Theoretical analysis reveals exact gauge coupling unification and regularized black holes in particle physics, predicting a leptonic CP phase between 1.8 and 6.3 degrees.
We write the source of the Einstein equation as a two-point, channel-resolved tensor whose internal indices label five interaction channels: electromagnetic, strong, weak, gravitational and Yukawa. Requiring that every Standard Model particle occupy exactly one slot forces the internal index to rank four, since a massive quark participates in four interactions at once; the object is then a rank-six tensor with 70 internal slots, three of which vanish by gauge invariance. We verify the assignment is a genuine partition by checking that the summed degrees of freedom reproduce g* = 106.75, a check that caught a three-degree-of-freedom double count between the Higgs doublet and the longitudinal W/Z modes. In this language the Higgs mechanism is an exact transfer of three degrees of freedom between slots, and metric contraction yields 67 equations of state separating the 9% of proton mass sourced through the Yukawa channel from the 23% generated by the QCD trace anomaly. Because a single Newton constant multiplies the whole sum, the contracted Bianchi identity forces channel-dependent gravitational couplings to vanish identically, making the equivalence principle a prediction protected by geometry rather than an input. A minimum length is implemented by smearing the source, leaving the graviton propagator unmodified. We show this placement is forced rather than chosen: chaining the theorems of Schoenberg and Bernstein, a smearing giving a positive energy density must be a superposition of Gaussians, and every such function grows exponentially in the physical timelike channel. The framework is an effective theory whose cutoff exceeds every scale it predicts by at least three orders of magnitude; the metric remains classical and no claim to ultraviolet completeness is made. Solving the field equation with a profile whose logarithmic slope saturates the dominant-energy bound gives a black hole with two horizons, minimum mass 3.0496 Planck masses, a temperature peaking and falling to zero, all four energy conditions satisfied, and Schwarzschild recovered to 5e-4 at 1000 Planck masses. The extremal remnant is shown to carry no charge and no spin, making it a parameterless object and the most collisionless dark-matter candidate proposed, with sigma/m = 1.7e-53 cm^2/g. Exact gauge coupling unification follows from two vector-like SU(2) triplets and a colour octet; the same triplets mediate the type-III seesaw, and a Boltzmann integration verified across nine solver settings gives washout efficiency 4.943e-3, at which standard thermal leptogenesis succeeds without resonance. We also report a negative result obtained by attempting to derive the tensor-to-scalar ratio rather than assume it. Six routes are closed by calculation: a quartic hilltop from the GUT sector cannot satisfy n_s and r together; Coleman-Weinberg inflation from our own spectrum overproduces perturbations by 10^11; and Starobinsky R^2 inflation, though it predicts n_s and r with no residual freedom, is incompatible with the leptogenesis sector through gravitational reheating, direct scalaron decay, a direct scalaron-triplet coupling, gravitational particle production, and primordial black hole emission, the last missing by only a factor of four. The inflaton must therefore be a field separate from both the GUT-breaking field and the scalaron, so r remains an input and the scalar quartic remains free. The framework has two free parameters, z and the scalar quartic, with z confined to 8.50 < z < 13.18 by threshold ordering, proton decay, and the requirement that primordial black holes emit X bosons before becoming relics. Within that window the leptonic CP phase is determined by z. Falsifiable predictions include a leptonic CP phase in the range 1.8 to 6.3 degrees for an assumed neutrino mass of 0.05 eV, mandatory neutrinoless double beta decay, and a channel-separated equivalence-principle test using isotope pairs. The claims tested and withdrawn during preparation are listed explicitly in the manuscript.
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Naphatsakorn Suriyawong (2026) studied this question.
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