The QCD Angle in the Bounce Frame: A Transfer Test of Counting Saturation, and a Fine-Tuning That Is Not a Counting Error
Year: 2026
Type: article
Abstract: The counting rule of the Einstein-Cartan bounce frame -- counting saturation, the rule whose application to the vacuum energy sum dissolves the 10^122 gap of the vacuum catastrophe and whose application to the Higgs quadratic correction removed 19.21 of its 32.69 orders of fine-tuning -- is here run at a third address: the strong CP problem, the unexplained smallness of the QCD angle theta-bar. The transfer test returns a negative result, and the result is structural, not numerical. The rule corrects accumulations: sums over modes whose addends are independent only below a derived density bound, rho_A = 9.7x10^54 g/cm^3, with independence ending at the crossing E_ind = 3.02x10^9 GeV. Theta-bar is not an accumulation. It is a single dimensionless parameter of the Lagrangian, and the observable that bounds it is a product, not a sum: the neutron electric dipole moment is d_n = c * theta-bar with a finite, convergent hadronic coefficient c = (2.4 +/- 40%)x10^-16 e cm from QCD sum rules (chiral estimates span 1.2-3.3x10^-16 e cm), so the 2020 nEDM limit |d_n| < 1.8x10^-26 e cm (90% CL) gives |theta-bar| < 7.5x10^-11, and below 1.5x10^-10 for every coefficient in the published envelope. The one formal sum in the problem, theta-bar = theta + arg det M_q, fails the rule's first condition on inspection: its addends are basis artefacts. Under chiral rotations the individual phases move by amounts of order one radian while theta-bar is invariant to machine precision (|Delta theta-bar| <= 8.0x10^-15 over 10^5 random rotations), and the decomposition can be gauged entirely into theta or entirely into the mass matrix without changing any physics. The one energy density the theta sector owns, the theta-bar-dependent vacuum energy, spans Delta V = 2.43x10^13 g/cm^3, 41.60 orders of magnitude below the bound at which the rule acts. The regulated and standard statements at this address are therefore identical, and the fine-tuning stands at full size: two independent angles, one from the gluon sector and one from the Yukawa sector, must sum to within 7.5x10^-11 of zero, a flat-prior probability of 2.39x10^-11, one part in 4.19x10^10. The strong CP problem is not a counting error. It is parameter smallness of the pure species, and no counting rule speaks to it. The Peccei-Quinn mechanism, which addresses exactly this species of problem by making the parameter dynamical, is untouched by this result in either direction. The vacuum grades are unchanged throughout: the dissolution of the vacuum catastrophe's magnitude stands established on its postulate, the surviving count stands unproduced, and the catastrophe stands not solved.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225753857
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