Mathematical Foundations of Structured Space Theory (SST) — Supplement 4: Cosmological Closure and Hierarchy Derivation

Cosmological Closure of the SST/UPF Framework and Structural Derivation of the Hierarchy Depth

Supplement to:
Mathematical Foundations of Structured Space Theory (SST) — DOI: 10.5281/zenodo.19080507
Structured Space Theory (SST), Version 3 — DOI: 10.5281/zenodo.18787608
Unified Pattern Framework (UPF) — DOI: 10.5281/zenodo.17900825

This supplement extends the Mathematical Foundations of Structured Space Theory (SST) into the cosmological sector and provides a structural derivation of the hierarchy depth within the present FCC/SpS worked realization. It derives four linked results from local FCC lattice geometry and the adjacent-SbS boundary realization: the dark-matter ratio Ω_DM/Ω_b = 75/14, the dark-energy ratio Ω_Λ/Ω_b = 14 with w = −1 by construction, the hierarchy depth k = 19 as the number of independent bond-selecting constraints required to specify a massive p6 pattern, and the baryon-to-photon ratio η = 3/12⁹, reinterpreted as a primordial closure fraction.

Together these results provide a unified cosmological closure of the SST/UPF framework while extending the mathematical foundations into the dark-sector and hierarchy domain.