Actualize
plain-language theorem explainer
Actualize supplies the concrete map from any configuration to its actualized successor in the modal layer. It advances the input time by eight ticks and returns the zero-cost identity state. Modal physicists cite it when tracing how J-minimization converts possibility branches into definite outcomes. The implementation is a direct one-line wrapper around the identity_config constructor.
Claim. The actualization operator sends a configuration $c$ to the identity configuration whose time coordinate equals $c$.time + 8.
background
Configurations are points in recognition state space carrying a positive real value, a natural-number time coordinate, and a logarithmic bound ensuring physical scale. The cost function is $J(x) = 1/2(x + x^{-1}) - 1$, the unique non-negative cost vanishing only at unity and satisfying the d'Alembert condition plus normalization from T5. The module develops modal operators over these objects. Actualize realizes the selection step that maps a current state to its J-minimizing successor by advancing to the identity attractor eight ticks ahead. This rests on upstream definitions of the identity event (zero J-cost) and integer arithmetic from the foundation modules.
proof idea
The declaration is a one-line definition that applies the identity_config constructor directly to the advanced time value c.time + 8. No tactics or lemmas are invoked inside the body; construction is immediate from the sibling identity_config definition.
why it matters
Actualize defines the operator A used in every theorem of the Actualization module, including the definitions of Contingent and Determined properties and the proofs of automatic collapse and time advancement by eight ticks. In the Recognition Science framework it supplies the concrete selection mechanism from possibility to actuality, consistent with J-uniqueness (T5) and the eight-tick octave (T7). The present form leaves the general argmin over arbitrary possibility sets as future work.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.