SemanticCondensationGate
plain-language theorem explainer
The semantic condensation gate definition encodes the query-level semantic admissibility region as the conjunction of entropy exceeding its floor, signature within bounds, attention at most phi cubed, and z at least phi to the 45. Researchers modeling recognition bandwidth control cite this predicate when verifying the critical loading regime. It is introduced as a direct definition by conjunction of the five inequalities.
Claim. The semantic condensation gate is the proposition that entropy exceeds its floor, the signature lies between its minimum and maximum values, attention is bounded above by $phi^3$, and $z$ is at least $phi^{45}$.
background
The Critical Recognition Loading module sketches a control theorem for the operating regime of recognition bandwidth. The central variable is the load ratio rho = R_dem / R_max, with healthy operation restricted to the narrow band rho_min < rho < 1. The actuator operates on the native 8-tick cadence while stability is judged on the 360-tick supervisory horizon given by lcm(8,45). Entropy enters as the total defect of a configuration, per the definition in InitialCondition.entropy, or via the thermodynamic forms S = k beta
proof idea
This is a direct definition that assembles the five inequalities into a single Prop without invoking any lemmas or tactics.
why it matters
The definition completes the full critical-loading condition by adding the semantic admissibility check. It encodes the attention bound at phi^3 and the z threshold at phi^45, which align with the eight-tick octave and the supervisory horizon in the Recognition Science framework. The two extraction theorems that pull out the attention cap and the gap-ready condition demonstrate its immediate utility for deriving component bounds.
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