Cognitive Metrology: Finite Causal Horizons, Balanced Ternary Lattices, and Measurement Metrology

We explore a straightforward toy model—termed Cognitive Metrology—which examines what happens when we replace continuous real-number infinities and perturbative approximations with a strict finite-state framework. Guided by the Kronecker constraint (c = 1, assuming a finite causal horizon of ~10^80 baryons), we model physical states using balanced ternary logic ({-1, 0, +1}). Measurement is treated as a closed three-body triadic loop (Observer, Instrument, Observed), honoring Schrödinger's insight that the observer is an inseparable part of the observed system. Within this discrete sandbox, we examine how stochastic noise can be interpreted as resolution aliasing, how topological solitons preserve Lorentz invariance across discrete lattices, and how the inverse fine-structure constant backbone (137) emerges naturally from base-3 ternary coordination shells (12002_3). Our goal is simply to present these calculations for peer review and invite fellow researchers to test the framework.