A Pure, No-Meta Synthesis of Functional-Information Selection and Propagative Organization

Abstract

We (i) formalize functional information (FI) via preregistered score/threshold grids and a test distribution, logging the selection operator itself; (ii) prove a weak order representation showing that any admissible functional—Blackwell-monotone and robust to symmetric coarse-graining—is order-embedded by a monotone transform of conditional mutual information (CMI) (no uniqueness claim without extra axioms); (iii) develop a heterogeneous FKPP framework on Rd R d (and graphs) with explicit standing assumptions, yielding an isotropic speed floor 2 v ⋆ ≥ 2 D m i n λ m i n and a directional lower bound v⋆(u)≥[ 2D(u)λmin⁡−Λ+(u) (u) - v ⋆ ( u ) ≥ [ 2 D ( u ) λ m i n − Λ + ( u ) ] + , including a nontriviality condition; (iv) establish coarse-graining monotonicity of the directional penalty under heat or Bakry–Émery (CD (κ,∞)( , ) ( κ , ∞ ) ) gradient contraction; and (v) propose an audited acceleration scheme with HAC-robust tests, moving block bootstrap CIs, negative controls, placebo selections, preregistered triggers, and falsifiers.

Keywords

• functional information
• selection
• lifi
• conditional mutual information
• blackwell order
• coarse-graining
• bakry-émery
• heat semigroup
• fkpp
• front propagation
• heterogeneous media
• directional speed

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