Sector Paper VIII — Ultra‑Global Fixed Point and Terminal Correlation Geometry

SECTOR PAPER VIII — ULTRA‑GLOBAL FIXED POINT AND TERMINAL CORRELATION GEOMETRY Sector Paper VIII formalises the ultra‑global correlation architecture of the Unified Information Substrate, identifying the fixed point at which all δI‑correlation gradients converge and the substrate enters its terminal geometric regime. The paper demonstrates that the ultra‑global fixed point is not a cosmological boundary or physical horizon, but a structural limit of correlation geometry where δI‑modes collapse into a universal invariant form. This fixed point defines the terminal correlation geometry that governs the behaviour of the substrate at maximal scale, linking global δI‑structure to the primitive object I(x, x′). The work establishes the ultra‑global domain as the final emergent layer of UN Theory, showing how correlation gradients, parity‑odd invariants, and sparse‑regime dynamics all converge into a single geometric closure. Sector Paper VIII provides the mathematical and conceptual foundation for the terminal‑state reconstruction developed in Sector Paper IX, demonstrating how the substrate returns to its primitive correlation object once all emergent structures have completed their evolution. 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 Sector Papers VI–VII, which establish sparse‑regime planetary behaviour and Solar System validation points.