The Harmonic Ladder

The Harmonic Ladder is a quantized framework for organizing energy-density gradients across physical systems, from atomic orbitals to astrophysical interiors. Defined by a fixed logarithmic stride, it reveals a consistent structure in how nature distributes curvature, and provides a unified scale on which to compare phenomena once thought unrelated.

This paper introduces the ladder’s construction and its empirical foundation. Each rung corresponds to a discrete coherence threshold, many of which are directly observed in spectroscopy, crystallography, and compact-object astrophysics.