Interference as Relative Holonomy: Gauge-Invariant Comparisons, Word Protocols, and Near-Identity Structure Tests

This record presents an updated and expanded version of the work previously released on Zenodo as “Interference as Relative Holonomy” (December 2025). The core viewpoint is unchanged: interferometric observables are gauge-invariant class functions of a relative holonomy element, rather than absolute path holonomies or phases. This formulation provides a single operational description encompassing the Aharonov–Bohm effect, Berry phases, and non-Abelian Wilczek–Zee holonomies, while keeping gauge covariance explicit and avoiding gauge fixing. The present version substantially extends the earlier note by: formalizing invariant readout via finite collections of class functions (trace moments) and associated pseudometrics; treating composed experimental protocols as words in a free group, with invariant “fingerprints” defining an operational equivalence relation; recording near-identity commutator expansions, holonomic order definitions, and two-scale order estimators based solely on invariant data; defining pairwise noncommutativity scores and interaction graphs that identify commuting Lie sectors under standard small-parameter assumptions; introducing a benchmark-suite format for comparing platforms using only basis-insensitive measurements; including numerical illustrations in SU(2) and SU(4). No claims of global Hamiltonian or connection reconstruction are made. The scope remains deliberately local and operational: the results characterize what can be inferred from invariant interferometric data and where additional assumptions would be required. This version supersedes the previous Zenodo upload and should be regarded as its continuation and technical expansion