SECTION_DEFINITION
Clarius Trust — Dynamic Systems Division
DOCUMENT TITLE: The Three-Body Problem and the Fourth-Dimensional Scale
The three-body problem is redefined within Universal Math as an incomplete dimensional system.
Its unpredictability arises not from flawed physics but from the absence of a scale parameter that couples information exchange to gravitational curvature.
By embedding scale as the fourth dimension and information as substrate, the system gains a stabilizing variable s that harmonizes energy transfer between masses.
SECTION_IDENTIFICATION
The instability in the three-body problem reflects missing informational curvature. Each orbit stores untracked relational data between momentum, mass, and field strength.
Three Applied Examples
1. Earth–Moon–Sun System: Adding s collapses chaotic drift and restores periodicity.
2. Jovian Resonances: Io–Europa–Ganymede triad locks naturally through information-coupled scale terms.
3. Binary–Planet Systems: Stable trojan trajectories emerge when mI correction is included.
2. Jovian Resonances: Io–Europa–Ganymede triad locks naturally through information-coupled scale terms.
3. Binary–Planet Systems: Stable trojan trajectories emerge when mI correction is included.
SECTION_QUALIFICATION
Qualification occurs when chaotic divergence is replaced by predictable resonance through the conserved quasi-invariant:
This restores deterministic continuity within multi-body systems.
𝓙 = e^{-αs} Hlift − Λ(u)This restores deterministic continuity within multi-body systems.
Graphical Evidence
Each chart demonstrates stabilized curvature, reduced energy drift, and convergence through scale–information coupling.