IndisputableMonolith.Relativity.Analysis
The Relativity.Analysis module supplies rigorous asymptotic and Landau notation tools for derivations in the Recognition Science relativity layer. It replaces informal error bounds with Filter-based predicates for big-O and little-o relations. Physicists modeling relativistic limits or expansions along the phi-ladder would invoke these definitions to keep asymptotic claims machine-checkable. The module achieves this by importing and re-exporting the dedicated Landau and Limits submodules.
claimThe module exposes asymptotic membership $f = O(g)$ as a Filter predicate together with limit operations that integrate Mathlib asymptotics, enabling arithmetic on expressions such as $f(x) = g(x) + o(h(x))$ in relativistic contexts.
background
Recognition Science requires precise asymptotic control when analyzing relativistic phenomena near Berry creation thresholds or along phi-ladder rungs. The imported Landau submodule implements $f ∈ O(g)$ via proper Filter predicates, supplying lemmas for addition, multiplication, and composition of asymptotic classes. The Limits submodule augments this with rigorous $o(·)$ notation and equivalences drawn directly from Mathlib's asymptotics library, replacing placeholder bounds with verifiable Filter statements.
proof idea
This is a definition module with no internal proofs; it simply imports and structures the Landau notation implementation together with the limits integration.
why it matters in Recognition Science
The module supplies the analytic substrate for all subsequent relativity theorems in the IndisputableMonolith, ensuring that asymptotic claims appearing in forcing-chain derivations or spacetime limits remain formally grounded. It directly supports the transition from informal relativistic approximations to machine-verified statements within the T0-T8 chain.
scope and limits
- Does not encode specific relativistic field equations or metrics.
- Does not perform numerical evaluation or approximation of limits.
- Does not extend the notation beyond Filter-based O and o classes.
- Does not introduce new constants or phi-ladder arithmetic.