Spontaneous Symmetry Breaking and Degenerate Vacua from the 90-Degree Floor: Symmetry Breaking by an Infinitesimal Seed and the Delta=-2pi/N Lock (Exhaustive N=6,...,40)

Paper 5 of the series "Foundations of Self-Consistent Relational-Wave Closed Systems" (10 papers). The 90-degree floor is an unstable maximally symmetric equilibrium (the summit of a Mexican hat). An infinitesimal seed of amplitude 1e-8 in different directions breaks the symmetry, inflates, and locks onto an isomorphic equilibrium (degenerate vacuum) with equal amplitude and exact Delta=-2pi/N; the phase configuration (vacuum orientation) is seed-dependent. Confirmed for all 35 systems N=6..40 (175 runs = 35 N x 5 seeds). The effective potential V(r) is reconstructed from measurements (an ansatz). A 720-permutation test at N=6 shows the vacuum valley is not a finite discrete S_N orbit (consistent with a continuous Mexican-hat valley); continuity itself is undecided. Author: Noriaki Kihara (WF System Co., Ltd.), ORCID 0009-0004-6753-4020.