Correct and adequate LENR theory must satisfy several fundamental principles and provide a justification for known experimental facts and paradoxes:

1. Abnormally high probability at low energy of interacting particles.
2. Significant suppression or absence of radioactive daughter isotopes and accompanying gamma-radiation.
3. The possibility of implementation in various material media and systems (solids, liquids, gases, low-temperature plasma, beams of low-energy particles, biological systems).
4. Abnormally selectivity of the LENR probability and its anomalous inversion during the transition from hot fusion to LENR for different isotopes of some elements (e.g., at high energies the probability of ⁶Li+p=³He+⁴He reaction is 100 times greater than ⁷Li+p=⁴He+⁴He, and at low energy is thousands of times less; at high energy the probabilities of d+d=³He+n and d+d=³H+p reactions are equal, and at low energy they differ by 10⁷ times).
5. LENRs are always implemented only under non-stationary local conditions.

These phenomena cannot be explained within the framework of traditional models of nuclear physics. On the other hand, the LENR theory must be based on the standard laws of quantum mechanics and electrodynamics.

All these LENR paradoxes find a comprehensive explanation using the LENR theory, based on coherent correlated states (CCS) of interacting particles. The specific mechanism for the formation of CCS is associated with the constructive interference of the particle’s eigen wave functions, which occurs when the parameters of the local environment of a given particle change (change of microcracks or magnetic field, rapid movement of neighboring particles, movement in inhomogeneous fields, dynamic processes such as cell division or DNA replication in biomolecules, etc.). The existence of such states is based on the fundamental Robertson-Schrödinger uncertainty relation and is fully consistent with the laws of quantum mechanics. The features of processes and paradoxes when using such states are associated with two fundamental reasons: the formation of very large (giant) fluctuations of the kinetic energy of particles (a,c,e) and the virtual (short-term) nature of these fluctuations with their obligatory disappearance after the completion of the fluctuation, which is fundamentally different from standard nuclear fusion using real (not virtual) energy (b,d).

V.I.Vysotskii, M.V.Vysotskyy. Cold Fusion. Advances in Condensed Matter Nuclear Science, Edited by Jean-Paul Biberian. Elsevier, 2020. CHAPTER 17 pp. 333-370;
V.I.Vysotskii, A.A.Kornilova. Cold Fusion. In the same book, CHAPTER 12 pp. 205-232;
V.I.Vysotskii, M.V.Vysotskyy. Coherent correlated states and low-energy nuclear reactions in non stationary systems. European Phys. Journal. A (2013) v.49 issue 8:99 (2013), p.1-12;
V.I.Vysotskii, M.V.Vysotskyy. Peculiarities of correlated states and the mechanism of automodeline selection of nuclear reaction channels with low energy of charged particles. J. Exp. Theor. Phys. v. 128 (6), (2019), 856–864
V.I.Vysotskii, M.V.Vysotskyy. Self-controlled Flashing Nuclear fusion in Stationary Magnetized Low-temperature Plasma. Fusion science and technology, v. 79:5 (2023), 537-552
V.I.Vysotskii, A.A.Kornilova. Transmutation of stable isotopes and deactivation of radioactive waste in growing biological systems. Annals of Nuclear Energy, 62 (2013), 626-633.