structural_parallel_certificate

formal source

 224
 225/-- The structural parallel: the number of properties shared between
 226    J-cost and the ζ functional equation. Each is a separately proved fact. -/
 227theorem structural_parallel_certificate :
 228    -- J is symmetric under inversion (like ξ(s) = ξ(1-s))
 229    (∀ (x : ℝ), 0 < x → Cost.Jcost x = Cost.Jcost x⁻¹) ∧
 230    -- J has a unique zero at the fixed point (like RH's critical line)
 231    (Cost.Jcost 1 = 0) ∧
 232    (∀ (x : ℝ), 0 < x → x ≠ 1 → 0 < Cost.Jcost x) ∧
 233    -- J satisfies d'Alembert (which forces zero-line confinement)
 234    SatisfiesDAlembert (fun t => Cost.Jcost (Real.exp t) + 1) ∧
 235    -- The d'Alembert identity governs cost composition
 236    (∀ (x y : ℝ), 0 < x → 0 < y →
 237      Cost.Jcost (x * y) + Cost.Jcost (x / y) =
 238      2 * Cost.Jcost x + 2 * Cost.Jcost y +
 239      2 * Cost.Jcost x * Cost.Jcost y) :=
 240  ⟨fun x hx => Cost.Jcost_symm hx,
 241   Cost.Jcost_unit0,
 242   fun x hx hne => Cost.Jcost_pos_of_ne_one x hx hne,
 243   rs_cost_satisfies_dalembert,
 244   fun x y hx hy => Cost.dalembert_identity hx hy⟩
 245
 246end
 247
 248end PrimeLedgerStructure
 249end NumberTheory
 250end IndisputableMonolith