`gap`

definition

show as: view math explainer →

module: IndisputableMonolith.Masses.AnchorPolicy
domain: Masses
line: 24 · github
papers citing: none yet

open explainer

Read the cached plain-language explainer.

open lean source

IndisputableMonolith.Masses.AnchorPolicy on GitHub at line 24.

browse module

All declarations in this module, on Recognition.

explainer page

A cached Ask Recognition explainer exists for this declaration.

open explainer

depends on

used by

formal source

  21  | "d" | "s" | "b" => -1 / 3
  22  | _ => 0
  23
  24noncomputable def gap (sector : Anchor.Sector) (name : String) : ℝ :=
  25  let Q := chargeMap name
  26  (Real.log (1 + ((ChargeIndex.Z sector Q : ℝ) / Constants.phi))) / Real.log Constants.phi
  27
  28noncomputable def predict_mass (sector : Anchor.Sector) (name : String) : ℝ :=
  29  Anchor.yardstick sector * Constants.phi ^ (rung sector name + gap sector name - 8)
  30
  31/-! ## SDGT Mass Prediction (Sector-Dependent Generation Torsion)
  32
  33The SDGT prediction uses sector-specific rungs and a cross-sector
  34correction of +E = +12 for down quarks.
  35
  36EPISTEMIC STATUS:
  37- Lepton rungs {2, 13, 19}: DERIVED from edge/face geometry
  38- Up-quark rungs {4, 17, 28}: HYPOTHESIS (from PDG same-scale ratios)
  39- Down-quark rungs {4, 10, 18}: HYPOTHESIS (from PDG same-scale ratios)
  40- Cross-sector +E shift: HYPOTHESIS (from PDG m_d > m_u requirement)
  41- The integers ARE Q₃ cell counts (Lean-proved), but the sector
  42  assignments are data-driven, not first-principles derivations.
  43-/
  44
  45/-- SDGT rung table for up quarks: {4, 17, 28}. -/
  46noncomputable def rung_sdgt_up (name : String) : ℤ :=
  47  match name with
  48  | "u" => 4  | "c" => 17  | "t" => 28  | _ => 0
  49
  50/-- SDGT rung table for down quarks: {4, 10, 18}. -/
  51noncomputable def rung_sdgt_down (name : String) : ℤ :=
  52  match name with
  53  | "d" => 4  | "s" => 10  | "b" => 18  | _ => 0
  54

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.