Discrete Curvature–Torsion Spectra and the Origin of Nuclear Stability

Title: Discrete Curvature–Torsion Spectra and the Origin of Nuclear Stability Author: A. E. C. BishopDate: February 11, 2026License: CC‑BY 4.0 Description: This work introduces a discrete curvature–torsion lattice framework in which nuclear stability, decay behavior, and binding‑energy extrema arise as spectral properties of an indexed Hamiltonian. Physical configurations are labeled by a successor‑ordered index ( n ), and their stability is determined by spectral gaps and arithmetic sectorization modulo four. Without invoking new particles, forces, or fitted parameters, the framework reproduces several long‑standing empirical regularities: the rarity of odd‑odd nuclei, the emergence of half‑lives as gap‑controlled metastability, and the global binding‑energy maximum at iron‑56. The Hamiltonian ( H_n ) encodes curvature ( kappa_n ) and torsion ( tau_n ) degrees of freedom on a discrete lattice. Its spectrum partitions into superselection sectors ( n equiv 0,1,2,3 mod{4} ), with the ( 3 mod{4} ) sector exhibiting maximal stability and the ( 1 \pmod{4} ) sector appearing metastable. Decay corresponds to spectral flow between these sectors, and the half‑life scales with the smallest excitation gap (Delta E_n ). Evaluating the lowest spectral branch reveals a global minimum at the index corresponding to iron‑56, where curvature and torsion are optimally balanced and the spectral gap is maximized. Nickel‑62 appears as a nearby local minimum but does not achieve global spectral closure. The framework also explains the termination of stellar fusion: fusion pathways correspond to monotonic descent along the spectral landscape until the iron minimum is reached, beyond which no further exothermic descent is possible. Rather than replacing the Standard Model, this approach constrains its collective outcomes. Arithmetic labels classify spectral sectors without introducing new degrees of freedom, and the observed nuclear regularities emerge from discrete spectral structure rather than continuous mean‑field dynamics alone. Keywords: curvature–torsion lattice, nuclear stability, spectral gaps, mod‑4 sectorization, iron‑56, discrete Hamiltonian, successor indexing, metastability, binding energy, arithmetic structure