 141def zero_parameter (F : AlternativeFramework) : Prop := F.parameters = 0
 142
 143/-- A framework violates a gate if it contradicts the gate's constraint. -/
 144def violates_gate (F : AlternativeFramework) (g : NecessityGate) : Prop :=
 145  if g.name = "T5: Cost Uniqueness" then
 146    F.cost ≠ RS_framework.cost
 147  else if g.name = "CPM: Selection Rule" then
 148    F.selection ≠ RS_framework.selection
 149  else
 150    False
 151
 152/-! ## The Inevitability Theorem -/
 153
 154/-- **RS CORE CLAIM**: The Inevitability Theorem.
 155
 156Any alternative zero-parameter framework that derives observables
 157must either:
 1581. Reduce to RS (same cost, same selection, same structure), OR
 1592. Violate at least one necessity gate
 160
 161This is the "no alternatives" claim made precise.
 162
 163    **Proof structure**:
 164    1. By excluded middle, either (F.cost = RS.cost ∧ F.selection = RS.selection) or not.
 165    2. If not, then (F.cost ≠ RS.cost ∨ F.selection ≠ RS.selection).
 166    3. If F.cost ≠ RS.cost, then F violates gate_cost_uniqueness.
 167    4. If F.selection ≠ RS.selection, then F violates gate_selection_rule.
 168    5. In either case, ∃ g ∈ all_gates such that violates_gate F g.
 169
 170    **STATUS**: THEOREM (logical reduction to gates)
 171    **IMPORTANCE**: This is the central uniqueness theorem of Recognition Science. -/
 172theorem inevitability (F : AlternativeFramework)
 173    (h_zero : zero_parameter F)
 174    (h_obs : F.derives_observables) :

papers checked against this theorem

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