actualize_valid
plain-language theorem explainer
Actualization maps every configuration to one whose value is strictly positive. Modal logicians in the Recognition Science setting cite this to guarantee that the selection operator preserves validity when moving from possibility to actuality. The proof is a one-line simplification that unfolds Actualize directly to the identity configuration.
Claim. For every configuration $c$ in recognition state space, the actualized successor satisfies $v > 0$ where $v$ is the value component of the configuration produced by the J-minimizing map.
background
Config is a structure consisting of a positive real value (generalizing bond multiplier), a natural-number time coordinate in ticks, and a log-bound constraint ensuring physical scale. Actualize is the selection map that sends a configuration to its J-minimizing successor; in the present development it is realized by identity_config, which places the state at value 1 (the J-cost minimum). The identity event from ObserverForcing supplies the canonical zero-cost point that Actualize targets.
proof idea
The proof is a one-line wrapper that applies simp to the definitions of Actualize and identity_config, reducing the positivity claim to the fact that the identity configuration carries value 1.
why it matters
The lemma supplies the well-definedness step for the actualization operator A. It is invoked directly by A_well_defined and by the adjoint monotonicity theorem in the Actualization module. It closes the modal link between possibility and the J-minimizer, aligning with the T5 uniqueness of J and the forcing chain that selects the identity attractor.
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