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

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 Ψ_c ≡ δΦ_N/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 ≃ Ψ_c. With cosmological background inputs and the local density prior ρ_DM,loc as external calibrations, all experimental information enters only through published upper-limit curves. Fixing the tested mass sector by the searched line frequency, f_line(m) = 2mc²/h, we map PTA limits into an upper bound f_SF,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 ρ_DM,loc = 0.43 GeV cm⁻³, a fully coherent local component (f_SF = 1) is excluded for m ∈ [1.04, 6.78] × 10⁻²⁴ eV (equivalently f_line ≈ 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.