Functional Form of Gravitational Acceleration in Hierarchical Interaction Theory (HIT v3.7.1)

We propose a closed-form analytical expression for gravitational acceleration g(r) that describes dynamics from solar systems to galaxy clusters without introducing dark matter or a cosmological constant. The formula is derived from the principles of hierarchical statistics and holographic projection. This preprint serves to fix the functional form and establish priority of the proposal. The full ontological derivation (tick ontology, integer geometry) will be presented in a subsequent publication.

This document serves as a timestamped record of the mathematical form of the HIT v3.7.1 gravity equation. The specific functional dependence on y, including the logarithmic correction term in the denominator, is proposed here as a fundamental law of hierarchical interaction. 

The ontological basis of this formula—specifically the derivation from tick-based ontology, continuous hierarchy principles, and the holographic boundary condition—is reserved for a detailed theoretical publication.