Vol. 8, Issue 1, Part A (2026)

Despite decades of effort, expressing the Planck length and Newton’s gravitational constant in terms of elementary constants remains a challenge; in this work, the 4G final-unification model is applied to relate the distance light travels during the neutron lifetime to nuclear parameters, proton mass, nuclear volume, and neutron–proton mass difference, showing that slight variations in the nuclear charge radius modulate neutron lifetime and resolve the beam–bottle discrepancy (≈885 s vs 875 s) through thermodynamic control of decay processes. This thermodynamic sensitivity finds experimental support in recent J-PARC pulsed cold-beam measurements that converge toward bottle-type lifetimes, strengthening the connection between nuclear structure, decay dynamics, and emergent Planck-scale signatures in low-energy observables. Remarkably, when the neutron’s 880-second laboratory lifetime is scaled by the neutron-proton mass ratio (Δm/mp ≈ 0.00138), it yields approximately 1.2 seconds, precisely matching the weak interaction freeze-out epoch in the early universe, about one second after the Big Bang. This cosmological coincidence reveals that the neutron carries within its decay properties an encoded memory of primordial conditions, establishing a direct bridge between laboratory nuclear physics and early universe dynamics where weak and gravitational interactions jointly determined the matter content of our cosmos. A semi-empirical expression for Newton’s gravitational constant is then derived from nuclear metrics and Fermi’s weak coupling constant, and combined with a 4G-based neutrino mass scheme that yields an electron-neutrino mass of order 0.3 meV, a total neutrino–antineutrino mass sum ≈0.124 eV, and a characteristic electroweak fermion of rest energy ≈585 GeV that acts as a zygote for all fermions. Remarkably, this 585 GeV scale aligns with multiple high-energy astrophysical indications: (i) TeV-scale breaks and excess features in the Galactic all-electron spectrum around 0.6–1.5 TeV, compatible with pair-production or cascade signatures of a ∼585 GeV charged fermion; and (ii) Totani’s 20 GeV Galactic-center gamma-ray excess, consistent with annihilation of neutral particles in the 500–800 GeV range, close to the neutral partner mass expected for a Higgsino-like state associated with the 585 GeV fermion. These converging nuclear, laboratory, cosmological, and Galactic observations suggest that a single electroweak–gravitational mass scale near 585 GeV may underlie both neutron-lifetime phenomenology and cosmic high-energy radiation, opening new avenues for testing quantum gravity, dark-matter–motivated Higgsino scenarios, and neutrino mass generation within an experimentally anchored 4G framework.