refl
plain-language theorem explainer
The reflexive equivalence on any vantage category V is obtained by taking the identity functor in both directions and confirming the inverse properties hold by reflexivity. Researchers formalizing the three equivalent vantages in recognition science cite this when building the categorical structure for strain-preserving maps. The construction is a direct definition that applies the identity functor and discharges the inverse conditions via rfl.
Claim. For any vantage category $V$, the reflexive equivalence $Vsimeq V$ is the structure whose forward and inverse functors are both the identity functor on $V$, with the left and right inverse conditions holding by reflexivity of equality on states.
background
A VantageCategory is a structure whose objects are states, whose morphisms are transitions, equipped with identity and composition operations together with the strain functional J that assigns a cost to each state. VantageEquiv between two such categories consists of a pair of functors that are mutually inverse on states and preserve the strain functional. The module sets the three vantages (Inside, Act, Outside) as formally equivalent via functors that preserve J, providing the precise statement that physics, meaning, and qualia are three views of one structure.
proof idea
The definition sets both toFun and invFun to the identity functor supplied by VantageFunctor.identity V. The left_inv and right_inv fields are then filled by the constant function returning rfl, which discharges the required equalities on states by reflexivity.
why it matters
This supplies the reflexive case of VantageEquiv required for the categorical equivalence of the three vantages. It directly supports the module claim that the functors F: Outside → Act → Inside → Outside preserve J, dissolving the hard problem by treating qualia as physics viewed from Inside. The construction closes the reflexive leg of the equivalence relation in the RRF foundation.
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