Foundation Inevitability Structure Upgrade Path

/-- The upgrade path: what needs to happen to make inevitability complete. -/
structure UpgradePath where
  /-- Current state -/
  current_state : String
  /-- Required steps -/
  steps : List String
  /-- Target state -/
  target_state : String

/-- **INEVITABILITY STRUCTURE SUMMARY**

The CPM/cost foundation provides a clean inevitability story:

1. **Cost is unique** (T5): J(x) = ½(x + x⁻¹) - 1
2. **Selection is coercive**: x exists ⟺ defect(x) → 0
3. **Discreteness is forced**: continuous configs can't stabilize
4. **Ledger is forced**: J-symmetry → double-entry
5. **φ is forced**: self-similar discrete → golden ratio
6. **D = 3 is forced**: linking requirements (scaffold)

Any alternative must violate one of these or add parameters.

The remaining work is closing the scaffolded choke points:
- CPM Universality
- Framework Exclusivity
- Dimension Forcing
-/
theorem inevitability_structure_summary :
    closed_count = 1 ∧ scaffold_count = 3 := by
  exact ⟨rfl, rfl⟩

/-- **RS CORE CLAIM**: The Inevitability Theorem.

Any alternative zero-parameter framework that derives observables
must either:
1. Reduce to RS (same cost, same selection, same structure), OR
2. Violate at least one necessity gate

This is the "no alternatives" claim made precise.

    **Proof structure**:
    1. By excluded middle, either (F.cost = RS.cost ∧ F.selection = RS.selection) or not.
    2. If not, then (F.cost ≠ RS.cost ∨ F.selection ≠ RS.selection).
    3. If F.cost ≠ RS.cost, then F violates gate_cost_uniqueness.
    4. If F.selection ≠ RS.selection, then F violates gate_selection_rule.
    5. In either case, ∃ g ∈ all_gates such that violates_gate F g.

    **STATUS**: THEOREM (logical reduction to gates)
    **IMPORTANCE**: This is the central uniqueness theorem of Recognition Science. -/
theorem inevitability (F : AlternativeFramework)
    (h_zero : zero_parameter F)
    (h_obs : F.derives_observables) :
    (F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection) ∨
    (∃ g ∈ all_gates, violates_gate F g) := by
  by_cases h_rs : (F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection)
  · left; exact h_rs
  · right
    -- h_rs : ¬(F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection)
    -- Split on whether costs match
    by_cases h_cost : F.cost = RS_framework.cost
    · -- Costs match, so selection must differ
      have h_sel : F.selection ≠ RS_framework.selection := by
        intro h_sel_eq
        exact h_rs ⟨h_cost, h_sel_eq⟩
      use gate_selection_rule
      constructor
      · simp [all_gates]
      · unfold violates_gate
        simp [gate_selection_rule, h_sel]
    · -- Costs differ
      use gate_cost_uniqueness
      constructor
      · simp [all_gates]
      · unfold violates_gate
        simp [gate_cost_uniqueness, h_cost]

/-- Gate 6: Dimension Forcing -/
def gate_dimension : NecessityGate := {
  name := "D = 3 Forcing"
  proven := false  -- Scaffold: requires linking + gap-45 proof
  violation_meaning := "Non-trivial linking in D ≠ 3"
}

/-- Choke Point 1: Universality of CPM -/
def choke_universality : ChokePoint := {
  name := "CPM Universality"
  status := "scaffold"  -- Labeled scaffold in spec
  consequence := "CPM selection is the ONLY selection mechanism"
}

/-- Choke Point 3: Exclusivity of RS -/
def choke_exclusivity : ChokePoint := {
  name := "Framework Exclusivity"
  status := "scaffold"  -- Labeled scaffold in spec
  consequence := "No alternative zero-parameter framework exists"
}