IndisputableMonolith.Relativity.Geometry.Manifold
The Manifold module defines a smooth manifold equipped with dimension and coordinate system as the base layer for relativistic geometry. It would be cited by anyone assembling spacetime models inside the Recognition Science framework. The module is purely definitional, importing Mathlib and exposing sibling structures that the parent Geometry aggregator re-exports.
claimA smooth manifold $M$ of finite dimension equipped with a coordinate system.
background
This module sits inside Relativity.Geometry and supplies the manifold substrate used by all subsequent relativity constructions. Its doc-comment states it introduces a smooth manifold with dimension and coordinate system. Sibling declarations include Point, TangentVector, Covector, Spacetime, and index utilities such as timeIndex and spatialIndices.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the manifold primitives re-exported by the Geometry module aggregator, which collects all geometry components for convenient import. It therefore underpins any downstream relativity development that relies on the Recognition Science manifold layer.
scope and limits
- Does not contain theorems or proofs.
- Does not fix a specific dimension or metric.
- Does not reference the J-cost function or phi-ladder.
- Does not import physics constants such as G or alpha.