What This Establishes and What Remains Open

9.1 — What this paper closes

It derives the floor acceleration exactly: a₀ = αcH₀/(2π), with the functional form and the exact coefficient α/(2π) ≈ 0.1662 parameter-free. It closes its local debts — D1 (the 2π coefficient, via the Poincaré–Hopf dipole and the Lemma 1 linear scaling) and D1′ (the correction factor α, via Propositions 2–3). It derives the dipolar topology from {S, B, C}, removing AP17’s structural assertion (KS-45.2 closed).

9.2 — What this paper does not close

It does not close the empirical confrontation: whether observation confirms a₀/(cH₀) = 0.1662 and H₀ ≈ 74 awaits the resolution of the Hubble tension (KS-45, KS-45.1). It does not derive the full tension-field equation (KS-42, closed downstream in Rosin V7, not here) or the interpolation function (KS-43, AP17).

9.3 — Items held open without claiming debt status

The empirical pending on a₀/(cH₀) and H₀ — a precision matter tied to the unresolved Hubble tension, not a structural gap. AP18 owes no structural debt.

9.4 — Where the philosophical-register implementations live

The expository-register companion for the MOND acceleration scale and the position that the dark-matter phenomena are substrate topology rather than a particle species lives in Ø Predictions. AP18 is the formal-register origin of the exact a₀. A dedicated expository twin of this specific derivation is not separately written; recorded honestly rather than filled with a manufactured citation.

9.5 — Structural relationships to subsequent work

AP18 strengthens AP17 (the claimed floor is now derived; the asserted dipole is now forced). AP21 uses AP18’s Lemma 1 as the record-measure-to-energy bridge and inherits the floor a₀ as the cosmic confining potential. Rosin V7 supplies the explicit tension-field equation AP18 does not derive, closing KS-42.

9.6 — The 420 Code placement

AP18 is a chapter of Notebook VI (Cosmology), the exact-scale derivation in the structure-formation chain AP06 → AP17 → AP18 → AP21.

9.7 — How the body of work reads now

With AP17, AP18, and AP21 in place, the 420 Code carries a complete structural account of galactic and cosmic structure from the tension field of ε: the floor that flattens rotation curves, the exact scale that floor sits at, and the web that floor builds. AP18 makes the scale parameter-free and turns it into a prediction of the Hubble constant — a falsifiable hostage to the next decade of measurement.

9.8 — The closing

The floor acceleration of the tension field is a₀ = αcH₀/(2π), with α = 2 ln(sec(½) + tan(½)) ≈ 1.0445. The functional form a₀ ∝ cH₀ is derived; the exact coefficient α/(2π) ≈ 0.1662 is derived; the result is parameter-free, with all local debts closed.

The field lines close because the sectors are connected. They cannot extend beyond Rₕ because propagation is bounded. The widest line curves at the boundary of the observable universe. Its acceleration is the product of the two conditions — c and H₀ — divided by the geometry of the loop. A derivation from four axioms matches a galactic-scale measurement to within the measurement uncertainty on a₀ itself, and predicts the Hubble constant as its bonus.