LLSVP Heat Flux Focusing and the Longevity of Earth's Geodynamo

This paper provides the quantitative companion to Biggin et al. (2025) 's empirical demonstration that core-mantle boundary heat flux heterogeneity controls ancient magnetic field behavior. We introduce a single parameter—the focusing contrast C = qₒut/qᵢn ≈ 1. 95 for Earth—that quantifies the strength of LLSVP-induced heat flux organization. A joint sensitivity analysis over C and the core adiabatic flux qₐdiab identifies three operational regimes (threshold-crossing, lateral-variance-driven, and compositional-buoyancy-dominated), with Earth's uncertainty spanning the first two. Within the plausible parameter box, the focusing differential between Earth-like and weak-pile configurations extends the dynamo-favorable window by up to ~1. 6 Gyr (median 1. 2 Gyr). The reduced-order model's domain is explicitly bounded: inner core nucleation partitions the parameter space into thermal-dominated and compositional-buoyancy regimes, and the framework applies to the former. A self-reinforcing feedback loop (inertial anchoring 10³–10⁵ yr, viscous adaptation 10⁵–10⁷ yr, structural feedback 10⁸–10⁹ yr) coincides with three Phanerozoic perturbation events (Siberian Traps, CAMP, Deccan) whose recovery signatures provide the diagnostic test distinguishing the LLSVP system from a passive thermochemical heterogeneity. Five testable predictions are formulated (P1–P5), including a proposed test against Biggin et al. (2025) 's paleomagnetic dipole-stability dataset (P4) and a pre-/post-inner-core-nucleation distinction in recovery dynamics (P5). Ontong Java Plateau is flagged as a candidate fourth event for dedicated followup work. The focusing contrast C is a candidate determinant of planetary habitability duration, connecting deep interior structure to the longevity of magnetic shielding. Version 2. 0 changes: Complete revision following peer review. Autopoiesis framing removed; regime structure and ICN boundary added; Phanerozoic section reframed as prospective rather than retrodictive; ROM validation explicit; Lay 2008 uncertainty propagated; Mars section reframed as regime-boundary diagnostic; Ontong Java Plateau scope addressed.