Analytic Resolution of the Dark Sector: A Zero-Parameter Geometric Derivation of Dark Matter, Dark Energy, and the Missing Baryon Problem

The Standard Model of Cosmology (\LambdaCDM) provides an exceptionally precise phenomenological description of the universe. However, the ontological nature of the Dark Sector—specifically Dark Matter and Dark Energy—remains a subject of extensive investigation, often modeled via independent exotic particles or scalar fields. This manuscript proposes a complementary analytic derivation through the Connecting Thread Theory (TBP), utilizing a zero-free-parameter framework within a 6-Dimensional topological manifold.

Rather than postulating new particulate entities, the framework evaluates the Dark Sector as deterministic geometric consequences of spatial topology and dimensional reduction. Dark Matter is analytically derived as the cross-interaction tension between the 6D total manifold and the 4D spacetime projection, converging at an observable metric of 26.68484...%. Dark Energy is evaluated not as a repulsive fluid, but as the residual factual energy capacity of the universe's active loop circuit after inertial symmetry breaking, yielding a deterministic ratio of 68.67828...%.

Furthermore, the framework introduces a Volumetric Tensor Distortion (\mathcal{V} = 0.036) to account for optical lensing biases in 4D observational instruments. By applying these exact spatial metrics, the physical ordinary matter is derived at 4.447...%. The fractional deviation of 0.45% between this geometric limit and the \LambdaCDM empirical estimate (4.9%) offers a rigorous analytical resolution to the "Missing Baryon Problem," aligning precisely with late-universe luminosity observations. This manuscript demonstrates that the cosmological energy budget can be deduced coherently from first principles of spatial architecture.