zenoAntiZenoCrossover
plain-language theorem explainer
The zenoAntiZenoCrossover definition states that Zeno suppression holds for short times with quadratic decay while anti-Zeno linear decay appears at longer intervals. Quantum information theorists studying measurement-induced dynamics in Recognition Science frameworks would reference this distinction. It is supplied as a direct string literal with no further reduction.
Claim. The transition between the Zeno regime (quadratic survival probability for short measurement intervals) and the anti-Zeno regime (linear decay for longer intervals) is determined by the ratio of the measurement rate to the spectral width of the system.
background
In the Recognition Science treatment of quantum measurement, the Zeno effect arises because each measurement commits a ledger entry that resets the system's state. Between measurements the evolution proceeds probabilistically according to the transition probability $P(t) = sin^2(Omega t / 2)$. The module QF-010 derives the suppression of transitions under frequent actualization from the ledger structure. Upstream results supply the Measurement structure as a triple of name, value and error, together with ledger-edge constructions that encode the actualization frequency.
proof idea
The definition is a one-line assignment of the descriptive string that summarizes the crossover behavior.
why it matters
This definition supplies the verbal bridge between the short-time quadratic expansion and the long-time linear regime inside the ZenoEffect module. It supports the derivation of the full quantum Zeno effect from ledger actualization as targeted in QF-010. The parent results on transition probabilities and survival probabilities in the same module rely on this distinction to separate the two dynamical regimes. It touches the open question of how the crossover scale maps onto the phi-ladder rung structure.
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