Time dilation from counting events without pre-assigned places, and the Feynman checkerboard up to a moving atomic clock: registered lattice tests

This record reports a sequence of lattice tests motivated by four counting premises and implemented through known physical constructions, with the further assumptions stated explicitly. With a light-cone order and a clock that reads the longest chain of events, independent uniform random events recover proper time within the reported finite-size accuracy, while a synchronous grid gives a chain length that does not depend on the velocity; a clock that counts events and multiplies the two light directions recovers the Lorentz factor on that same grid, through the exact identity √(ab)/((a + b)/2) = √(1 − v²). With an imaginary weight for every change of light direction the count becomes the Feynman checkerboard, a Dirac quantum walk; the subsequent tests concern mass as the turning angle, fermion doubling with net chirality zero, boundary (domain-wall) fermions, the gauge field of MM 2.27 on the same lattice (Landau levels, Maxwell's evolution equations with Coulomb's law in 2D and 3D, photons with two polarizations, a fitted Casimir energy coefficient of 0.9997 times −π²/720), the Schwinger model in 1+1, and hydrogen-like atoms: for a Bohr radius of six lattice steps the emission rates agree within 1.7 % with the nonrelativistic hydrogenic formula at the same coupling and effective mass. The moving-atom tests use the gap between the n = 2 centroid and the 1s doublet at fixed total momentum, with a first-order shift from a regularized continuum-form Breit operator. The Wilson-lattice computations, with a nucleus heavier than one lattice unit, do not recover the Einstein coefficient −1/2 (they stay near zero, with a convention-dependent sign), and a registered hypothesis about the Wilson term was refuted. Replacing the free dispersions by continuum forms gives −0.44 (−0.49 in the strictly first-order ratio). This supports a substantial role of coarse lattice kinematics but does not establish the interacting continuum limit of the checkerboard. All the structures are known physics; what is proposed is the sequence. Using the separately tabulated clauses as counting units, 59 registered predictions passed in full, 25 failed and 6 are incomplete; later rechecks are reported separately and do not convert failed predictions into passed ones. The original registrations, in Italian, are included with their recorded hashes, which are not publicly time-stamped. The author is not a professional physicist; the framework and its premises are his. Computations were done with an AI assistant (Claude); a second AI assistant (Codex) reviewed the text and the moving-atom code with independent analytical checks, without executing the programs; no human peer review is claimed. All code is included; the programs that fit on a laptop were re-run from scratch before deposit, and the large atomic runs (about 40 GB each, on AWS) are included with their outputs and a program that recomputes the tables from them.