IndisputableMonolith.Relativity.Analysis
This module assembles asymptotic analysis tools for relativity derivations within Recognition Science. It imports Landau notation for Filter-based big-O predicates and Limits for Mathlib-integrated asymptotics to replace ad-hoc error bounds. Researchers formalizing relativistic expansions would cite it when manipulating O(·) terms in J-cost or phi-ladder contexts. The module achieves its purpose through direct submodule imports rather than new definitions.
claimSupplies Filter predicates for $f = O(g)$ with arithmetic lemmas, plus limit-based asymptotic integration, for error control in relativity expansions.
background
The module establishes the analytic setting for relativity within Recognition Science, where asymptotic bounds support expansions tied to J-cost and the phi-ladder. It draws directly from the Landau submodule, which implements $f ∈ O(g)$ as a proper Filter predicate equipped with arithmetic operations for manipulating asymptotic expressions. The Limits submodule integrates Mathlib's asymptotics library to enforce rigorous O(·) and o(·) notation and eliminate placeholder error bounds.
proof idea
This is a definition module, no proofs. Its structure consists of two module imports that expose Landau notation for big-O predicates and Limits for Filter-based asymptotics, forming a shared utility layer for downstream relativity work.
why it matters in Recognition Science
This module supplies the analytic foundation required by parent theorems in the Relativity domain of the Recognition framework. It enables precise error bounds in derivations that connect to framework landmarks such as the eight-tick octave and D = 3. No specific used-by theorems appear in the current graph, indicating its role as a reusable utility for future relativity results.
scope and limits
- Does not define physical constants or mass formulas.
- Does not contain theorems or proofs of its own.
- Does not address non-asymptotic aspects of relativity.
- Does not depend on J-uniqueness or phi fixed-point results.