Wormhole-induced gravi-axion mass distributions and the second-harmonic crossover

Abstract

We compute the distribution of the wormhole-induced gravi-axion curvature mass across baby-universe sectors when the first two harmonics are retained. For independent complex Gaussian coefficients, with an optional displacement of the first channel, an exact global-minimum condition gives the mass distribution and its threshold coefficient. At fixed nonzero second-harmonic width, the cumulative probability below mass $M$ scales as $M^5$. For a weak second harmonic, the unit-harmonic $M^4$ behavior is recovered in an intermediate low-mass range above the crossover scale. We also distinguish the actual relative mass-squared error from the probability that a phase-independent bound fails to certify the unit-harmonic approximation. In the common-background quadratic correlator with unit residues, the lower threshold remains zero and the two-harmonic tail produces an $s^{3/2}$ nonanalytic term in the Euclidean momentum squared $s$. The results are conditional on the chosen state and effective wormhole coefficients.