Baryonic Matter Physics: A Deterministic Atom-to-Galaxy Unified Framework for Nuclear Structure, Black Hole Dynamics, and Cosmic Architecture

<b>Unified Curvature Dynamics from Nuclei to Galactic Black Holes (BM Physics)</b><br>This work formalizes a scale-invariant physical mechanism governing nuclear stability, black hole curvature, galactic structure, and large-scale cosmological behavior within the Baryonic Matter (BM) framework. The central result is that <i>mass generates deterministic curvature in the baryonic compression field σ</i>, producing a hierarchy of curvature wells across all physical scales.At the nuclear level, protons generate micro-curvature pockets that merge into a unified compression field. As density increases, this field approaches the <b>Snap Point</b>, the curvature-saturation threshold at which the compression gradient exceeds Coulomb repulsion, locking protons into stable, deterministic geometric arrangements. Nuclear binding is shown to emerge from curvature physics rather than probabilistic force-carrier models.At galactic scales, central black holes represent macro-scale analogues of the same compression mechanism. Galactic rotation curves, spiral arm structure, halo geometry, and long-term orbital stability arise from σ-field curvature gradients and non-linear mass-coupled amplification, removing the need for dark matter or dark energy.The framework provides a continuous, deterministic bridge between quantum, classical, and cosmological physics. It replaces fragmented force categories and speculative components with a single curvature-saturation law governing structure formation from atoms to galaxies._{<strong>Layperson Description </strong>}This paper explains how the same physical mechanism that holds the nucleus of an atom together also shapes entire galaxies. Every proton creates a tiny pocket of curved spacetime. When several protons are packed together in a nucleus, these pockets merge into a stronger curvature field. As this field strengthens, it reaches a limit—the <b>Snap Point</b>—where its inward pull becomes stronger than the electrical repulsion between protons. This locks the nucleus into a stable configuration.The same process happens on a much bigger scale at the center of galaxies, where massive black holes form deep curvature wells that organize stars and spiral arms. Instead of needing dark matter or dark energy, this unified model shows how mass-driven curvature can explain cosmic structure directly.This theory connects the smallest parts of nature with the largest, showing that atoms, black holes, and galaxies are built by one universal rule of curvature and compression.