IndisputableMonolith.Information
The Information module aggregates five submodules to position the J-cost as the unique symmetric minimal information cost in Recognition Science. It assembles compression priors, EML and FEP bridges, necessity proofs, and thermodynamic links under a single scaffold. The structure relies on importing specialized modules whose individual results combine to support the calibrated reciprocal form without claiming a complete aggregator unification.
claimThe J-cost function satisfies $J(x) = (x + x^{-1})/2 - 1$ and is the unique symmetric minimal information cost obeying the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, with the uniqueness theorem established inside the reciprocal affine family.
background
This module collects the information-theoretic side of Recognition Science. It imports the compression prior equating minimum description length to ledger cost J, the EML bridge from oriented recognition coordinates (noting J forgets orientation), the FEP bridge comparing variational free energy to reciprocal cost, the JCostNecessity module proving uniqueness within the calibrated family a*(x + 1/x) + b, and the Thermodynamics module anchoring to the Landauer limit and 8-tick dissipation. The local setting treats J as the phi-prior for universal coding, with symmetry and convexity insufficient by themselves to force the canonical form.
proof idea
This is a module with no single proof body; it organizes the argument by importing five submodules. The core uniqueness step is supplied by the JCostNecessity submodule, which restricts to the reciprocal affine family, imposes unit minimum, and calibrates a = 1/2 to recover J. The remaining imports supply supporting bridges and thermodynamic relations without deriving EML or full unification from J alone.
why it matters in Recognition Science
This module supplies the information-cost foundation for T5 J-uniqueness in the forcing chain and anchors the phi-ladder mass formula through the calibrated J. It feeds the overall Recognition monolith by linking compression, free-energy comparisons, and Landauer thermodynamics, with the scaffold status highlighting the remaining TODO of full aggregator unification. The JCostNecessity submodule contains the established proof of the calibrated-family claim.
scope and limits
- Does not claim J alone derives the EML gate.
- Does not complete unification of uniqueness with the aggregator.
- Does not extend the FEP comparison beyond local KL versus reciprocal cost.
- Does not derive thermodynamic relations outside the Landauer and 8-tick setting.