IndisputableMonolith.Masses.Anchor

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.AlphaDerivation
   4
   5namespace IndisputableMonolith
   6namespace Masses
   7
   8/-!
   9# Canonical Mass Constants — DERIVED from First Principles
  10
  11This module centralises the parameter-free constants described in the mass
  12manuscripts. Everything lives in the `Model` layer; no proofs claim
  13experimental agreement.
  14
  15## DERIVATION CHAIN
  16
  17All sector constants are derived from cube geometry (D=3):
  18
  19### Cube Geometry
  20- `E_total = cube_edges(3) = 3 × 2² = 12` edges
  21- `E_passive = E_total - 1 = 11` passive edges (the "11")
  22- `W = wallpaper_groups = 17` (crystallographic constant)
  23- `A = active_edges_per_tick = 1` (one transition per tick)
  24
  25### Sector Formulas
  26| Sector      | B_pow formula        | B_pow value | r0 formula           | r0 value |
  27|-------------|---------------------|-------------|----------------------|----------|
  28| Lepton      | -(2 × E_passive)    | -22         | 4W - (8 - 2)         | 62       |
  29| UpQuark     | -A                  | -1          | 2W + A               | 35       |
  30| DownQuark   | 2E_total - 1        | 23          | E_total - W          | -5       |
  31| Electroweak | A                   | 1           | 3W + 4               | 55       |
  32
  33## Contents
  34
  35* `E_coh` – bridge coherence energy (φ⁻⁵ eV)
  36* Sector yardsticks `(B_pow, r0)` encoded as powers of two and φ
  37* Fixed rung integers `r_i` per species (charged fermions and bosons)
  38* Charge-based integer map `Z` (matches Paper 1)
  39
  40Downstream modules should import these definitions instead of duplicating
  41literals.
  42-/
  43
  44open IndisputableMonolith.Constants
  45open IndisputableMonolith.Constants.AlphaDerivation
  46
  47namespace Anchor
  48
  49/-! ## First-Principles Building Blocks -/
  50
  51/-- Passive edge count: 12 - 1 = 11 -/
  52abbrev E_passive : ℕ := passive_field_edges D
  53
  54/-- Wallpaper groups: 17 -/
  55abbrev W : ℕ := wallpaper_groups
  56
  57/-- Total cube edges: 12 -/
  58abbrev E_total : ℕ := cube_edges D
  59
  60/-- Active edges per tick: 1 -/
  61abbrev A : ℕ := active_edges_per_tick
  62
  63/-- Coherence energy unit: `E_coh = φ⁻⁵` (dimensionless; multiply by eV externally). -/
  64@[simp] noncomputable def E_coh : ℝ := Constants.phi ^ (-(5 : ℤ))
  65
  66/-- Sector identifiers. -/
  67inductive Sector | Lepton | UpQuark | DownQuark | Electroweak
  68  deriving DecidableEq, Repr
  69
  70/-! ## Sector Constants — DERIVED from Cube Geometry -/
  71
  72/-- Derived powers of two for each sector.
  73    These are NOT arbitrary—they come from cube edge counting. -/
  74@[simp] def B_pow : Sector → ℤ
  75  | .Lepton      => -(2 * (E_passive : ℤ))     -- = -(2 × 11) = -22
  76  | .UpQuark     => -(A : ℤ)                    -- = -1
  77  | .DownQuark   => 2 * (E_total : ℤ) - 1       -- = 2 × 12 - 1 = 23
  78  | .Electroweak => (A : ℤ)                     -- = 1
  79
  80/-- Derived φ-exponent offsets per sector.
  81    These are NOT arbitrary—they come from wallpaper + cube geometry. -/
  82@[simp] def r0 : Sector → ℤ
  83  | .Lepton      => 4 * (W : ℤ) - 6             -- = 4 × 17 - (8 - 2) = 62
  84  | .UpQuark     => 2 * (W : ℤ) + (A : ℤ)       -- = 2 × 17 + 1 = 35
  85  | .DownQuark   => (E_total : ℤ) - (W : ℤ)     -- = 12 - 17 = -5
  86  | .Electroweak => 3 * (W : ℤ) + 4             -- = 3 × 17 + 4 = 55
  87
  88/-! ## Verification: Derived values match expected integers -/
  89
  90theorem B_pow_Lepton_eq : B_pow .Lepton = -22 := by
  91  simp only [B_pow, E_passive, passive_field_edges, cube_edges, active_edges_per_tick, D]
  92  norm_num
  93
  94theorem B_pow_UpQuark_eq : B_pow .UpQuark = -1 := by
  95  simp only [B_pow, A, active_edges_per_tick]
  96  norm_num
  97
  98theorem B_pow_DownQuark_eq : B_pow .DownQuark = 23 := by
  99  simp only [B_pow, E_total, cube_edges, D]
 100  norm_num
 101
 102theorem B_pow_Electroweak_eq : B_pow .Electroweak = 1 := by
 103  simp only [B_pow, A, active_edges_per_tick]
 104  norm_num
 105
 106theorem r0_Lepton_eq : r0 .Lepton = 62 := by
 107  simp only [r0, W, wallpaper_groups]
 108  norm_num
 109
 110theorem r0_UpQuark_eq : r0 .UpQuark = 35 := by
 111  simp only [r0, W, wallpaper_groups, A, active_edges_per_tick]
 112  norm_num
 113
 114theorem r0_DownQuark_eq : r0 .DownQuark = -5 := by
 115  simp only [r0, E_total, cube_edges, D, W, wallpaper_groups]
 116  norm_num
 117
 118theorem r0_Electroweak_eq : r0 .Electroweak = 55 := by
 119  simp only [r0, W, wallpaper_groups]
 120  norm_num
 121
 122/-- Sector yardstick `A_s = 2^{B_pow} * E_coh * φ^{r0}`. -/
 123@[simp] noncomputable def yardstick (s : Sector) : ℝ :=
 124  (2 : ℝ) ^ (B_pow s) * E_coh * Constants.phi ^ (r0 s)
 125
 126end Anchor
 127
 128namespace Integers
 129
 130/-- Generation torsion (global, representation-independent).
