THE ABÏON METRIC: A Momentum-Sourced Family of Warp Solutions in Linearized General Relativity

We present a new family of stationary spacetime geometries — the ABÏON metric — sourced entirely by organized momentum current (the T⁰ⁱ sector of the stress-energy tensor) within the framework of linearized General Relativity. Unlike diagonal-deformation approaches (Alcubierre 1994), which require exotic matter violating the energy conditions, the ABÏON metric is constructed from a physically realizable source: pressureless dust arranged on a double-paraboloid geometry with Archimedes-screw helical threading. By construction, the solution satisfies all four classical energy conditions (NEC, WEC, SEC, DEC) identically and analytically for every observer and at every point. The central physical mechanism is the conversion of rotational frame-dragging (h₀φ) into an axial gravitomagnetic component (h₀z) via the helical source geometry, yielding a geometric amplification factor F_geo ≈ 3.8–6.1 beyond the bare Lense–Thirring prediction for an equivalent point source. For the ABÏON 500m reference design (R₀ = 100 m, M = 1.61 × 10⁸ kg, ω = 30 rad/s), the predicted frame-dragging angular velocity Ω(0,0) ≈ 1.23 × 10⁻⁸ rad/s is three orders of magnitude above the sensitivity of existing ring laser gyroscopes, making the prediction directly testable with current technology. The paper includes: (i) the complete source-first derivation from the linearized Einstein equations; (ii) a gauge-invariance analysis identifying a gravitational Aharonov–Bohm phase from the multiply-connected exterior topology; (iii) a full validation suite (energy conditions, stability under 7 independent criteria, geodesic analysis, Newtonian limit recovery, curvature analysis, asymptotic flatness); (iv) second-order perturbative corrections establishing the domain of validity; (v) comparison with the Alcubierre metric and natural astrophysical topologies exhibiting analogous frame-dragging structures; and (vi) a complete Python implementation for independent verification of all numerical results. Companion paper: "The ABÏON Vehicle: Engineering Architecture for Momentum-Sourced Metric Displacement" (Paper 2 of 2).