The Snap and the Gate

The second paper in this series developed the substrate's temporal structure as a two-scoperecursion: a within-level recursion that saturates and a across-level recursion that opens thenext level. This paper develops the transition between the two — the event at which a levelsaturates and the next is opened — and the single most consequential property of thattransition: the fraction of structure it transmits.The central claim is that this transition is not an actor that chooses what to pass, but athreshold condition whose crossing constitutes the event. Because a condition cannotdiscriminate between inputs, the transmitted fraction is necessarily the same for every input— one fraction, by definition rather than by stipulation. That fraction is the reciprocal of thelevel's prime. We argue that this "one fraction for all inputs, no drift across cycles" isdefinitional within the framework, on two independent grounds: a threshold condition hasno capacity to discriminate, and the transition is prior to time (time being defined as thecount of such transitions), so its definition cannot itself vary in time.From this single definitional commitment, several within-framework results follow asconsequences rather than as separate assumptions. We catalogue the transition'sproperties, including the careful sorting of what the transition reaches (rates and partitionsmade at the event) from what it does not (static coefficients of the action, and emergentvalues produced where a transition-governed rate meets external physics). We then statethe results the framework derives from the fixed fraction — a vacuum-expectation-valueratio, a per-level attenuation, and a dark-to-baryonic ratio — recording each at its honeststatus. Finally we describe what the transition writes at a level: not a bare prime but thecomplete accumulated state crossing the threshold, a distinction whose neglect produced adocumented mis-computation.The empirical anchoring of the results catalogued here is developed in the companionpapers; this paper specifies the mechanism and its consequences.