Operational Holonomy: A Null Test for Non-Metric Signal Degradation in Vacuum

Arc VI — Experiment Paper 1 Title Operational Holonomy: A Null Test for Non-Metric Signal Degradation in Vacuum Zenodo DOI 10.5281/zenodo.18180824 This paper proposes a precision null test for metric gravity based on the operational recoverability of timing and phase information along distinct vacuum propagation paths. In stationary general relativity, any two null paths connecting the same emission and reception events must exhibit identical recoverability; irreversible degradation of phase or timing is strictly path independent. The paper formalizes this statement using an operational transport law for distinguishability loss, introducing a scalar degradation functional whose path integral defines an observable invariant. Differences in degradation between two paths constitute operational holonomy, analogous to geometric holonomy but defined entirely in terms of record recoverability rather than spacetime curvature. A nonzero operational holonomy in vacuum—after subtraction of known instrumental and environmental effects—constitutes a direct falsification of metric gravity as a complete operational description of signal propagation, independent of microscopic mechanism. The test is explicitly model-agnostic and applies equally to optical interferometry, atomic clocks, and gravitational-wave detectors. The work reframes multipath coherence stability as a fundamental calibration target rather than a technical nuisance and identifies operational holonomy as a new experimental observable sensitive to non-metric structure in vacuum. Keywords tests of general relativity; interferometry; operational holonomy; signal recoverability; vacuum propagation; null tests; precision measurement Notes Arc VI — Experiment (null-test cornerstone) Defines operational holonomy as a two-path invariant Path dependence forbidden in stationary metric gravity Nonzero signal falsifies GR operational completeness Directly testable with existing interferometric and clock technologies