IndisputableMonolith.Information.CompressionPrior
The CompressionPrior module establishes that the φ-prior is the unique minimum description length prior obtained directly from T5 J-uniqueness. Physicists and information theorists working on recognition-derived foundations cite it when grounding MDL priors in the J-cost function. The module defines mdl_prior and coding_length then proves prior_holds by algebraic reduction from the J-functional equation.
claimThe golden-ratio prior is the unique minimum description length prior: $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ where $J(x) = (x + x^{-1})/2 - 1$.
background
This module belongs to the Information domain and imports the Cost module, which supplies the J-cost function central to Recognition Science. J-cost is defined by $J(x) = (x + x^{-1})/2 - 1$, equivalently cosh(log x) - 1, and obeys the Recognition Composition Law. The module introduces mdl_prior as the minimum description length prior, coding_length as the associated length measure, and prior_holds as the uniqueness theorem. The local setting is the information-theoretic foundation of the forcing chain, where priors are derived from T5 J-uniqueness before aggregation into the broader Information bridge.
proof idea
The module structures its argument around three sibling declarations. mdl_prior and coding_length supply the definitions of the prior and length measure. prior_holds then asserts uniqueness as a direct algebraic consequence of the J-uniqueness property imported from the upstream Cost module.
why it matters in Recognition Science
This module supplies the MDL grounding that the parent Information module aggregates into the information-theoretic and thermodynamic foundation of Recognition Science. It realizes the step from T5 J-uniqueness to a unique φ-prior, closing part of the information bridge. The downstream aggregator uses it to connect to EMLFromRecognition and other components in the overall foundation.
scope and limits
- Does not derive thermodynamic extensions beyond the information prior.
- Does not compute explicit numerical values for the φ-prior.
- Does not address multi-particle or higher-dimensional coding schemes.