On a Routing Network of Causal Flow and Its Reading under Relationalism

Abstract

This paper builds a causal network as an explicit mathematical structure and reads physics from inside it. The network stores no coordinate, shared clock or field, and only routes causal flow along bands on the Laves graph of a three-torus. The graph is a cubic crystal net, the discrete frame for the symmetries named CP and CPT. A single irreversible event, the lock, twists every band with one handedness and leaves an extra half twist on some band ends; only at a vertex whose three band ends all carry one can flow be held and delayed, and holding gives the network's history an arrow. Swaps behind the lock's front mix the flow into a causally trivial medium, the datum of every reading: only what departs from it is nontrivial and can be read. Under coarse-graining the lattice detail of the routing becomes irrelevant and one collective mode survives, isotropic in its stride, which is fixed in cells per update. Physics enters through readers inside the network, which receive only counts of the flow passed between them and a source. An incidence transform turns the counts into an image on the reader's sky, and demodulation decodes the nontrivial part, carried on phase and frequency channels. Under conventions of scale and of relativity, with light's speed as the conversion ratio between space and time, the decoded signals read as rest mass, charge and motion. The readings span four dimensions: three from the translations of the Laves graph, time from the reader's own count, and Lorentz invariance at readout from the relativity principle. Defects move by the glide, a two-tick event of the routing machine, and the machine hands up its transport coefficients and shows what it lacks. A second, coarse machine, with declared design choices, supplies what is missing, and toy-universe experiments on it read gravitational, wave and scattering phenomena. Every claim is graded, from forced to conjectured, and since both machines are programs, every measured claim is checked by released code and records; what stays open is listed.

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