 131    τ(0) = 0, τ(1) = E_passive = 11, τ(2) = W = 17 -/
 132@[simp] def tau (gen : ℕ) : ℤ :=
 133  match gen with
 134  | 0 => 0
 135  | 1 => (Anchor.E_passive : ℤ)  -- = 11
 136  | _ => (Anchor.W : ℤ)          -- = 17
 137
 138/-- Verify tau values. -/
 139theorem tau_values : tau 0 = 0 ∧ tau 1 = 11 ∧ tau 2 = 17 := by
 140  simp only [tau, Anchor.E_passive, Anchor.W, passive_field_edges, cube_edges,
 141             active_edges_per_tick, D, wallpaper_groups]
 142  norm_num
 143
 144/-- Rung integers for charged leptons.
 145    e: 2 (baseline), mu: 2 + tau(1) = 13, tau: 2 + tau(2) = 19 -/
 146@[simp] def r_lepton : String → ℤ
 147  | "e"   => 2
 148  | "mu"  => 2 + tau 1  -- = 2 + 11 = 13
 149  | "tau" => 2 + tau 2  -- = 2 + 17 = 19
 150  | _     => 0
 151
 152/-- Verify r_lepton values. -/
 153theorem r_lepton_values : r_lepton "e" = 2 ∧ r_lepton "mu" = 13 ∧ r_lepton "tau" = 19 := by
 154  simp only [r_lepton, tau, Anchor.E_passive, Anchor.W, passive_field_edges,
 155             cube_edges, active_edges_per_tick, D, wallpaper_groups]
 156  norm_num
 157
 158/-- Rung integers for up-type quarks.
 159    u: 4, c: 4 + tau(1) = 15, t: 4 + tau(2) = 21 -/
 160@[simp] def r_up : String → ℤ
 161  | "u" => 4
 162  | "c" => 4 + tau 1  -- = 4 + 11 = 15
 163  | "t" => 4 + tau 2  -- = 4 + 17 = 21
 164  | _   => 0
 165
 166/-- Rung integers for down-type quarks.
 167    d: 4, s: 4 + tau(1) = 15, b: 4 + tau(2) = 21 -/
 168@[simp] def r_down : String → ℤ
 169  | "d" => 4
 170  | "s" => 4 + tau 1  -- = 4 + 11 = 15
 171  | "b" => 4 + tau 2  -- = 4 + 17 = 21
 172  | _   => 0
 173
 174/-- Rung integers for electroweak bosons (structural baseline). -/
 175@[simp] def r_boson : String → ℤ
 176  | "W" => 1
 177  | "Z" => 1
 178  | "H" => 1
 179  | _   => 0
 180
 181end Integers
 182
 183namespace ChargeIndex
 184
 185/-- Integer map used by the anchor relation (Paper 1). -/
 186@[simp] def Z (sector : Anchor.Sector) (Q : ℚ) : ℤ :=
 187  let Q6 : ℤ := (6 : ℤ) * Q.num / Q.den
 188  match sector with
 189  | .Lepton      => (Q6 ^ (2 : ℕ)) + (Q6 ^ (4 : ℕ))
 190  | .UpQuark     => 4 + (Q6 ^ (2 : ℕ)) + (Q6 ^ (4 : ℕ))
 191  | .DownQuark   => 4 + (Q6 ^ (2 : ℕ)) + (Q6 ^ (4 : ℕ))
 192  | .Electroweak => 0
 193
 194end ChargeIndex
 195
 196/-! ## Summary: Parameter-Free Derivation
 197
 198All sector constants trace back to:
 1991. D = 3 (dimension, from T9 linking)
 2002. cube_edges(D) = 12 (hypercube formula)
 2013. active_edges_per_tick = 1 (atomic tick, from T2)
 2024. passive_field_edges = 11 (12 - 1)
 2035. wallpaper_groups = 17 (crystallographic, Fedorov 1891)
 204
 205NO free parameters. NO fitting to mass data.
 206-/
 207
 208end Masses
 209end IndisputableMonolith
 210