Unfinished fabric of the three neutrino paradigm

In the current 3ν paradigm, neutrino flavor oscillations probe three mixing angles (θ₁₂,θ₂₃,θ₁₃), one $CP$-violating phase δ, and two independent differences between the squared masses mᵢ², that can be chosen as δm²=m₂²-m₁²>0 and Δm²=m₃²-(m₁²+m₂²)/2, where sign(Δm²)=+(-) for normal (inverted) mass ordering. Absolute ν masses can be probed by the effective mass m_β in beta decay, by the total mass Σ in cosmology and---if neutrinos are Majorana---by another effective mass m_ββ in neutrinoless double beta decay. Within an updated global analysis of oscillation and nonoscillation data, we constrain these 3ν parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters (δm²,|Δm²|,θ₁₂,θ₂₃,θ₁₃) are consistently measured, with an overall accuracy ranging from ~1% for |Δm²| to ~6% for sin²θ₂₃ (due to its persisting octant ambiguity). We find overall hints for normal ordering (at ~2.5σ), as well as for θ₂₃<π/4 and for sinδ<0 (both at 90% C.L.), and discuss some tensions among different datasets. Concerning nonoscillation data, we include the recent KATRIN constraints on m_β, and we combine the latest ⁷⁶Ge, ¹³⁰Te and ¹³⁶Xe bounds on m_ββ, accounting for nuclear matrix element covariances. We also discuss some variants related to cosmic microwave background (CMB) anisotropy and lensing data, which may affect cosmological constraints on Σ and hints on sign(Δm²). The default option, including all Planck results, irrespective of the so-called lensing anomaly, sets upper bounds on Σ at the level of ~10^-1 eV, and further favors normal ordering up to ~3σ. An alternative option, that includes recent ACT results plus other independent results (from WMAP and selected Planck data) globally consistent with standard lensing, is insensitive to the ordering but prefers Σ~few×10^-1 eV, with different implications for m_β and m_ββ searches. In general, the unfinished fabric of the 3ν paradigm appears to be at the junction of diverse searches in particle and nuclear physics, astrophysics and cosmology, whose convergence will be crucial to achieve a convincing completion.