ConfigSpaceDecomposition

formal source

  64def configSpaceDim : ℕ := 5
  65
  66/-- Decomposition of the 5 dimensions. -/
  67structure ConfigSpaceDecomposition where
  68  spatial_dims : ℕ := 3        -- From D=3 (T9)
  69  temporal_dim : ℕ := 1        -- From 8-tick cycle (T6)
  70  balance_dim : ℕ := 1         -- From conservation constraint (T3)
  71  total_eq : spatial_dims + temporal_dim + balance_dim = configSpaceDim := by native_decide
  72
  73/-- The canonical decomposition. -/
  74def canonicalDecomposition : ConfigSpaceDecomposition := {}
  75
  76/-- The dimension is exactly 5. -/
  77theorem config_space_is_5D : configSpaceDim = 5 := rfl
  78
  79/-! ## Part 2: Each Dimension is Forced -/
  80
  81/-- **Spatial Dimensions (D=3)**: Forced by the linking requirement.
  82
  83In D dimensions, linking of closed curves is only non-trivial when D ≥ 3.
  84For D > 3, the link penalty vanishes (curves can pass through each other).
  85Therefore D = 3 is the unique stable dimension. -/
  86def spatial_dims_forced : ℕ := D
  87
  88theorem spatial_dims_eq_3 : spatial_dims_forced = 3 := rfl
  89
  90/-- **Temporal Dimension (1)**: Forced by the 8-tick cycle.
  91
  92The ledger evolves in discrete time with period 8 (T6).
  93This periodic evolution adds one effective dimension to the configuration space.
  94The "temporal dimension" here is the phase θ ∈ [0, 2π) ≃ [0, 8τ₀). -/
  95def temporal_dim_forced : ℕ := 1
  96
  97/-- The 8-tick cycle is forced by T6: period = 2^D for D=3. -/