We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings–Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of 1014, and this same model is favored over an uncorrelated common power-law spectrum model with Bayes factors of 200–1000, depending on spectral modeling choices. We have built a statistical background distribution for the latter Bayes factors using a method that removes interpulsar correlations from our data set, finding p = 10−3 (≈3σ) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of interpulsar correlations yields p = 5 × 10−5 to 1.9 × 10−4 (≈3.5σ–4σ). Assuming a fiducial f −2/3 characteristic strain spectrum, as appropriate for an ensemble of binary supermassive black hole inspirals, the strain amplitude is 2.4 − 0.6 + 0.7 × 10 − 15 (median + 90% credible interval) at a reference frequency of 1 yr−1. The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings–Downs correlations points to the gravitational-wave origin of this signal.

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The 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons.

The present study demonstrates the importance of adequate precision when reporting the δ and J parameters of frequency domain 1H NMR (HNMR) data. Using a variety of structural classes (terpenoids, phenolics, alkaloids) from different taxa (plants, cyanobacteria), this study develops rationales that explain the importance of enhanced precision in NMR spectroscopic analysis and rationalizes the need for reporting Δδ and ΔJ values at the 0.1–1 ppb and 10 mHz level, respectively. Spectral simulations paired with iteration are shown to be essential tools for complete spectral interpretation, adequate precision, and unambiguous HNMR-driven dereplication and metabolomic analysis. The broader applicability of the recommendation relates to the physicochemical properties of hydrogen (1H) and its ubiquity in organic molecules, making HNMR spectra an integral component of structure elucidation and verification. Regardless of origin or molecular weight, the HNMR spectrum of a compound can be very complex and encode a wealth of structural information that is often obscured by limited spectral dispersion and the occurrence of higher order effects. This altogether limits spectral interpretation, confines decoding of the underlying spin parameters, and explains the major challenge associated with the translation of HNMR spectra into tabulated information. On the other hand, the reproducibility of the spectral data set of any (new) chemical entity is essential for its structure elucidation and subsequent dereplication. Handling and documenting HNMR data with adequate precision is critical for establishing unequivocal links between chemical structure, analytical data, metabolomes, and biological activity. Using the full potential of HNMR spectra will facilitate the general reproducibility for future studies of bioactive chemicals, especially of compounds obtained from the diversity of terrestrial and marine organisms.