Sector Paper VI - Prediction of Ultra‑Low‑Density Planets and Forced 5-3 Resonance in the TOI‑791 System

SECTOR PAPER VI — PREDICTION OF ULTRA‑LOW‑DENSITY PLANETS AND FORCED 5:3 RESONANCE IN THE TOI‑791 SYSTEM Sector Paper VI presents the first full sparse‑regime planetary prediction derived from the Unified Information Substrate, demonstrating how δI‑correlation geometry forces the emergence of ultra‑low‑density planetary envelopes and stabilises non‑classical orbital resonances. The paper applies the substrate’s sparse‑regime correlation law to the TOI‑791 system, showing that planets with effective density scaling p_eff = M ε⁻³ arise naturally when correlation gradients collapse in the outer‑shell domain. It further identifies the forced 5:3 mean‑motion resonance as a direct consequence of δI‑mode stability, revealing that the resonance is not an accidental dynamical configuration but a structural requirement of the underlying correlation geometry. The work establishes the full sparse‑regime planetary framework, detailing how envelope inflation, correlation‑gradient thinning, and resonance locking emerge from the same δI‑substrate mechanisms that govern quantum discreteness and ultra‑global correlation closure. Sector Paper VI provides the first astrophysical validation point for UN Theory, linking microstructure‑level correlation behaviour to observable planetary anomalies. As part of the multi‑volume UN Theory corpus, this paper connects directly to Sector Papers I–III, which define the global δI‑geometry and parity‑odd invariants, and Sector Papers VII–IX, which extend sparse‑regime dynamics to Solar System bodies, ultra‑global fixed‑point behaviour, and terminal correlation geometry.