IndisputableMonolith.Information
The Information module aggregates submodules on the information-theoretic foundations of Recognition Science, with its central hypothesis that the J-cost is the unique symmetric minimal information cost. Researchers linking minimum description length, free-energy principles, and thermodynamic limits to the Recognition forcing chain would cite it. The module organizes its content through five imported submodules, treating the uniqueness result as a scaffold whose proof sits in JCostNecessity.
claimThe J-cost is the unique symmetric minimal information cost: inside the reciprocal affine family $a(x + x^{-1}) + b$, the conditions of symmetry, a minimum at unity, and calibration $a = 1/2$ force $J(x) = \frac12(x + x^{-1}) - 1$.
background
The module sits inside the information-cost side of Recognition Science (Phase 7.5). It imports CompressionPrior, which equates minimum description length to the universal ledger cost J via the φ-prior. EMLFromRecognition supplies the honest RS/EML bridge while recording that J alone forgets orientation. FEPBridgeFromJCost supplies the first Lean comparison of Recognition Science with Friston-style free-energy mechanics, replacing KL divergence by the reciprocal cost. JCostNecessity contains the calibrated-family theorem that forces J from symmetry, convexity, and the unit minimum. Thermodynamics anchors the same cost to the Landauer limit and eight-tick dissipation.
proof idea
The module itself contains no proofs; it is an aggregator. The uniqueness claim is discharged inside the imported JCostNecessity submodule by the calibrated-family theorem. The remaining submodules supply the compression, EML, FEP, and thermodynamic bridges. The overall claim is left as scaffold pending unification with the aggregator.
why it matters in Recognition Science
The module packages the information-cost half of the J-cost story and therefore feeds the T5 J-uniqueness step of the forcing chain. It supplies the content for the sibling hypotheses H_UniquenessVerified and H_ThermodynamicsVerified. The doc-comment explicitly marks the claim as scaffold and records the open task of fully unifying the uniqueness theorem with the aggregator.
scope and limits
- Does not derive the EML gate from J alone.
- Does not claim a complete unification of the uniqueness theorem with the aggregator.
- Does not extend the calibrated-family argument beyond the reciprocal affine family.
- Does not replace the Landauer limit with an independent thermodynamic derivation.