KThetaFailureFloorHypothesis
plain-language theorem explainer
KThetaFailureFloorHypothesis encodes the assumption that every gate failing the balanced phase condition at scale n incurs cost at least KTheta. Researchers bounding phase visibility under stable budgets cite it to accumulate minimal total failure cost. The declaration is introduced as a structure whose single field directly imports the GateFails predicate and the uniform floor constant.
Claim. Let $n\in\mathbb{N}$ and $\mathrm{costOf}:\mathbb{N}\to\mathbb{R}$. The hypothesis asserts $\forall c,\,\neg\mathrm{HitsBalancedPhase}(n,c)\implies K\Theta\le\mathrm{costOf}(c)$.
background
The module studies conditions under which finite phase invisibility cannot persist when a stable unresolved-phase budget exists and failed gates obey a uniform cost floor. GateFails holds precisely when a gate does not hit the balanced square-budget phase. KTheta is the uniform failure floor imported from UniformFailureFloor at the Recognition Science scale.
Upstream results supply the eight-tick phases (periodic with period $2\pi$) and the active edge count $A=1$ that fix the dimensionless units in which the floor is stated. The module doc states that the actual floor theorem is kept explicit as this hypothesis so that budget arithmetic can be applied without constructing the subset-product divisor.
proof idea
This is a structure definition. The single field directly encodes the floor condition using the imported GateFails predicate; no lemmas or tactics are applied.
why it matters
The hypothesis supplies the floor interface to BoundedVisibilityEngine, to the theorem that failed gate counts remain bounded by the stable budget at KTheta, and to the breakthrough result that some admissible gate must hit the balanced phase. It closes the interface between the uniform failure floor at the eight-tick scale and the budget arithmetic that prevents persistent invisibility in the Recognition framework.
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