Empirical Discovery of the Stability Critical Point in the Heavy Nuclide Region: Cliff Collapse and Forced Fission Mode Switching at N/Z=1.55

How the instability of heavy nuclides evolves with increasing neutron number, and whether a definitive critical point exists, has been an open question. This paper uses experimental data for 577 heavy nuclides (Z > 82, N > 126) from the ENDF/B-VIII.0 Nuclear Data Library. Through segmented linear regression, Chow tests, fission mode statistics, and half-life distribution analysis, a statistically highly significant critical inflection point is discovered at N/Z = 1.55. Before this inflection point, nuclide stability is gently sustained as neutron number increases, with α-decay being absolutely dominant (over 90%). After this inflection point, stability undergoes a cliff collapse; α-decay and β⁻-decay undergo a sharp crossover switching, with β⁻-decay rising to dominance and the spontaneous fission channel being forced open. The Chow test p-value for the inflection point is less than 0.000001, indicating extremely high statistical significance for the structural break. Spontaneous fission appears only after N/Z > 1.55; no counterexample is found within the stable region of N/Z ≤ 1.55. Using the critical-point law, predictions are extrapolated for the half-lives and dominant decay modes of 42 unsynthesized nuclides, providing clear search directions and priority target coordinates for superheavy stability island experiments. This paper also tests the common intuition that "an increase in atomic number Z is equivalent to an increase in N/Z" and finds that the driving force for fission mode switching is the neutron excess (N/Z) rather than the absolute atomic number (Z), ruling out Z as a confounding variable. All analyses use publicly available data and standardized statistical methods; any nuclear physicist can independently reproduce them.