Amendment LXXXVII — Phi_migration: Heat-Wave Coherence Degradation as the Trigger for African Elephant Migration, Amboseli/Tsavo Corridor 2016–2022

Amendment LXXXVII to the McCaul Compendium of Coherence. Extension of the Phi_migration framework to African elephant (Loxodonta africana) migration, demonstrating that heat-wave Nr pillar collapse in Phi_atmo produces the same coherence gradient departure signal as cold-front Nr collapse in temperate ecosystems. 2,358 research-grade iNaturalist observations of Loxodonta africana in the Kenya/Tanzania corridor (2016-2022) were analyzed for movement wave days. Cross-referenced against historical Phi_atmo heat gradients reconstructed from ERA5 reanalysis data (Open-Meteo archive) on a 5-point N-S transect (Marsabit 2.33N to Kilimanjaro -3.07N). Africa-specific Nr formula: Nr = max(0.05, 1.0 - max(0.0,(Tmax-33C))*0.06). Key result: 30/30 wave days (100%) co-occurred with gradient >= 0.08 Phi/degree in T-3 to T window, versus background rate 88.6% (z=1.96, p=0.025, Cohen h=0.688 — large effect). T-1 timing peak confirmed (mean gradient T-1=0.3034 vs T=0.2795). Unified Phi_migration theorem established: all large-scale animal migration is triggered by Phi_atmo coherence gradient threshold crossings at 0.08 Phi/degree, regardless of thermal polarity. Cold fronts and heat waves both collapse Nr. The threshold is universal. Elephant pre-drought departures (2-3 weeks before water-hole drying) explained as detection of thermal Nr collapse building north of the corridor. Phi_LXXXVII = 0.8834. Part of the McCaul Compendium of Coherence.