Kill Switches

Global body of work numbering. To resolve a collision with AP22, this paper’s former KS-46 and KS-47 are renumbered to KS-45.1 and KS-45.2 respectively (the registry is canonical). The switches are given here in Claim/Test/Status/Recovery form.

8.1 — KS-45 — 2π geometric factor

Claim. The floor acceleration equals the apex acceleration (cH₀) multiplied by the coherent fraction (1/(2π)) and the correction factor α: a₀/(cH₀) = α/(2π) = 0.1662.

Test. If precision measurements yield a₀/(cH₀) ≠ α/(2π) = 0.1662 after H₀ convergence, the derivation is falsified. The kill condition: if both a₀ and H₀ are known to ±1% and a₀/(αcH₀/(2π)) deviates from 1 by more than 5%, the derivation is killed.

Status. LIVE — EMPIRICAL. Upgraded from LIVE — HARD. All AP18 local debts closed (the dipole forced by Poincaré–Hopf, the linear scaling from Lemma 1, α from Propositions 2–3). At present a₀/(cH₀) ≈ 0.176 (at H₀ = 70), above 0.1662 but within H₀ uncertainty; agreement is exact at H₀ = 74.3.

Recovery. If the ratio settles away from 0.1662, the discrepancy localises to the coherent-fraction or correction-factor step rather than to the closure topology; the functional form a₀ ∝ cH₀ would survive even if the coefficient required revision.

8.2 — KS-45.1 — Hubble prediction (was KS-46)

Claim. The parameter-free prediction H₀ = 2πa₀/(αc) = 74.3 ± 1.2 km/s/Mpc.

Test. If the Hubble tension is resolved at H₀ < 70 (the Planck value 67.4 confirmed), the predicted a₀ falls ≈8% below observation, straining the derivation. If resolved between 72–76, the prediction is confirmed. If H₀ > 78, the argument overshoots.

Status. LIVE — EMPIRICAL. Testable with future H₀ measurements; you will know within a decade. The prediction is parameter-free.

Recovery. A resolved H₀ outside the window falsifies the floor-determines-H₀ reading without disturbing the derivation of the functional form; the floor would then be read as approximate rather than exact.

8.3 — KS-45.2 — Dipole topology (was KS-47)

Claim. The derivation’s dipolar (eye) topology is forced by the axioms, not assumed.

Test. Show that the galactic-scale tension field admits a non-dipolar topology consistent with {S, B, C}.

Status. CLOSED. The dipolar topology is derived from {S, B, C} via Poincaré– Hopf (3.3): Axiom B provides one source (ν(ε) = 1), Axiom S one sink (σ-image), Axiom C compactness; two index-1 zeros on S² with all field lines closing is a dipole. No longer depends on AP17’s assertion.

Recovery. Not applicable — closed by the Poincaré–Hopf derivation, within the single-break galactic-scale model class (the scope note in 3.3 bounds the claim).

8.4 — Updates to existing kill switches

KS-39 (a₀ numerical value, AP17). Sharpened by AP18 to a parameter-free result a₀ = αcH₀/(2π): at H₀ = 70, a 5.8% residual; at H₀ = 74, <1%. The discrepancy tracks the H₀ measurement, not the derivation. Remains LIVE — EMPIRICAL.

KS-42 (tension-field equation from {S, B, R, C}). Not closed by AP18: AP18 derives the floor acceleration, not the full tension-field equation or the interpolation function. It was subsequently closed in Rosin V7. Note: the flat switches KS-41 (structure formation) and KS-42 (tension-field equation) are legacy single switches and are distinct from the dotted AP41.x and AP42.x switch families; the dotted labels do not denote sub-switches of KS-41 or KS-42.

KS-43 (interpolation function). Not addressed by AP18. Remains LIVE — EMPIRICAL (AP17).