Multiscale Elastokinematics, Ground-Effect Aeroelastic Porpoising Limit Cycles, Burdet-Ferrandiz Singular Contact Regularization, and [8/8] Sz.-Nagy Viscoelastic Friction: A Unified Hamiltonian and Lie-Group Platform for Formula 1 Vehicle Dynamics

High-performance Formula 1 vehicle dynamics, full-car aerothermal development, and real-time Driver-in-the-Loop (DIL) simulation operate at the intersection of non-smooth multibody contact mechanics, nonlinear unsteady aerodynamics, and stiff multi-timescale thermodynamic systems. Conventional commercial solvers rely on ad-hoc empirical slip clamping, quasi-static wind-tunnel aerodynamic maps, and uncoupled co-simulation loops that diverge or suffer severe step-size collapse during zero-speed transitions, high-frequency curb strikes, and underfloor diffuser boundary-layer stalling. In this monograph (Pillar IX of the Sovereign Corpus, Zenodo DOI: 10.5281/zenodo.23467501), we translate the rigorous Hamiltonian mechanics, singular perturbation theory, operator dilations, and topological invariants established in Pillars I-VIII directly into an industrial-grade, mathematically complete Formula 1 multi-physics architecture, establishing Gates 108-112 to complete the 112-Gate Sovereign Grand Corpus. [F1-1] 14D Burdet-Ferrandiz Focal Regularization for Tire Contact (THM-F1-V1-01, Gate 108, Section 2): We project the 6-DOF unsprung wheel contact kinematics into the 14-dimensional Burdet-Ferrandiz (BF) projective focal manifold equipped with Mikkola regularized logarithmic time. This analytically eliminates the kinematic slip singularity as forward speed approaches zero and regularizes high-stiffness suspension bump-stop impacts during aggressive curb strikes, bounding relative energy drift across 10^5 simulation cycles with strictly zero solver restarts. [F1-2] Ground-Effect Aeroelastic Porpoising Limit Cycles (THM-F1-V1-02, Gate 109, Section 3): We couple the vertical heave and pitch degrees of freedom to a dynamic reduced-order model (ROM) of the underfloor Venturi tunnels. By formulating the adverse pressure gradient boundary-layer separation as an algebraic bifurcation, we prove that the onset of Formula 1 ground-effect porpoising represents a supercritical Hopf bifurcation yielding a stable limit-cycle attractor, which cannot be captured by quasi-steady aerodynamic look-up tables. [F1-3] [8/8] Sz.-Nagy Viscoelastic Friction & Flash Temperature (THM-F1-V1-03, Gate 110, Section 4): Applying the commutative restriction of Stinespring's dilation theorem from Pillar III, we prove that non-Markovian viscoelastic tire rubber memory and ISO 8608 road profile power spectral densities admit an exact minimal 8-dimensional Markovian state augmentation. Combined with a 3-layer transient thermal network (bulk, tread, and flash temperature), the model reproduces frictional thermal fading and compound glass-transition shifts. [F1-4] Phase-Plane Yaw Separatrix & Invariant Oversteer Recovery (THM-F1-V1-04, Gate 111, Section 5): Formulating the vehicle sideslip and yaw rate phase plane as a nonlinear dynamical system, we isolate the unstable saddle equilibria at the tire adhesion limit. Computing the stable invariant manifold establishes the analytical separatrix dividing recoverable oversteer from catastrophic spin-out, providing an optimal control law for electronic differential torque vectoring. [F1-5] Tikhonov Multiscale Contraction, Artin Braid Overtaking & WASM SIMD (THM-F1-V1-05, Gate 112, Section 6): We prove that the complete multi-domain vehicle operator is a block-triangular Banach contraction. Multi-car collision avoidance is encoded algebraically via the pure Artin braid group, guaranteeing zero overtaking collisions without distance polling. Hosted in our pre-allocated 1 MB WebAssembly v128 SIMD linear arena, the loop executes at high operational throughput with zero heap allocation.