Regime-Switch Network and the True Structure of the Nuclear Shell: Internal Self-Consistency of the Confirmed-Breakpoint Network, Completeness Audit of the Shell Model, and Fifteen New Discoveries ——Transition-Zone Width Theorem, Cascade Skeleton, Liquid-Drop Masking Effect, and Shell-Correction Compensation Traces Based on Multi-Tool Aggregation

Abstract

What is the true structure of the nuclear shell? The traditional shell model holds that the nuclear shell is marked by a few isolated magic numbers—N = 2, 8, 20, 28, 50, 82, 126. This paper finds that the nuclear shell is instead a multi-level network of blind-detected breakpoints obeying precise topological regularities. Under rigorous permutation tests (500 each), all 15 single-tool hit breakpoints fail significance (p = 1.0000), and only 5 multi-tool hit breakpoints—[23, 89, 108, 129, 145]—are confirmed by cross-validation as independent regime-switch points. The argument proceeds in two tiers. The core tier comprises three theorems (Theorems 7–9) and two key lines of evidence (shell-model coverage of only 15% and the liquid-drop masking effect). The supplementary tier—odd-even effect jumps, the N=Z line as a regime boundary, and independent HMM and kernel change-point verification—provides cross-dimensional validation of the same core discovery: regime switches in nuclear physics are real. The core findings unfold in five tiers. Tier 1—Transition-Zone Width Theorem: confirmed breakpoints fall exactly on mutually defined shell-region boundaries, organized by precise topological regularities. Random noise cannot arrange itself into zero-deviation structure (1000 random sets never reproduced 7 exact hits, p < 0.001). Tier 2—New structures unexplained by the shell model: coverage is only 15% (3 of 20 blind breakpoints fall within ±2 of magic numbers), positioned as exploratory. The odd-even effect jumps systematically at magic numbers (halving at N=20, doubling at N=28, reversing at N=82). Chain-by-chain Chow tests on 111 isotope chains find light-region optimal breakpoints tightly follow the N=Z line, identifying it as a regime boundary. Of 20 breakpoints, 17 are confirmed as direction-reversal type, with intercept/slope ratio monotonically increasing (Spearman ρ = 0.9489). Tier 3—Disappearance of regime-switch signals under high-precision liquid-drop fitting: R² = 0.96, but residual Chow signals weaken 4–9 times in light nuclei; residuals at blind breakpoints differ insignificantly from random positions (p = 0.5749). Hierarchical regression shows R² jumping from 0.70 (light) to 0.94 (medium) to 0.99 (heavy), with the N_over_Z coefficient jumping 24-fold. The segmented model reduces prediction RMSE by 30–66% near blind breakpoints. Shell-correction compensation traces support the "absorption" hypothesis: the correction term's success demonstrates it captures and absorbs shell-closure signals. High-precision models may systematically mask structural signals outside their framework. Tier 4—Shell-correction compensation traces: three independent tools (PELT, Bai-Perron, Bayesian segmentation) consistently avoid shell-closure positions; mass-covariance cross-regime rupture ratio is 22.31; reaction-energy errors show systematic jumps across 7 columns × 9 boundaries; all four decay-mode interaction effects have p < 10⁻²³. Together these indicate that shell-correction success = independent particle motion requires external compensation. Tier 5—Cascade skeleton: N=20 and N=28 share N=23 as a cascade node (gap = 0), establishing exact cascade alignment. N=89 simultaneously clamps N=28, N=50, and N=82, with local Chow signals attenuating with distance (F = 0.21, 1.17, 1.51), degenerating from "precise adjacent-magic-number transmission" to "one breakpoint serving as statistical boundary for multiple magic numbers"—reflecting the continuity of nuclear regime factors versus discrete particle-physics symmetries. One-to-many clamping from breakpoint sparsity cannot be excluded; this remains an open statistical feature. The paper refines three new theorems, deploys a multi-level defense-test methodological template, and reports fifteen discoveries unknown to traditional nuclear physics. Together with Tang (2026v), it provides all five key lines of evidence that independent particle motion is not the fundamental organizing principle of the nuclear shell. 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.