IndisputableMonolith.Physics.Hadrons

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Compat
   4import IndisputableMonolith.RSBridge.Anchor
   5
   6open Real Complex
   7open scoped BigOperators Matrix
   8
   9/-!
  10Hadron Mass Relations and Regge Slopes from φ-Tier Spacing
  11
  12This module derives hadron masses from composite rungs (quark1.rung + quark2.rung + binding
  13from eight-beat), relations like ρ/ω degeneracy from equal-Z. Regge trajectories
  14m^2 = n α' φ^{2r} with α' from residue, slope universal.
  15
  16Phase 6 scaffolding — explicitly out of scope for Level A completion.
  17-/
  18
  19namespace IndisputableMonolith
  20namespace Physics
  21
  22/-- Simple hadrons as quark pairs (e.g., meson = up-bar down). -/
  23structure Hadron where
  24  q1 : RSBridge.Fermion
  25  q2 : RSBridge.Fermion
  26  binding : ℤ := 1
  27
  28noncomputable def composite_rung (h : Hadron) : ℤ :=
  29  RSBridge.rung h.1 + (- RSBridge.rung h.2) + h.3
  30
  31noncomputable def hadron_mass (h : Hadron) : ℝ :=
  32  Constants.E_coh * (Constants.phi ^ (composite_rung h : ℝ))
  33
  34-- Regge trajectory: excited states n=0,1,2,... m_n^2 = n α' φ^{2 r} (r=base rung)
  35noncomputable def regge_mass_squared (r n : ℕ) (alpha_prime : ℝ) : ℝ :=
  36  (n : ℝ) * alpha_prime * (Constants.phi ^ (2 * (r : ℝ)))
  37
  38/-- External certificate seam for Regge slope reporting.
  39This keeps hadron slope provenance explicit (analogous to RG transport seams). -/
  40structure ReggeSlopeCertificate where
  41  source : String
  42  alphaPrime_GeV_inv2 : ℝ
  43  uncertainty_GeV_inv2 : ℝ
  44  uncertainty_nonneg : 0 ≤ uncertainty_GeV_inv2
  45
  46/-- Current external Regge slope placeholder (PDG-facing convention). -/
  47def pdg_regge_slope_cert : ReggeSlopeCertificate where
  48  source := "PDG display placeholder"
  49  alphaPrime_GeV_inv2 := 0.9
  50  uncertainty_GeV_inv2 := 0.1
  51  uncertainty_nonneg := by norm_num
  52
  53/-- Regge slope value consumed by the structural trajectory formulas. -/
  54@[simp] def pdg_regge_slope : ℝ := pdg_regge_slope_cert.alphaPrime_GeV_inv2
  55
  56/-- Equal-Z hadrons are degenerate at leading order. -/
  57theorem hadron_equal_z_degenerate (h1 h2 : Hadron)
  58  (h_same_rung : composite_rung h1 = composite_rung h2) :
  59  hadron_mass h1 = hadron_mass h2 := by
  60  simp [hadron_mass, h_same_rung]
  61
  62/-- Regge mass squared is non-negative. -/
  63theorem regge_mass_squared_nonneg (r n : ℕ) : regge_mass_squared r n pdg_regge_slope ≥ 0 := by
  64  have hphi_pow_nonneg : 0 ≤ Constants.phi ^ (2 * (r : ℝ)) :=
  65    le_of_lt (Real.rpow_pos_of_pos Constants.phi_pos _)
  66  have hslope_nonneg : (0 : ℝ) ≤ pdg_regge_slope := by
  67    norm_num [pdg_regge_slope, pdg_regge_slope_cert]
  68  have hn_nonneg : 0 ≤ (n : ℝ) := by exact_mod_cast (Nat.zero_le n)
  69  have h1 : 0 ≤ (n : ℝ) * pdg_regge_slope := mul_nonneg hn_nonneg hslope_nonneg
  70  have h2 : 0 ≤ (n : ℝ) * pdg_regge_slope * (Constants.phi ^ (2 * (r : ℝ))) :=
  71    mul_nonneg h1 hphi_pow_nonneg
  72  simpa [regge_mass_squared, pdg_regge_slope, mul_comm, mul_left_comm, mul_assoc] using h2
  73
  74/-- Regge trajectory is linear in n. -/
  75theorem regge_linearity (r : ℕ) (n₁ n₂ : ℕ) :
  76    regge_mass_squared r (n₁ + n₂) pdg_regge_slope =
  77    regge_mass_squared r n₁ pdg_regge_slope + regge_mass_squared r n₂ pdg_regge_slope := by
  78  simp [regge_mass_squared]
  79  ring
  80
  81end Physics
  82end IndisputableMonolith
  83