WindowLeakageBound
plain-language theorem explainer
WindowLeakageBound defines the predicate asserting that localization error from restricting analysis of the zeta function to a finite rectangular region R is controlled by a nonnegative scalar E_win. Researchers decomposing attachment error in the Christmas route to the Riemann Hypothesis would cite this predicate when assembling the three-budget hypothesis for attachmentWithMargin_of_threeBudgets. The definition is a direct conjunction of nonempty region and nonnegative error bound with no further lemmas.
Claim. The predicate WindowLeakageBound holds for a region $R subset mathbb{C}$ and error bound $E_{win}$ precisely when $R$ is nonempty and $E_{win} geq 0$.
background
The module decomposes the attachment error norm of J_N minus J_cert,N into three separately verifiable budgets: det2 Lipschitz continuity, prime-tail truncation, and window leakage. Window leakage isolates the contribution arising when the contour or sum is restricted to a finite rectangle R inside the half-plane Re s greater than sigma_0. The module imports AttachmentWithMargin and relies on upstream structures including PrimitiveDistinction.from (seven axioms to four structural conditions), UniversalForcingSelfReference.for (meta-realization orbit axioms), CirclePhaseLift.and (explicit log-derivative bound M), and PhiLadderLattice.that (phi-ladder Poisson summation hypothesis).
proof idea
This is a definition whose body is the conjunction R.Nonempty and 0 leq E_win. No lemmas or tactics are invoked; the predicate serves directly as a hypothesis interface for the window component inside the three-budget decomposition.
why it matters
The definition supplies the window-leakage budget required by attachmentWithMargin_of_threeBudgets to conclude attachment-with-margin. It corresponds to the localization term in the Christmas-paper decomposition (Riemann-Christmas.tex, eq:attachment and Lemma attachment-error-decomp). Within Recognition Science it supports error control steps that sit between the phi-ladder lattice sums and the final verification of the Riemann Hypothesis via the forcing chain T0-T8.
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