IndisputableMonolith.NumberTheory.RiemannHypothesis.AttachmentWithMargin
This module defines the attachment-with-margin predicate on a set R for the Christmas route to the Riemann hypothesis. It encodes the pointwise analytic gap from Riemann-Christmas.tex (eq:attachment). Researchers decomposing attachment errors in the bounded-real function approach would cite it when building the ErrorBudget module. The module contains only definitions and no proofs.
claimLet $R$ be a set. The predicate attachment-with-margin on $R$ holds when the pointwise gap condition from the Christmas attachment equation is satisfied (implied by the corresponding supremum version).
background
The module imports BRFPlumbing, which formalizes the algebraic part of the bounded-real/Schur/Herglotz route: a function $H$ is Herglotz when $0 ≤ Re H$, and its Cayley transform $Θ = (H-1)/(H+1)$ is Schur when $‖Θ‖ ≤ 1$. The attachment-with-margin predicate supplies the one-line analytic gap from Riemann-Christmas.tex expressed pointwise on $R$. This setting feeds the downstream ErrorBudget module, which decomposes the attachment error $‖J_N - J_cert,N‖$ into continuity/Lipschitz and prime-tail budgets.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the attachment-with-margin predicate that ErrorBudget decomposes for the Christmas route to RH. It fills the analytic gap from Riemann-Christmas.tex (eq:attachment) and connects the BRF plumbing upstream to the error-budget analysis downstream.
scope and limits
- Does not prove the Riemann hypothesis.
- Does not contain the supremum version of the attachment predicate.
- Does not address continuity or prime-tail budgets directly.
- Does not define Herglotz or Schur functions.