ActualizationPrinciple

formal source

  57
  58    If there's a unique minimum, actualization is deterministic.
  59    If there are multiple minima (degeneracy), further structure resolves. -/
  60structure ActualizationPrinciple where
  61  /-- Current configuration -/
  62  current : Config
  63  /-- The actualized successor -/
  64  successor : Config
  65  /-- Successor is in possibility set -/
  66  in_possibility : successor ∈ Possibility current
  67  /-- Successor minimizes cost among possibilities -/
  68  minimizes_cost : ∀ y ∈ Possibility current, J successor.value ≤ J y.value
  69
  70/-- An actualization witness for a configuration. -/
  71def has_actualization (c : Config) : Prop :=
  72  ∃ ap : ActualizationPrinciple, ap.current = c
  73
  74/-- Every configuration has an actualization (toward identity). -/
  75theorem every_config_actualizes (c : Config) : has_actualization c := by
  76  use {
  77    current := c
  78    successor := identity_config (c.time + 8)
  79    in_possibility := identity_always_possible c
  80    minimizes_cost := by
  81      intro y hy
  82      simp [identity_config, J_at_one]
  83      exact J_nonneg y.pos
  84  }
  85
  86/-! ## Degeneracy and Contingency -/
  87
  88/-- **DEGENERACY**: When multiple configurations have the same minimal cost.
  89
  90    This is the origin of contingency in RS—when the universe "could have gone either way"