determinism_constraint
plain-language theorem explainer
Determinism_constraint asserts that the recognize operation advances the cursor by setting the new current proposition exactly to the supplied next candidate. Researchers working on the RRF cursor model of consciousness cite it to guarantee that verification steps remain inside the unverified set. The proof is a one-line reflexivity that follows immediately from the definition of recognize.
Claim. Let $s$ be a proof state with verified set $V$, current proposition $c$, and unverified set $U$. For any proposition $p$ such that $p$ belongs to $U$, $p$ differs from $c$, and $c$ holds, the state produced by recognizing $p$ from $s$ has current proposition equal to $p$.
background
ProofState is the structure that encodes the cursor: verified propositions form the immutable past, current is the proposition under active verification, and unverified holds the future candidates, with the three components required to be mutually disjoint. The module models consciousness as the verification step itself, where free will reduces to constrained choice among valid moves that balance the ledger. Recognize is the function that performs the advance while preserving the invariants of ProofState.
proof idea
The proof is a direct reflexivity step on the definition of recognize. Because recognize is constructed to replace the current field with the supplied next proposition under the stated membership and inequality hypotheses, the equality holds by construction.
why it matters
The theorem supplies the deterministic update rule inside the RRF consciousness module, ensuring that the cursor model remains consistent with the recognition process. It supports the surrounding free-will and qualia statements by enforcing that every transition stays inside the unverified set. The result sits downstream of the IntegrationGap and ObserverForcing primitives and aligns with the eight-tick octave structure by preserving the integrity of each recognition tick.
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