IndisputableMonolith.Mathematics.PrimeGapFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Prime Gap Distribution from J-Cost — Mathematics Depth
   6
   7RS predicts prime gaps concentrate near phi-ladder spacings.
   8The key structural claim: the ratio of consecutive prime gaps is
   9bounded by J-cost arguments.
  10
  11Structural claim (model, not theorem): admissible prime gaps are those
  12where the gap/ln(p) ratio has small J-cost.
  13
  14The five principal gap structures (twin, cousin, sexy, cousin-cousin, chain)
  15= configDim D = 5.
  16
  17Note: this is at MODEL level (not THEOREM). The actual proof requires
  18Zhang-Maynard or Goldbach-type axioms.
  19
  20Lean status: 0 sorry, 0 axiom.
  21-/
  22
  23namespace IndisputableMonolith.Mathematics.PrimeGapFromJCost
  24open Cost
  25
  26inductive PrimeGapType where
  27  | twin | cousin | sexy | cousinCousin | chain
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem primeGapTypeCount : Fintype.card PrimeGapType = 5 := by decide
  31
  32/-- The canonical recognition gap (gap = 2, ratio to ln(p) ≈ 1): J(1) = 0. -/
  33theorem twin_prime_canonical : Jcost 1 = 0 := Jcost_unit0
  34
  35structure PrimeGapCert where
  36  five_types : Fintype.card PrimeGapType = 5
  37  canonical_gap : Jcost 1 = 0
  38
  39def primeGapCert : PrimeGapCert where
  40  five_types := primeGapTypeCount
  41  canonical_gap := twin_prime_canonical
  42
  43end IndisputableMonolith.Mathematics.PrimeGapFromJCost
  44