Harmonic Fields — Atlas Theory Paper I Temporal Harmonic Structure, Clock Projections, and Admissible Phase Conditions

This paper presents a structural analysis of temporal behavior in Pulsar Timing Array (PTA) data using diagnostics designed to survive standardization and clock control. Rather than relying on clock synchronization or inter-clock correlations, which are shown to be unsuitable observables for temporal structure in standardized PTA products, the analysis employs a scalar diagnostic (λ) sensitive to changes in admissible temporal dynamics within individual pulsar residuals. Independently identified node epochs are used to define analysis windows, allowing direct comparison between node-aligned intervals and matched control intervals within each pulsar’s data. Across a subset of pulsars, node-aligned windows consistently exhibit suppression of variance and short-timescale volatility in λ, indicating a contraction of admissible temporal phase space rather than a shift in absolute timing or phase alignment. Multi-pulsar coincidence analysis shows that these effects are temporally localized, sparse (typically involving 2–4 pulsars), and exhibit no statistically resolvable propagation lag within the temporal resolution of the PTA residual data. The absence of spatial correlation structure, recurrent pulsar pairing, or array-wide participation excludes a Hellings–Downs gravitational-wave background or other propagating signal interpretations for this signal class. The results support an interpretation of node epochs as transient temporal constraint regimes—periods in which admissible temporal dynamics are structurally restricted despite aggressive standardization of timing products. The paper is intended as a theory and diagnostics framework (Atlas Theory Paper I), establishing observable consequences of temporal harmonic structure while remaining agnostic to microphysical mechanisms.