Stable Matter from Curvature Closure: Electrons, Nucleons, Alpha Particles, Neutrinos, and Dark Matter in the ACORN Framework

We present a geometric classification of matter based on curvature closure within the ACORN (Alternating Curvature Ontology of Nature) framework. Stable matter states arise as closed curvature circulations in five-dimensional SpaceTime$^{+}$, while near-closure and projection effects account for instability, binding, and invisibility.

Within this framework, the electron–proton mass ratio is recovered from integer curvature synchronization, electric charge emerges from conserved holonomy under dimensional projection, and the neutrino is identified as a curvature defect whose action is fixed by the Planck constant. Composite nuclear stability is illustrated by the alpha particle as a higher-order synchronized closure with a small internal binding curvature fraction.

The same principle of curvature closure admits a class of stable, electromagnetically silent states that possess gravitational mass, providing a natural geometric realization of dark matter consistent with galactic rotation curves and gravitational lensing. Dark energy is interpreted as the large-scale open curvature response of the same underlying geometry.

Together, these results establish a coherent ladder of matter and dark matter states classified by curvature closure, recovering known physical behavior without introducing new particles, forces, or postulates.