or EML gates.
- Does not extend to the eight-tick octave or spatial dimensions.
- Does not treat mass formulas or Berry creation thresholds.