Universal Vector White Paper

Abstract Abstract We define and operationalize a single, reproducible statistic for testing large-scale isotropy: the energy-density–weighted mean peculiar-velocity vector of observable contents, evaluated in the cosmic microwave background (CMB) rest frame on a fixed time slice. For brevity only, we refer to this quantity as the “universal vector” (quoted descriptive label; not a new term). We specify component weightings, reference frame details, baseline and hierarchical estimators, prescriptive systematics tests, reporting schema, and governance. The statistic is expected to be approximately zero (within uncertainties) in ΛCDM; robust non-zero values should trigger systematic audits and re-examination of isotropy assumptions.