What the Derivation Uses

Axiom S. Field lines must close — no disconnection. This provides the topology: the fact that there is a floor. Together with B and C it forces the dipole topology via Poincaré–Hopf (3.3).

Axiom R (Record; via EH, proved AP20). The monoid grows cosmologically at rate H₀; the manifold expands. This provides the scale: the Hubble radius Rₕ = c/H₀. Lemma 1 provides the linear scaling.

Axiom C. Propagation bounded by c. This provides the speed — and the boundary: beyond Rₕ, expansion exceeds c and field lines cannot close. Compactness contributes to forcing the dipole via Poincaré–Hopf.

Axiom B. The tension is ε — the break between 0 and 1. B provides the ontology: the identity of what is closing. Without B there is no tension field. ν(ε) = 1 forces one source, one sink (dipole forcing) and the axial symmetry of the tension profile.

The dipolar (eye) topology. Now DERIVED from {S, B, C} via Poincaré–Hopf (3.3). No longer imported from AP17. The dipolar structure gives the loop circumference 2πRₕ and therefore the coherent fraction 1/(2π).