Newtonian self-gravity from tick consumption in a Planck-frame Dirac quantum walk

In the Planck-frame reading of the Dirac quantum walk, a mass m turns its internal phase by θ = m/mP per frame (the coin) and every gap moves the walker by one pixel (the shift). We add one physical postulate — matter consumes ticks: a cell containing matter loses frame rate at the rate θ|ψ|2, and the deficit spreads to the neighbouring cells by a local rule on the same lattice — and recompute the lapse at every frame from the walkers' own density. Two walkers then attract each other with Newton's law: force within 0.2% of the field prediction, acceleration proportional to the source angle and independent of the test angle (equivalence principle), action and reaction equal to 7×10-4, constant force in 1+1 and a 1/r potential on the cubic 3D lattice (coefficient 1.012 ± 0.002) with a finite Planck-cell self-potential; with a wave rule the lapse front moves at one pixel per frame. Test particles fall with a = −NcNc′ and light is blue-shifted on the way down. To our knowledge a self-gravitating discrete-time Dirac walk has not been reported before. We also record three exact properties of the frame: a coin↔shift symmetry of the free walk, the closed dispersion with separate clock and light lapses, and the fact that a mass at rest sees only the clock lapse. The last one explains why the light-bending factor 2 (γ = 1) does not follow from the postulate: the walk reproduces any γ ≥ −1 that is put into the deficit split, and the rules that give γ ≈ 1 are postulates or import general relativity. γ = 1 is therefore compatible, not derived. Negative results of pre-registered alternative routes are listed. The mass values themselves are not addressed: the coin angle is an input, and why me/mP ≈ 4×10-23 remains open. The source package contains the LaTeX source, figures, the scripts that regenerate every number (check_numbers_v2: 118/118 values found in their source files) and the re-run of the source experiments.