IndisputableMonolith.Relativity.Calculus
The Relativity.Calculus module supplies differential calculus infrastructure for spacetime calculations within Recognition Science. It imports the Derivatives submodule that defines the standard basis vector e_μ. Researchers deriving null geodesics, FRW metrics, or post-Newtonian expansions cite this module for coordinate manipulations. This is a definition module with no proofs.
claimThe module provides the differential calculus framework on the spacetime manifold equipped with the standard basis $e_\mu$ in the tangent space.
background
This module belongs to the Relativity domain and imports only IndisputableMonolith.Relativity.Calculus.Derivatives. The upstream doc-comment states that Derivatives supplies the 'Standard basis vector e_μ.' The local setting is coordinate-based differential geometry supporting derivations of relativistic effects from the J-cost and phi-ladder structures of the parent framework.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module is imported by StaticSpherical, FRWMetric, NullGeodesic, and Metric1PN. NullGeodesic uses it as foundation for computing gravitational lensing deflection angles and time delays; Metric1PN uses it for post-Newtonian potentials. It fills the calculus layer required by the T8 spatial-dimension and geodesic constructions in the forcing chain.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not define spacetime metrics or curvature tensors.
- Does not implement physical predictions such as lensing angles.
- Does not reference the Recognition Composition Law or phi-ladder mass formula.