Refinement Reflexivity

Abstract

Every concept readout refines itself through the identity forgetting map.

Theorem 1.1 (Every concept readout refines itself).

$$\forall X,B,q:X\to B,\mathrm{Refines}(q,q).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/Refinement/RefinementReflexivity.refinement_reflexive (✓ std3). ∎

Source. Repository-derived.

Commentary.

Refinement is imported from the canonical concept-family module: a coarse readout factors through a finer one by a forgetting map.

For a readout compared with itself, the forgetting map is the identity. Its factorization equation holds by reflexivity, so no duplicate refinement relation or auxiliary runtime type is introduced.

References

• Truth anchor: D5/S3/ConceptDynamics/Refinement/RefinementReflexivity.refinement_reflexive
• Dependency: D5/S3/ConceptDynamics/ConceptJoinUniversal