Unfinished fabric of the three neutrino paradigm

In the current 3. paradigm, neutrino flavor oscillations probe three mixing angles (theta(12),theta(23),theta(13)), one CP-violating phase d, and two independent differences between the squared masses m(i)(2), that can be chosen as delta m(2) = m(2)(2) - m(1)(2) > 0 and Delta m(2) = m(3)(2) - (m(1)(2) (m(2)(2))=2, where sign (Delta m(2)) = +(-) for normal (inverted) mass ordering. Absolute. masses can be probed by the effective mass m(beta) in beta decay, by the total mass S in cosmology and-if neutrinos are Majorana-by another effective mass m(beta beta) in neutrinoless double beta decay. Within an updated global analysis of oscillation and nonoscillation data, we constrain these 3. parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters vertical bar delta m(2)broken vertical bar, vertical bar Delta m(2)vertical bar; theta(12); theta(23); theta(13)) are consistently measured, with an overall accuracy ranging from similar to 1% for j.m2 j to similar to 6% for sin2. 23 (due to its persisting octant ambiguity). We find overall hints for normal ordering (at similar to 2.5 sigma), as well as for theta(23) < pi/4 and for sin delta < 0 (both at 90% C.L.), and discuss some tensions among different datasets. Concerning nonoscillation data, we include the recent KATRIN constraints on m(beta), and we combine the latest Ge-76, Te-130 and Xe-136 bounds on m(beta beta), 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 S and hints on sign(Delta m(2)). The default option, including all Planck results, irrespective of the so-called lensing anomaly, sets upper bounds on S at the level of similar to 10-1 eV, and further favors normal ordering up to similar to 3 sigma. 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 Sigma similar to few x 10(-1) eV, with different implications for m(beta) and m(beta beta) searches. In general, the unfinished fabric of the 3. 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.