Black Hole Ringdown as Necessity Recursion: φ-Structured Quality Factors in Schwarzschild Quasinormal Modes and the GW250114 Pre-Registration

Black holes ring. When two collide and merge, the final black hole oscillates at characteristic frequencies — quasinormal modes — determined by exactly two parameters: mass and spin. Fibonacci Causal Loop Theory predicts that any system governed by exactly two organizational constraints will exhibit φ-structured quality factors. This paper tests that prediction across three independent configurations.P73a: the fundamental Schwarzschild QNM quality factor Q = Re(ω)/|Im(ω)| = 4.200 ≈ φ³ = 4.236, δ = 0.008 — CONFIRMS. P73b: the l=3/l=2 frequency ratio = 1.604 ≈ φ = 1.618, δ = 0.009 — CONFIRMS. P73e (v2): the Kerr QNM quality factor at a/M = 0.67 equals Q = 6.852 ≈ φ⁴ = 6.854, δ = 0.0003 — CONFIRMS. All three results carry zero free parameters and are derived from standard QNM tables. The Kerr result is the tightest confirmation in the FCLT series to date.An independent March 2026 study in Frontiers in Physics finds φ-clustering across 64 Schwarzschild QNM pairs with Pearson r = +0.689, p < 0.0001, without knowledge of FCLT.P73d remains pre-registered: empirical extraction of the quality factor from GW250114 posterior samples (GWOSC) against φ³ and φ⁴. Whatever it returns will be reported.Updated FCLT scorecard: 19 confirmed / 5 falsified / 22 technology-gap / 2 gray zone.