The Tension Field: A Standalone Summary

For readers without AP17 and AP18, the essential claims are summarised here.

What the tension field is. Gravity is the condition of the 0-pole (the fold) and propagation at c is the condition of the 1-pole. The break ε sits between them: the wave function collapsing from probability to actuality. The tension field is the field of ε between 0 and 1 — the substrate under tension between its two conditions.

What closure means. Field lines of the tension field must close. This follows from Axiom S (the two sectors are connected by σ) and AP06 Theorem 3.1 (leakage is nonzero: the sectors cannot fully disconnect). A field line that leaves the 1-pole must return to a 0-pole. Disconnection violates the involution.

What a₀ claims. The acceleration floor a₀ is the minimum gravitational acceleration the tension field enforces. AP18 derives the scale: a₀ = αcH₀/(2π), where α ≈ 1.0445 is the apex-symmetry factor from AP18. Below this floor, Newtonian gravity would predict zero acceleration, but the topological closure of field lines prevents this. The widest field line extends to the Hubble radius Rₕ = c/H₀; its curvature at the apex gives the floor.

What is still open. The 2π geometric factor in a₀ = αcH₀/(2π) is derived from dipolar loop geometry (AP18). With α = 2 ln(sec(½) + tan(½)) ≈ 1.0445 (AP18, from the Z₂ symmetry of Axiom S) and H₀ = 74 km/s/Mpc, the numerical result matches the empirical MOND scale (1.20 ± 0.02 × 10⁻¹⁰ m/s²) to approximately 0.4% (exact at H₀ = 74.3; AP18 §5). The residual is within measurement uncertainty. KS-39 (the numerical value) remains LIVE — EMPIRICAL in AP18; this paper inherits that uncertainty.