Topological Nuclear Physics and Civil Nuclear-Energy Science: A Three-Axiom Reconstruction of Nuclear Structure, Reactions, Transport, Safety, and Phase-Locked Waste Transformation

Abstract

We develop a unified theoretical architecture for nuclear physics and peaceful nuclear-energy science from three physical axioms: finite microscopic localization, a dynamical spacetime-vacuum substrate, and persistent causal source–response coupling. Finite nuclei are formulated as antisymmetric many-nucleon states within specified baryon-number, charge, angular-momentum, parity, isospin, and topological sectors. Nuclear binding, spectra, decay, scattering, fission, fusion, neutron and radiation transport, thermal–hydraulic evolution, material damage, safeguards, and waste management are constructed as controlled reductions of a common finite-core Hamiltonian and conservation ledger. Conventional natural decay, neutron transmutation, photonuclear reactions, accelerator-driven processes, conditioning, and geological disposal are retained as experimentally established baselines. In parallel, we formulate a distinct hypothetical branch of direct phase-locked topological-wave nuclear transformation. A finite-power causal wave couples directly to admissible nuclear operators in the Hamiltonian, drives an intermediate nuclear state, undergoes spatial phase capture and locking, and transfers population into explicitly tracked drain channels. Selection rules, finite-nucleus form factors, complete positivity, branching normalization, daughter inventories, heat, radiation, boundary leakage, and energy conservation constitute noncompensatory acceptance conditions. The direct branch is developed from zero-dimensional density-matrix and Floquet models to a spatially and temporally resolved multiphysics initial–boundary-value problem coupling a positive-energy hyperbolic wave equation, local Lindblad dynamics, noisy phase reaction–diffusion, nuclide reaction–transport networks, heat conduction, and radiation transport. Numerical regressions verify causal propagation, zero-drive and natural-decay limits, probability positivity, inventory conservation, spatial and temporal refinement, shutdown decay, boundary-flux accounting, and separated field and thermal–radiation energy ledgers. Conditional inverse calculations determine the coupling, coherence, locking, detuning, and drain domains required to reach a specified 90-day half-inventory target without assigning unmeasured generator power or nuclear matrix elements. The calculations establish a falsifiable mathematical and numerical research framework, not experimental evidence for rapid waste elimination. Direct nuclear matrix elements, complete low-hazard drain branches, source calibration, scale-up behavior, and independent experimental replication remain unresolved. If these certificates are eventually satisfied, the theory would motivate investigation of large conditioned waste inventories on an order-of-years treatment timescale while preserving conventional containment, safeguards, secondary-waste management, and final-disposal requirements. Keywords Topological nuclear physics; nuclear many-body theory; causal response fields; phase locking; Floquet nuclear dynamics; open quantum systems; nuclear transmutation; radioactive waste; nuclide evolution; reaction–diffusion networks; radiation transport; multiphysics simulation; energy conservation; nuclear safety; falsifiability.