validMoves
plain-language theorem explainer
The definition supplies the set of propositions that can be verified next without contradicting the verified history in a proof state. Modelers of consciousness in Recognition Science cite it when formalizing free will as selection among consistent future paths. The definition is realized by a direct set comprehension that retains only those unverified propositions satisfying the consistency predicate.
Claim. For a proof state $s$, the valid moves are the set of propositions $p$ in the unverified component of $s$ such that $p$ is consistent with the verified component of $s$.
background
A proof state consists of three disjoint sets of propositions: the verified set representing the immutable past, the current proposition under verification, and the unverified set representing potential futures. The module models consciousness as the verification cursor advancing from past through present into future, with free will realized as selection among paths that preserve ledger balance.
proof idea
The definition is a one-line set comprehension that intersects the unverified set with the subset of propositions satisfying the isConsistent predicate relative to the verified history.
why it matters
This definition underpins the free_will_exists theorem and the NavigationPoint structure, which formalize choice at points where multiple consistent futures exist. It fills the free will postulate in the RRF consciousness model, where consciousness selects among valid moves to balance the recognition ledger. The construction touches the open question of formalizing the choice operator itself.
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