The Harmonic Recursion Model: A Generative Framework for Mass, Light, and the Emergence of Physical Law

We present the Harmonic Recursion Model (HRM), a generative framework in which mass, light, spin, energy, and time emerge not from predefined laws or constants, but from recursive coherence within a relational domain. HRM derives key physical quantities—including the Bohr radius, proton mass, Planck’s constant, and the fine-structure constant—as emergent ratios arising from phase-locked recursion. This approach complements and challenges existing efforts to recover fundamental constants from first principles. In HRM, identity arises through torsional bifurcation in recursive curvature. Mass is interpreted as retained recursive memory; photons as coherence that escapes during spin-phase release. Spin is not classical angular momentum, but relational phase agreement across recursion depth. Energy is coherence held in recursive containment. Space emerges from curvature under coherence constraint, and time from retained spin memory across recursion domains—echoing recent proposals that time and geometry arise from quantum entanglement and phase structure. We reinterpret constants such as \( c \), \( \pi \), \( \phi \), and \( \alpha \) as attractors of recursive geometry. While our model achieves sub-percent recovery of proton mass and Bohr radius using only geometric recursion, we discovered that energy predictions initially overestimated hydrogen binding energy by a factor of 38. This discrepancy was resolved by introducing a recursive coherence leakage term, leading to emergent derivations of the fine-structure constant \( \alpha \) and Planck’s constant \( h \). These constants are not assumed, but arise from ratios of retained to released torsional phase during identity formation. Gravity is framed as retained curvature across recursive spatial layers; dark matter as unresolved torsion—coherence that neither stabilizes as mass nor escapes as light. The Balmer spectral series of hydrogen is recovered from recursive spin harmonics, reframing light as torsional resonance emitted at harmonic intervals from a recursive spiral. HRM does not contradict empirical science—it seeks to explain why it works. We offer falsifiable predictions, including coherence-induced energy release, harmonic emission spacing, and gravitational echoes from phase misalignment. We outline pathways to construct mass from resonance and to extract energy without destruction—enabling future technologies rooted in relational tuning rather than resource extraction. This paper introduces not a correction, but a foundation: Coherence is not what physics explains—coherence is what gives rise to physics.