Dark matter as the response of a flat spacetime

We propose a framework in which dark matter and dark energy are properties of spacetime itself, tied to its observed spatial flatness. Two axioms are added to General Relativity, which is left unchanged. The first: spacetime is compared at all times with an abstract, perfectly Euclidean reference with no length or time of its own, against which every curvature is a departure, and on average the Universe keeps this reference. The second: spacetime is a homogeneous medium with a finite stiffness and no further structure. From the axioms we prove that the deficit angle is the measure that can register departures from this reference, the quantity in which Regge wrote General Relativity. With covariance, the axioms then fix the properties of the object they define, each by a single principle given a few stated choices: the medium has nothing of its own beyond its stiffness. These properties constrain a covariant action, whose static, spherical equilibrium gives the radial acceleration relation found empirically by McGaugh, Lelli and Schombert, g = g_N / (1 − e^(−√(g_N/a₀))), with flat rotation curves and a baryonic Tully–Fisher slope of exactly 4. The paper writes the field equations and checks their consistency, but solves them only in the static, spherical case. Fitted to 171 SPARC galaxies with one global a₀, the law is the best of four candidate laws, slightly ahead of the "simple" function of MOND (total χ² of 27,128 against 28,036; better in 69 galaxies, worse in 45). As a programme for future work, we outline how the same medium would account for the cold dark matter of the cosmic microwave background, for negatively curved seams between galaxies, and for dark energy, as a positive cosmological constant tied to a₀.