IndisputableMonolith.Relativity.Calculus
Relativity.Calculus supplies the differential infrastructure for spacetime tensor operations. It imports the Derivatives submodule that defines the standard basis vector e_μ and related derivative structures. The module is imported by four downstream relativity components to support metric, geodesic, and post-Newtonian calculations. Its content consists entirely of definitions with no theorems or proofs.
claimThe module introduces the standard basis $e_μ$ and derivative operators $∂_μ$ acting on the spacetime metric $g_{μν}$ and its derived tensors.
background
The module sits inside the Relativity domain of Recognition Science and imports only the Derivatives submodule. That submodule supplies the standard basis vector $e_μ$ used for coordinate expansions of tensors. The local setting is a pseudo-Riemannian manifold equipped with metric $g_{μν}$, where ordinary and covariant derivatives are required for geodesic equations and curvature computations.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds StaticSpherical, FRWMetric, NullGeodesic, and Metric1PN. NullGeodesic uses it to implement $dx^μ/dλ$ with $g_{μν} dx^μ dx^ν = 0$ for light propagation and lensing. Metric1PN relies on it for post-Newtonian potentials. It therefore supplies the shared calculus layer for all metric-based calculations in the framework.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not define specific spacetime metrics or solutions.
- Does not perform numerical evaluations or physical predictions.
- Limits scope to algebraic and differential definitions only.