We introduce E0, a formal framework for discrete transition systems that derives complexpath amplitudes from three structural primitives: difference, resistance, and historization.Through a constructive chain—tension, coherence, Helmholtz field decomposition, connection,and phase—we obtain amplitudes Ψ = exp(−S + iΘ) that exhibit constructive anddestructive interference without postulating quantum mechanics. Probability is not assumedbut emerges from interference: normalized intensities P(a) = I(a)/PI(a′) form a distributionderived from structural amplitudes, not from axiomatic measure theory. We prove aHolonomy Independence Theorem establishing that phase differences between paths dependonly on path-local quantities. A hybrid controller uses this interference to escape structuraltraps undetectable by greedy methods. Our central empirical finding, validated across 380graph topologies, is that the choice of summation geometry—which paths contribute to theamplitude—dominates over the choice of decision rule: switching geometry changes trapescapesuccess from 0% to 100%, while switching from deterministic to stochastic selectionchanges it by at most 24 percentage points. We identify path-family count and phase oppositionas structural predictors for when interference-based routing provides advantage. Allclaims are explicitly classified as derived, empirical, or heuristic.
Thomas Wehner (Wed,) studied this question.