A Cycle-Projection Ontology of Mass, Distance, and Structure: From Atomic Boundaries to Galactic Halos

This paper develops a cycle-projection framework whose central purpose is to separate physical process from observational chart. Standard physics often begins from observables already separated into mass, distance, field, force, particle, and spacetime. Here, these quantities are treated as regime-dependent readings of a single underlying process: a boundary-cycle irruption characterized by one full-cycle action \(h\), one cycle period \(T_p\), and one propagation length \(L_p=cT_p\).

The primitive cycle energy is
\[
E_{\rm tot}=\frac{h}{T_p}.
\]
Physical distance is defined operationally by cycle-counted propagation, while the Aiónic projection variable \(x\) denotes the effective number of primitive cycle-energy units composing the structure. The central energy partition is 
\[
E=\frac{h}{T_p}x =E_{\rm core}+m_{\rm obs}c^2.
\]
As a concrete consequence, the proton radius is obtained as the Euclidean projection of the non-observable \(E_{\rm core}\) boundary:
\[
r_p^{\rm eucl}
=
\frac{2}{\pi}\frac{h}{m_pc}
=
0.841235641483\ {\rm fm},
\]
while the observed proton mass is the asymptotic projection extending from that boundary toward infinity.
Thus Einstein's mass--energy relation is retained as the observable projected sector, but it is not identified with the full ontological energy. The missing sector is the confined core reservoir.

Within this framework, Euclidean geometry is retained only as a weak-field observational chart, and Maxwellian field-current dynamics is the mechanism by which projected structure becomes physically manifest. Matter is therefore modeled not as an ensemble of point-like corpuscles, but as boundary-active field-current structure with observable centers, extended projections, and regime-dependent closure.

The same grammar is applied across scales. In the atomic and nuclear regimes, electronic modes are treated as boundary-coupled closures rather than primitive point particles. In the gravitational regime, Newtonian dynamics is recovered in weak field, the Mercury correction appears as the first nonlinear near-source residue of shared projected energy, and halo-like behavior is interpreted as a large-radius regime of projected mass rather than as an immediately separate matter ontology.

The framework treats established physics as a high-precision observational map, not as a target for rejection. Its central methodological claim is that reproducible observables are stable outputs of process--lens couplings, not automatically ontological primitives.
The task of the theory is therefore to recover the physical process beneath the observational charts.