Determinate Being and Its Ground: The Sufficient–Necessity Argument

This paper provides a concise canonical spine for a larger metaphysical project, Agápēic Relational Metaphysics (ARM). The full argument for a triadic, non‑coercive, intrinsically relational ground of determinate being is developed across several technical papers; this work gathers the core structure into a single, self‑contained derivation. Beginning from the minimal fact that determinate being has contrast and shape, the Sufficient–Necessity Argument traces the constraints that determinacy itself imposes on any adequate ground. Determination requires contrast; contrast requires real relation; and relation adequate to grounding must be necessary, non‑coercive, and intrinsic. A systematic elimination of alternative relational modes shows that monadic and dyadic structures cannot satisfy these constraints, while a triadic relational form is the minimal stable configuration capable of doing so. The argument is not intuitive and is intended for readers comfortable with modal and structural reasoning; for others, including those using AI tools to navigate complex systems, the paper offers a clear map of the architecture and its points of resistance. Its aim is not to close debate but to present, in one place, the distilled reasoning that underlies the broader ARM series.