IndisputableMonolith.Relativity.Calculus
The Relativity.Calculus module supplies the differential calculus layer for spacetime calculations in the Recognition framework by importing the Derivatives submodule. It equips coordinate-based work with the standard basis vector e_μ. Researchers building gravitational models or geodesic equations cite it as the shared foundation. The module is a thin import wrapper containing no internal definitions or proofs.
claimStandard basis vectors $e_μ$ and associated derivative operators on the tangent space of four-dimensional spacetime.
background
The module sits in the Relativity domain and performs a single import of IndisputableMonolith.Relativity.Calculus.Derivatives. That submodule's doc-comment identifies its core object as the standard basis vector $e_μ$. No additional definitions appear in the present module; the theoretical setting is the application of Recognition Science differential geometry to metric-based physics, with the imported basis serving as the coordinate foundation for all downstream relativity work.
proof idea
This is a definition module, no proofs. It consists solely of the import statement that re-exports the Derivatives submodule.
why it matters in Recognition Science
The module is imported by Compact.StaticSpherical, Cosmology.FRWMetric, Geodesics.NullGeodesic (which implements null geodesics $dx^μ/dλ$ subject to $g_{μν} dx^μ dx^ν = 0$ for lensing and time delays), and PostNewtonian.Metric1PN. It therefore supplies the common calculus substrate required by every metric-dependent development in the relativity section.
scope and limits
- Does not define or prove properties of any metric tensor.
- Does not introduce the J-cost, phi-ladder, or forcing-chain objects.
- Does not contain any theorem statements or Lean proofs.
- Does not specify coordinate charts or connection coefficients.