Orbital Nodal Phase as a Pipeline Invariant in Black Hole Timing

Timing analyses of accreting black holes often package nodal information in ways that depend on benign choices of time and azimuthal convention. We identify the corresponding pipeline-invariant content for slightly tilted circular rings and express it as an orbital nodal phase, Δψ orb . In Kerr, this quantity gives the clean geodesic baseline for nodal timing: it equals the nodal precession per orbit, is invariant under the benign remappings considered here, and decreases monotonically with radius outside the innermost stable circular orbit. A fixed-Ω φ . response framework then isolates genuine metric sensitivity from trivial radius drift and yields a leading far-field quadrupolar response that falls as r −3 . Two small analysis-level corrections are also identified, namely a second-order bias from coherent radial breathing and a geometric offset from slow two-parameter loops. A limited published-data illustration for GRO J1655.40 shows that the observational proxy for Δψ orb can be reconstructed directly from standard reported quasi-periodic oscillation frequencies once an orbital-frequency anchor and an identification convention are specified. Within the thin-ring limit, Δψ orb therefore provides a pipeline-robust reporting quantity and a Kerr-baseline diagnostic for source-level, simulation-level, and strong-gravity applications.