IndisputableMonolith.Relativity.Analysis.Landau
The Landau module supplies hypothesis classes for composition bounds on big-O notation in asymptotic analysis. It extends the Limits module to handle rigorous error term operations under Mathlib filters. Researchers deriving perturbative expansions in relativity cite it for bounding remainders. The module structure consists of definitions and facts for addition, multiplication, and composition of big-O classes.
claimHypothesis class capturing composition bounds for big-O: if $f = O(g)$ and $g = O(h)$ then $f = O(h)$ (and similarly for addition and scalar multiplication) in the filter sense.
background
This module sits inside Relativity.Analysis and imports Mathlib together with the Limits module. Limits integrates Mathlib's asymptotics library, replacing placeholder error bounds with proper Filter-based definitions for O(·) and o(·) notation. The module itself introduces hypothesis classes that encode how these big-O terms compose under the usual algebraic operations.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module is imported by the parent Analysis module, which lists Landau as the provider of big-O notation for error bounds alongside Limits for continuity and limit theorems. It supplies the algebraic closure properties needed for rigorous remainder tracking in relativity derivations.
scope and limits
- Does not implement concrete big-O instances for specific functions.
- Does not cover little-o notation or higher-order asymptotics.
- Does not include numerical verification or convergence-rate estimates.
- Does not address multi-variable or vector-valued extensions.