SemanticCondensationGate
plain-language theorem explainer
SemanticCondensationGate encodes the query-level semantic admissibility region as the conjunction of entropy above its floor, signature inside closed bounds, attention at most phi cubed, and z at least phi to the 45. Researchers assembling critical recognition loading conditions cite this predicate when building IsCriticalRecognitionLoading from bandwidth and entropy data. The definition is assembled as a direct conjunction of the five inequalities.
Claim. The semantic condensation gate holds when $entropyFloor < entropy$, $signatureMin ≤ signature ≤ signatureMax$, $attention ≤ ϕ^3$, and $z ≥ ϕ^{45}$.
background
The Critical Recognition Loading module sketches a control theorem for the operating regime of recognition bandwidth. The load ratio rho equals demanded recognition rate over maximum bandwidth; healthy operation is claimed to lie in the narrow band rho_min < rho < 1. The controller uses the native 8-tick cadence but judges stability on the 360-tick supervisory horizon fixed by lcm(8,45). Entropy is the total defect of a configuration in InitialCondition, or the thermodynamic form beta times average energy plus k ln Z in BoltzmannDistribution, and likewise k_B (ln Z + beta average energy) in PartitionFunction.
proof idea
The definition is the direct conjunction of the five inequalities on entropy, signature, attention, and z.
why it matters
This predicate is assembled into IsCriticalRecognitionLoading and directly supplies the attention cap and gap-ready projections. It fills the control theorem sketch for the operating regime suggested by recognition bandwidth, using the phi-ladder and eight-tick octave from the forcing chain. It supports the structural claim that healthy operation stays inside the sub-saturation band on the 360-tick horizon.
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