The deep-MOND limit as a Newton-Hooke contraction of de Sitter spacetime

Milgrom's deep-MOND limit is the scaling limit G → 0, a0 → infinity with G·a0 fixed, while the de Sitter-to-Newton–Hooke contraction is c → infinity at fixed Hubble time. We point out that, if the empirical relation a0 = kappa·c·H is promoted to a structural identification and G·a0 is held fixed, the two limits become a single scaling problem. This does not derive MOND from de Sitter space; rather, it organizes the deep-MOND sector. Within the AQUAL family K ~ |grad phi|^(2p), p > 1/2, the contraction selects p = 3/2 as the unique finite nontrivial exponent: smaller-p terms vanish and larger-p terms diverge. We also show that the contraction does not transport the de Sitter so(4,1) isometry algebra: the rescaled boosts become an abelian ideal. The relevant so(4,1) symmetry is instead the standard boundary action on conf(E3), matching the conformal invariance of the three-dimensional p-Laplacian at p = 3. Expanding around a uniform-gradient background gives a static stiffness anisotropy 2p-1 = 1/gamma, the same combination that fixes the force law. Phenomenological consequences are stated as falsifiable tests: the primary de Sitter-invariant reading predicts constant a0, while a phenomenological a0 ~ H(z) running gives a distinct high-redshift Tully–Fisher/RAR evolution. All symbolic and numerical verifications are reproducible from the accompanying repository.