Blind Gate Uniqueness

Abstract

Status blindness reduces the gate equation to pointwise equality with one fixed context section, giving existence and uniqueness without finiteness assumptions.

Theorem 1.1 (Status-blind gates have unique solutions).

$$\begin{array}{r}\forall Context,Entry,Status:\mathrm{Type},\\ D:SelfReadingDeriver(Context,Entry,Status),\\ StatusBlind(D)\Rightarrow \forall context:Context,\\ \exists !handwritten:Entry\to Status,Gate(handwritten,D(context,handwritten)).\end{array}$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/GovernanceFixedPoint/BlindGateUnique.status_blind_gate_has_unique_solution (✓ std3). ∎

Source. Repository-derived.

Commentary.

Factoring the self-reading deriver through the blind lift supplies the context section as a solution.

Pointwise gate agreement then makes every other solution equal to that section by function extensionality.

References

• Truth anchor: D5/S3/ConceptDynamics/GovernanceFixedPoint/BlindGateUnique.status_blind_gate_has_unique_solution
• Dependency: D5/S3/ConceptDynamics/GovernanceFixedPoint/Core