Cancellation of Renormalization in Hyperbolic Unity Theory (HUT): How the Finite Geometric Correction 𝛿 Replaces the Infinite Loop Series

Renormalization remains one of the most controversial and inelegant techniques inquantum field theory: infinite loop integrals are subtracted using infinite counterterms,while bare parameters are introduced by hand. For nearly 80 years this method has savedthe theory of divergences, yet it has provoked deep distrust among the founders of thediscipline — Dirac, Feynman, Schwinger. Hyperbolic Unity Theory (HUT) proposes a radically different approach: infinitiesdo not need to be subtracted — they are prevented from the very beginning.The cubic curvature correction R3 in the Lagrangian automatically cuts off the ul-traviolet at the Planck scale, transforming an infinite series of loops into a single finitegeometric correction 𝛿, expressed through five fundamental entities: the Planck length ℓPl,the golden ratio 𝜙, the numbers 𝜋 and 𝑒, and the resonant number 1729. This universal correction 𝛿 simultaneously describes several key anomalies of theStandard Model with accuracy within experimental error:• the muon anomalous magnetic moment (𝑔 − 2)𝜇 (tension 2–4𝜎),• the Lamb shift in hydrogen (accuracy 10−9–10−10),• the proton anomalous magnetic moment (𝑔𝑝 − 2)/2 (non-perturbative QCD, error0.3 ppb). In all cases calculations take seconds instead of years of supercomputer time, andinfinite series are replaced by a single geometric formula. The theory is stable (no ghost fields), finite by construction, and does not requirerenormalization because the Planck scale is built into the vacuum structure.HUT reveals a unified pattern: all radiative corrections are deformations of the dualvacuum (local cubic layer + nonlocal hyperbolic {5, 3, 3} tessellation), balanced by the1729 resonance. This is a step toward a physics where infinities never appear and parameters are derivedfrom geometry rather than fitted by hand.