gate_dimension

formal source

 105}
 106
 107/-- Gate 6: Dimension Forcing -/
 108def gate_dimension : NecessityGate := {
 109  name := "D = 3 Forcing"
 110  proven := false  -- Scaffold: requires linking + gap-45 proof
 111  violation_meaning := "Non-trivial linking in D ≠ 3"
 112}
 113
 114/-- All necessity gates. -/
 115def all_gates : List NecessityGate :=
 116  [gate_cost_uniqueness, gate_selection_rule, gate_discreteness,
 117   gate_ledger, gate_phi, gate_dimension]
 118
 119/-! ## The Alternative Framework Structure -/
 120
 121/-- An alternative framework to RS. -/
 122structure AlternativeFramework where
 123  /-- The cost functional -/
 124  cost : ℝ → ℝ
 125  /-- The selection rule -/
 126  selection : ℝ → Prop
 127  /-- Number of free parameters -/
 128  parameters : ℕ
 129  /-- Whether it derives observables -/
 130  derives_observables : Bool
 131
 132/-- The RS framework. -/
 133noncomputable def RS_framework : AlternativeFramework := {
 134  cost := LawOfExistence.J
 135  selection := fun x => LawOfExistence.defect x = 0
 136  parameters := 0
 137  derives_observables := true
 138}