From fixed-size quanta of space to Einstein's equations and the radial acceleration relation

In a picture proposed by the author, space is a sequence of static slices made of modes of fixed size, each with a resting energy, and matter passes from slice to slice as an electron passes between levels. From the author’s picture of modes we draw five rules and one founding postulate, and derive from them, with the conditions and known laws stated in the text, the equations of gravitation and the form of galactic dynamics. Requiring that modes resist differing from their neighbours, at minimum energy, makes every mode equal to the mean of its neighbours, which gives Newton’s law; fixing the length of a jump by the mean of the rates of passage at its two ends is equivalent to space flowing towards a mass at the escape speed, and with flat slices one flow equation gives the Schwarzschild, Friedmann and Schwarzschild–de Sitter solutions; counting the passage of matter equally in the four directions gives the gravitating density ρ+3p and, with the theorems of Lovelock and Deser, Einstein’s equations where gravity is much stronger than a0; fixed-size modes give the repulsion −2ρs, the balance k=2 and an exact geometric form of the author’s exchange law. Beyond Einstein’s equations, the period of the closed slice gives a0 = cH0/2π; the rule of the mean of neighbours gives surface waves ω² = gk; the band of the lattice makes a jump exchange one quantum proportional to √gN; and repeated absorption gives g = gN/[1 − exp(−√(gN/a0))], which with a0 not fitted matches 147 SPARC rotation curves with a scatter of 0.133 dex. A first test with galaxy groups shows the predicted transition between groups without and with dark matter. The founding postulate is the author’s image: a jump is a quantum transition between two levels.