The Regime Nuclide Map (I): Cross-Property Verification, Two-Dimensional Structure, and Network Update of the Confirmed Breakpoint Network ——Predictive Test and New Discoveries Based on the Nuclear Shell Regime-Switching Theory

Abstract

The nuclear shell regime-switching theory (Tang, 2026v–y) predicts that the confirmed breakpoint network should be consistently established across independent physical quantities. This paper verifies this prediction for the first time and discovers new structures guided by the theory. The main findings include: (1) The confirmed breakpoint network consistently passes cross-property verification on two independent physical quantities—two-neutron separation energy and α-decay energy—with both quantities achieving a 100% fracture rate at N=129, and both exceeding 84% at N=23; the newly confirmed breakpoints N=40 and N=64 also pass verification (fracture rates 23.8%–66.7%). This is decisive evidence that the confirmed breakpoint network is not a statistical artifact of the binding energy equation. (2) For the first time, the confirmed breakpoint network is found to possess a rigorous two-dimensional (N,Z) structure—Z itself regulates all three execution factors through interaction effects (ΔR²=0.0006–0.0909), and the N-Z synergistic effect (p=9.04×10⁻¹⁹³) confirms for the first time that neutron-proton asymmetry is an independent regime modulator. All five confirmed breakpoints are highly significant on the Z-axis (p=1.11×10⁻¹⁶). This is the first purely data-driven two-dimensional regime-switching network in the history of nuclear physics. (3) On the full N-axis breakpoint scoring curve, N=40 and N=64 are identified as confirmed breakpoints for the first time—integrating multi-dimensional evidence (local Chow F, multi-tool cross-validation, cross-property fracture rates), both rank within the top 40% stably under multi-scheme scoring, and within the top 25% under the composite scheme. The traditional shell model underestimates them as "subshell closures", while the nuclear shell regime-switching theory correctly positions them as major shell closure levels. After forced inclusion of N=40/64, BIC increases (+129–135), but the economy of BIC does not equal physical reality—the local Chow F and cross-property fracture rates independently confirm them as genuine physical signals. After expanding the confirmed breakpoint network from 5 to 7, the deviations of Theorem 7 across six shell regions are all zero, and the extended version of Theorem 8 adds secondary cascade nodes. The confirmed breakpoint network remains robust after removing the superheavy region (all confirmed breakpoints p=1.11×10⁻¹⁶). All findings pass rigorous verification by the CUSUM test (7/7 significant), 500 permutation tests (empirical p=0.0000, binomial test p=0.000000), instrumental variable method (first-stage F=309.33, IV and OLS coefficient sign reversal), and fake data audit (Chow F=0.15, p=0.8572). This paper releases version 1.0 of the Regime Nuclide Map and the nuclide regime coordinate database (3558 nuclides × 25 fields) as open data assets. Research Paradigm Statement: The core methodology, research direction, and final decisions were independently directed by the author. DeepSeek assisted with code implementation, data presentation, and text drafting. The author takes full academic responsibility for the final content.