Fragment XV — Existence and Uniqueness of the Coherence Knot from the GC Lattice Action

This paper establishes the existence and uniqueness of the neutrino coherence knot directly from the General Connectivity lattice action, completing the foundational stability programme initiated in Fragments XII–XIV. Working on the golden‑ratio shell lattice, it proves existence by the direct method using discrete trap compactness and weak lower semicontinuity, and proves uniqueness of the positive ground state via a discrete Wronskian argument in which the defocusing sign of the GC quartic is load‑bearing. The amplitude Hessian is shown to have trivial kernel, matching the spectral count of Fragment XIII, and the result synthesises with the VK slope of Fragment XIV to yield the unique orbitally stable standing wave of the GC lattice. The paper also derives the continuum nonlinear Schrödinger equation as only the formal leading order of the lattice energy, valid when the knot is wide in logarithmic radius, and shows that the physical electron lies in the sub‑lattice regime where the continuum approximation fails by O(1). This lattice remainder is identified as the source of the two‑loop g‑factor flank resolved by the exact golden‑shell profile. The lattice is thereby established as the theorem, with the continuum as its wide‑knot shadow, and the coherence knot as a fully derived, unique, stable object of the GC framework.