Nested-Space Cosmology: The Geometry of a Universe

Nested-Space Cosmology (NSC) investigates whether one inherited geometric law can connect nested regions, their exchange of energy across event horizons, and the quantities measured by an interior observer. The foundation rests on five openly declared geometric axioms (A0-A4): least-resistance minimization of a 1D generator stretch cost plus enclosing compression work; a 1D spatial seed plus an inherited compression offset (time) generating a closed circle and sphere; the edge-on harmonic pendulum R(tau)=R0 cos(omega tau) crossing 0 smoothly into a negative, orientation-flipped region; a moving wavelength band bounded by a Planck cutoff and an absolute-zero horizon; and rooms bounded by an outer birth valve and inner black-hole valves on a closed vortex-diffusion ring. Section 9 presents the axiom-to-theorem non-local atlas; Appendix A preserves the full technical record. Code and reproducible tests: https://github.com/kodareken/nested-space-cosmology (commit 460ca87). Foundation Edition, version 0.27.1 (3 November 2026): the 21-page Foundation Edition (commit 460ca87), condensed from the earlier 260-page edition; the full earlier edition remains available as the previous version of this record. Douglas Ek developed this work with computational and drafting assistance from Google Gemini, which interpreted and implemented his geometric ideas.