IndisputableMonolith.Information
The Information module aggregates five submodules to establish that the J-cost is the unique symmetric minimal information cost in Recognition Science. Researchers deriving physics from information theory or bridging to FEP and thermodynamics would cite it. The structure is a scaffold that imports specialized results on MDL priors, EML bridges, FEP comparisons, calibrated uniqueness inside the reciprocal affine family, and Landauer limits.
claimThe function $J(x) = \frac{1}{2}(x + x^{-1}) - 1$ is the unique symmetric minimal information cost satisfying the Recognition Composition Law inside the calibrated reciprocal affine family.
background
This module resides in the Information domain and imports CompressionPrior (MDL equals ledger cost J via the phi-prior), EMLFromRecognition (RS/EML bridge that requires orientation beyond J alone), FEPBridgeFromJCost (local comparison of RS reciprocal cost with variational free energy), JCostNecessity (symmetry, unit minimum, and convexity force J inside a*(x + 1/x) + b with a = 1/2), and Thermodynamics (Landauer limit and 8-tick dissipation). The module doc states the hypothesis that J-cost is the unique symmetric minimal information cost, with proof established in JCostNecessity but unification with the aggregator still pending.
proof idea
This is a scaffolding module with no proofs of its own; it aggregates the five imported submodules whose individual doc-comments supply the component arguments on priors, bridges, and calibrated uniqueness.
why it matters in Recognition Science
The module supports the J-cost uniqueness hypothesis (T5) that anchors the Recognition Science derivation of constants and the phi-ladder. It feeds the aggregator unification step noted in the module doc and supplies the information-theoretic side of the eight-tick octave and D=3 results downstream in the framework.
scope and limits
- Does not derive the EML gate from J alone.
- Does not complete unification of uniqueness with the aggregator.
- Does not extend uniqueness outside the reciprocal affine family.
- Does not claim global FEP equivalence.