From Brane Geometry to Fundamental Constants

From Brane Geometry to Fundamental Constants This document presents an exploratory version of the Yin–Yang Cosmological Model (YY), understood not as a finished theory, but as a geometric research program in progress. The starting point is a deliberate postulate: all observable physics is the expression of a single tension between two extreme modes of geometric behavior, Yin (concentrating, curving) and Yang (diluting, memory-recording). The 3D reality we observe arises as a finite-thickness brane – the Now (Agora) – where this tension balances, and where particles, fields, and physical constants appear as projections of one underlying structure. The text explores which minimal geometric relations would be required to make this postulate at least numerically plausible. Starting from a reduced set of parameters (the radii of Yin and Yang, the brane thickness, and the discrete slip step) combined with (c,ℏ,kB), the YY model attempts to reproduce and correlate quantities that, in standard physics, are treated as independent: the Planck length and the effective thickness of the Now (δ=127/6 ℓP), the gravitational constant G, the fine-structure constant α, the temperature of the cosmic microwave background (CMB) (TCMB≈2.725 K), and cosmological clock factors associated with expansion. A specific highlight of this article is the proposed geometric resolution of the “Hubble tension”. Instead of introducing new exotic fluids or modifying the standard cosmological dynamics, the YY model interprets the discrepancy between the local value of H0 (distance ladder) and the value inferred from the CMB as the effect of a clock factor C, defined by the embedding of the brane between Yin and Yang. The model distinguishes a “geometric” baseline H0, tied to 1/t0, and shows how measurements performed in regimes with different coupling to the Yin–Yang tension can yield two effective values of H0, approaching the ranges currently associated with the local ladder (∼73 km/s/Mpc) and the CMB (∼68 km/s/Mpc), without changing the underlying coasting-like geometric law. In its current state, the YY model should be read as a conceptual laboratory: an explicit attempt to test whether a single geometric tension, applied to a brane between two hyperspheres, can coherently organize fundamental constants, the CMB, and the Hubble tension within one unified framework.