Entanglement at the Saturation Boundary: Resolving the AMPS Paradox Without Firewalls, Nonlocal Signaling, or Violations of Monogamy

This paper resolves the AMPS paradox by identifying a single structural assumption inherited from semiclassical quantum field theory: the infalling mode is treated as a valid degree of freedom at the horizon. In the informational framework, this assumption fails because the horizon is a saturation boundary where the channel C(x) reaches its critical capacity C₍crit₎. When an eigenmode crosses this boundary, it exits the unsaturated spectrum and ceases to exist as a distinct informational degree of freedom. Its distant partner decoheres structurally—not dynamically—because the geometric anchor maintaining the entanglement correlation is erased. This mechanism resolves the paradox without firewalls, nonlocal signaling, or violations of monogamy, and provides a unified informational account of black hole entropy, decoherence, and horizon behavior.Mathematical Notation Statement.All mathematical expressions in this manuscript use a dual‑inline format in which each expression appears first in bold Unicode, followed by its archival LaTeX form in square brackets. This ensures stability across Word, PDF, and archival repositories. No external references or prior results were required for the development of the mechanism presented in this work.Conical Source Statement.This work is part of a unified research program developed across multiple volumes. Each volume is designed to stand on its own while also forming a coherent component of a larger theoretical structure. Readers encountering this volume independently are encouraged to view it as one face of a conical source: a single underlying framework projecting into multiple disciplinary domains. The geometry, gauge structure, and emergent thermodynamics presented here are consistent with and derived from the same substrate‑level principles articulated throughout the series. This manuscript is intentionally concise, self‑contained, and free of references. All results follow directly from the saturation‑boundary mechanism and the informational curvature identity. The author acknowledges Dr. Mark A. Barber for the catalytic question that motivated this work, and acknowledges the use of AI‑assisted drafting tools for formatting stability and structural clarity.