A Complete Global-Realist Theory of Nuclear Fusion: From Finite-Core Reaction Dynamics and Terrestrial Confinement to Stellar Burning, Massive Stars, and Supermassive-Star Stability

We construct a unified, calculable, and falsifiable theory of nuclear fusion as a conservative extension of the three-axiom global-realist framework. The theory covers finite-core nuclear reactions, thermonuclear rates, reaction networks, terrestrial controlled fusion, ordinary stellar burning, advanced burning in massive stars, and the stability and evolution of very massive and supermassive stars. A unified state vector and parent action couple gravity, plasma kinetics, nuclear reactions, electromagnetism, radiation, material boundaries, and retarded historical response while enforcing an explicit no-double-counting ledger. The standard astrophysical \(S\)-factor, Breit–Wigner resonances, Maxwellian reaction rates, Gamow windows, screening limits, detailed balance, and positive abundance networks are recovered as controlled classical limits. Finite-core and historical-response corrections enter as signed, experimentally calibratable residuals; neither their sign nor their effect on fusion is assumed in advance. The stellar branch combines nuclear networks with mass-coordinate structure, entropy evolution, composition transport, radiation and neutrino losses, convection, rotation, accretion, winds, and moving-boundary inventories. It distinguishes ordinary hydrogen and helium burning from carbon, neon, oxygen, and silicon burning, quasi-statistical and nuclear statistical equilibrium, photodisintegration, electron capture, pair softening, and core collapse. Newtonian hydrostatic structure, the Tolman–Oppenheimer–Volkoff equations, relativistic radial Sturm–Liouville stability, and a coupled nonadiabatic operator pencil are formulated within one stability hierarchy. Terrestrial magnetic, inertial, magneto-inertial, pulsed, and electrostatic branches are evaluated through kinetic, magnetohydrodynamic, transport, Lawson, fuel-cycle, tritium, neutron, material, exergy, maintenance, and lifecycle constraints. Sustained fusion is defined by membership in a joint infinite-horizon viability kernel rather than by a positive reaction \(Q\)-value or isolated gain metric. Executable regressions recover the declared classical baselines and provide Level-II results for specified reduced models. They do not establish a universal classification of supermassive stars or a universal prohibition of terrestrial fusion power. Accordingly, the proposed Level-IV terrestrial statement remains the explicitly falsifiable **Fusion No-Go Conjecture**. Keywords **nuclear fusion; global realism; finite-core dynamics; historical response; thermonuclear reaction rates; astrophysical S-factor; Gamow peak; nuclear reaction networks; controlled fusion; Lawson criterion; stellar nucleosynthesis; massive stars; supermassive stars; relativistic stellar stability; TOV equation; radial pulsations; pair instability; plasma confinement; energy and exergy accounting; viability theory**