Emergent Field Physics from Balanced-Ternary Microstates

CAELIX presents a constructive substrate programme for exploring whether continuum-like field signatures can arise from an explicitly discrete structural layer under purely local rules.

The system is built from balanced-ternary microstates s ∈ {−1, 0, +1}. These microstates are mapped through a deterministic, local load functional that acts as an interface-density proxy. The resulting load is then coupled into a continuous carrier field φ evolved by local stencil updates in two families, diffuse and telegraph. The core question is methodological: if carrier dynamics are held fixed, do changes in microstate structure drive systematic changes in measurable observables.

The paper specifies the substrate, the carrier rules, the coupling, and a reproducible experiment programme. It reports a suite of observable signatures that emerge without hard-coded distance kernels or prescribed force laws, including a far-field inverse-radius vacuum profile (≈ 1/r), stable wave interference patterns, sign-structured interaction proxies, geometric confinement spectra, calibrated near-isotropic propagation, and latency proxies consistent with refraction-style and kinematic-dilation effects. Non-linear extensions (ϕ⁴ and Sine–Gordon carriers) produce stable localised structures and reusable sprite assets, which are then used to demonstrate confinement routing behaviours such as T-junction fan-out and controlled signal disposal via geometric dump chambers.

The work is deliberately concrete. It does not present a new physical theory at the level of a Lagrangian. Instead, it offers a specified, ablatable pipeline from minimal discrete structure to measured continuum-like observables, with explicit controls, known failure modes, and provenance-logged artefacts to support replication and falsification.

A full 2D working version of CAELIX can be viewed at https://caelix.co.uk/