THE KEPLERIAN HELICOID A Power-Law Helicoidal Surface

We identify a previously uncharacterized geometric surface — the Keplerian Helicoid — defined by z ∝ θ r^(3/2), which constitutes the envelope of planetary orbits when a gravitationally bound system is observed in a translating reference frame. This power-law helicoidal surface is the unique geometric fingerprint of 1/r² Newtonian gravity: no other force law produces the exponent 3/2. The familiar ecliptic plane is the instantaneous cross-section of this helicoid in the Sun's co-moving frame — the same object viewed from inside by an observer riding along its axis. We compute the complete angular momentum budget of the Solar System (including all planets, satellites, and solar rotation), finding that planetary orbital momentum dominates solar rotation by 29:1, with Jupiter contributing 59.3% of the total (J_total = 3.255 × 10⁴³ kg·m²/s). The r^(3/2) power law creates a frame-dragging concentration that scales as r⁻⁴, meaning Mercury contributes 36 million times more gravitomagnetic field density per unit axial length than Neptune, despite possessing negligible angular momentum. This produces a natural dual architecture: outer planets serve as the angular momentum reservoir (96.5% of J_total), while inner planets serve as the gravitomagnetic field amplifier. The Lense-Thirring torque from this organized angular momentum is secular — unlike oscillatory gravitational perturbations, it accumulates unidirectionally. Mercury has undergone 2,072° of frame-dragging precession over 4.6 Gyr (nearly six complete cycles), with a crossover time of ~50,000 years after which the cumulative secular effect exceeds the amplitude of gravitational oscillations. Frame-dragging does not create the ecliptic — angular momentum conservation does — but it provides the only secular, non-oscillatory, cumulative stabilizing torque, a contribution that gravity alone cannot provide. The helicoid surface at ~30 AU marks a coherence boundary confirmed by the observed transition from coplanar orbits (planets, < 7°) through the Kuiper belt (0–30°) and scattered disk (0–40°) to isotropy (Oort cloud). The Solar System is nine orders of magnitude below the MIND coherence threshold (π ~ 10⁻⁵ vs n₀ ~ 10⁴ kg·m⁻¹·s⁻¹), confirming that frame-dragging is perturbative at this scale — exactly as the framework predicts. Most remarkably, the Keplerian Helicoid naturally realizes the dual-component architecture of the ABÏON Metric: the helical geometry, the separation of rotational and translational momentum regimes, the Archimedes screw pitch of the Sun's galactic trajectory (3.23 AU per solar rotation), and the complete MIND constitutive chain from organized momentum to metric perturbation. The Solar System is a natural, unoptimized ABÏON architecture connected to engineered warp by a continuous function of five parameters — with no discontinuity, no new physics, and no phase transition separating them. Six falsifiable predictions are proposed. Keywords Keplerian Helicoid; power-law helicoidal surface; planetary geometry; galactic reference frame; ecliptic plane; angular momentum budget; frame-dragging; Lense-Thirring effect; secular stabilization; r⁻⁴ concentration law; dual architecture; momentum separator; MIND framework; momentum coherence; coherence boundary; Kuiper belt; Oort cloud; ABÏON Metric; Archimedes screw geometry; organized momentum; gravitomagnetism; stress-energy tensor; warp metric; General Relativity; Kepler's third law; BepiColombo; planetary coplanarity; falsifiable predictions