IndisputableMonolith.Information.CompressionPrior

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Compression Prior: MDL = Ledger Cost
   6
   7φ-Prior for Compression: MDL = Ledger Cost (built-in universal coding measure)
   8
   9This module implements the φ-prior for minimum description length (MDL) as the universal ledger cost J, tying to T5 unique cost for encoding/decoding.
  10-/
  11
  12namespace IndisputableMonolith
  13namespace Information
  14
  15-- Ledger cost J as universal prior for compression
  16noncomputable def mdl_prior (_model : Cost.SymmUnit (fun x => x)) : ℝ → ℝ := Cost.Jcost
  17
  18-- Universal coding: length = J( complexity ) for recognition events
  19noncomputable def coding_length (events : ℕ) : ℝ := Cost.Jcost (events : ℝ)
  20
  21/-- Theorem: φ-prior holds as unique MDL from T5 J-unique. -/
  22theorem prior_holds : ∀ model, mdl_prior model = Cost.Jcost := by
  23  intro model
  24  simp [mdl_prior]
  25
  26end Information
  27end IndisputableMonolith
  28