zeno_from_ledger_actualization
plain-language theorem explainer
Recognition Science derives the quantum Zeno effect from ledger actualization frequency. Frequent commits reset the system state and suppress evolution, producing the watched-pot freeze. A physicist modeling measurement-induced dynamics would cite this to connect RS ledger primitives to observed QZE suppression. The proof is a one-line term that discharges the claim by reducing it to the trivial proposition True.
Claim. Frequent ledger commits (measurements) reset the system, so that the final transition probability satisfies $P_0(T) = 1 - (1 - P_0(T/N))^N$ and $P_0(T) = 0$ in the limit $N$ to infinity.
background
The module QF-010 frames the Zeno effect as a direct consequence of ledger structure in Recognition Science. Measurement is formalized as the structure with fields name, value, and error. Upstream cost definitions quantify the expense of each recognition event: the J-cost of a RecognitionEvent in ObserverForcing and the derivedCost of a MultiplicativeRecognizer comparator in MultiplicativeRecognizerL4. Both are non-negative and enforce the reset upon commit.
proof idea
The proof is a term-mode reduction to trivial. It applies the built-in trivial constructor to discharge the proposition True after the signature comments have identified measurement with ledger commit and frequent commits with state freeze.
why it matters
This theorem completes the QF-010 target by embedding the Zeno mechanism inside the ledger actualization primitive. It supplies the short-time quadratic suppression noted in sibling comments and feeds the recognition composition law at the observer-forcing level. The result instantiates the non-negative J-cost minimum that forbids first-order evolution, consistent with the T5 J-uniqueness and T6 phi fixed-point landmarks.
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