Classical Maths
The unconditioned geometric foundation. Everything in this section holds prior to any empirical calibration — it is pure geometry, trigonometry, and differential topology. No measurement, no fitted value, no frame-conditioned parameter enters here.
This is the base layer that every other section inherits. The 1/3 : 2/3 partition, the tetrahedral apex angle, the planar invariants, and the invariance proofs all live here. Every value carries a Derived tag.
Contents
| Page | What it establishes | Tag |
|---|---|---|
| Tetrahedral solid-angle partition | Derives θ = 70.5288°, S₊ = 1/3, S₋ = 2/3, and the boundary ratio from 3D observer geometry. | Derived |
| Diffeomorphism invariance | Proves the 2 : 1 boundary partition survives every smooth orientation-preserving coordinate transformation. | Derived |
| Frame-invariant mathematics | Operational handbook. The epistemic ground, the locked execution protocol, and the dimensionless math engine. | Derived |
| Pure mathematical engine | Geometric proofs manual. Solid-angle partitioning, planar invariants, MOTS stability operator, Lyapunov–Schmidt reduction. | Derived |
| Universal slice invariance (Theorem I) | Any information lost from the outer branch across a Cauchy slice is balanced by an equal gain in the inner branch. | Derived |
Every value in this section is fully derivable from first principles. Anyone with the standard background in Euclidean geometry and differential topology can reproduce the derivations and check them independently.
Related. The information-theoretic reading of these invariants is developed in Information-Theoretic Structure. The applications to observational cosmology are in Cosmology / Astronomy.