IndisputableMonolith.Masses.MassLaw

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Masses.Anchor
   4
   5/-!
   6# The Master Mass Law
   7
   8This module formalizes the master mass formula derived from first principles in Recognition Science.
   9
  10## The Theory
  11
  121. Every stable recognition state (particle) occupies a rung on the φ-ladder.
  132. The mass m is proportional to the coherence energy E_coh, scaled by sector yardstick and rung position.
  143. The master formula: m = yardstick(Sector) * φ^{r - 8 + gap(Z)}
  15
  16Where:
  17- yardstick(Sector) is the sector prefactor (binary and φ-offset)
  18- r is the species-specific rung integer
  19- 8 is the fundamental cycle period (τ₀)
  20- Z is the charge-based shift index
  21- gap(Z) is the correction term from the recognition gap series
  22-/
  23
  24namespace IndisputableMonolith
  25namespace Masses
  26namespace MassLaw
  27
  28open Constants
  29open Anchor
  30open Integers
  31open ChargeIndex
  32
  33/-- The recognition gap correction term: gap(Z) = log_φ(1 + Z/φ).
  34    This term corrects the rung position based on the charge-induced skew. -/
  35noncomputable def gap_correction (Z_val : ℤ) : ℝ :=
  36  Real.log (1 + (Z_val : ℝ) / phi) / Real.log phi
  37
  38/-- **THE MASTER MASS LAW**
  39    Predicts the mass of a species in a given sector. -/
  40noncomputable def predict_mass (sector : Sector) (rung : ℤ) (Z_val : ℤ) : ℝ :=
  41  yardstick sector * (phi ^ ((rung : ℝ) - 8 + gap_correction Z_val))
  42
  43/-- Mass is positive for any valid configuration. -/
  44theorem predict_mass_pos (s : Sector) (r : ℤ) (Z_val : ℤ) :
  45    predict_mass s r Z_val > 0 := by
  46  unfold predict_mass
  47  apply mul_pos
  48  · -- yardstick is positive
  49    unfold yardstick Anchor.E_coh
  50    apply mul_pos
  51    · apply mul_pos
  52      · exact zpow_pos (by norm_num) (B_pow s)
  53      · exact zpow_pos phi_pos (-5 : ℤ)
  54    · exact zpow_pos phi_pos (r0 s)
  55  · -- phi^... is positive
  56    exact Real.rpow_pos_of_pos phi_pos _
  57
  58/-! ## Derived Properties -/
  59
  60/-- The mass law exhibits φ-scaling: increasing rung by 1 scales mass by φ. -/
  61theorem mass_rung_scaling (s : Sector) (r : ℤ) (Z_val : ℤ) :
  62    predict_mass s (r + 1) Z_val = phi * predict_mass s r Z_val := by
  63  unfold predict_mass
  64  -- φ^(r+1-8+gap) = φ^1 * φ^(r-8+gap)
  65  set gap := gap_correction Z_val
  66  have h_add : (((r + 1 : ℤ) : ℝ) - 8 + gap) = 1 + (((r : ℤ) : ℝ) - 8 + gap) := by
  67    push_cast
  68    ring
  69  rw [h_add, Real.rpow_add phi_pos]
  70  rw [Real.rpow_one]
  71  ring
  72
  73/-- The "gap" term corrects for the charge-based shift.
  74    When Z=0 (neutral sector baseline), gap(0) = 0. -/
  75theorem gap_zero_neutral : gap_correction 0 = 0 := by
  76  unfold gap_correction
  77  simp only [Int.cast_zero, zero_div, add_zero, Real.log_one, zero_div]
  78
  79end MassLaw
  80end Masses
  81end IndisputableMonolith
  82