Pulsar timing limits as clock-modulation bounds on coherent ultralight dark matter

Abstract We present a deterministic no-refit recast of pulsar-timing array (PTA) line-search limits on ultralight scalar-field dark matter (ULDM) into constraints on a single operational clock-modulation observable, δω_Φ/ω_∞, whose weak-field limit is the standard oscillatory potential amplitude Ψc ≡ δΦN/c². The construction is recovery-first: in stationary segments we identify the general-relativistic lapse with the normalized carrier phase-rate, N ≡ ω_Φ/ω_∞, so linear perturbations satisfy δω_Φ/ω_∞ ≃ δN ≃ Ψc. With cosmological background inputs and the local density prior ρDM, loc as external calibrations, all experimental information enters only through published upper-limit curves. Fixing the tested mass sector by the searched line frequency, fₗine (m) = 2mc²/h, we map PTA limits into an upper bound fSF, max (m) on the locally coherent ULDM fraction, without refitting cosmology or introducing a new PTA response model. Using provenance-tracked digitizations and a public figure-regeneration script, we form a conservative envelope across pulsar-correlated (common) PTA datasets and find that, for ρDM, loc = 0. 43 GeV cm⁻³, a fully coherent local component (fSF = 1) is excluded for m ∈ 1. 04, 6. 78 × 10⁻²⁴ eV (equivalently fₗine ≈ 5 × 10⁻¹⁰–3 × 10⁻⁹ Hz). Because the constrained quantity is a clock-modulation amplitude, the same observable provides a portable standard for cross-comparing PTA and precision-clock limits under explicitly stated priors.