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All current versions of the UTI framework papers are available here: https://linktr.ee/uti_papers

VERSION 2.6

Author: Christopher Gu [ georgeguiscool@gmail.com ]

Software Developer based in El Monte, California, USA

April 2026

Abstract

The Universal Topological Impedance (UTI) framework derives a short-range scalar eta from the QCD trace-trace correlator in the scalar-isoscalar 0++ channel, with characteristic mass m_eta ~ 450 MeV and correlation length xi_eta = hbar c / m_eta ~ 0.44 fm. Impedance Contrast Theory (ICT) identifies the de Sitter horizon as the infrared scale setting the transition acceleration a_0 = c H_0 / (2 pi). We combine these two inputs into a constructive Scale-4 model of dark energy in which a collective horizon phase Theta_H(t) is introduced as the zero mode of a postulated horizon-sector phase variable whose coupling to bulk physics is through the trace-channel spectral-asymmetry of local weak and hadronic events rather than through direct bulk propagation of the short-range eta field, and the dark-energy density is identified with a periodic horizon-boundary potential rho_Lambda = chi_H (1 - cos Theta_H), where chi_H has units of energy density. We establish four quantitative results. (i) The horizon cell count from the UTI coherence length: N_cell = 2 (c / H_0 xi_eta)^2 = 1.82 x 10^83. (ii) The horizon susceptibility scale from the chirally-suppressed part of the QCD trace anomaly: E_chiH = chi_H^(1/4) ~ sqrt(mbar_q * Lambda_QCD) ~ 26.5 MeV, which with E_Lambda = 2.30 meV gives Theta_H ~ 1.06 x 10^-20. (iii) A conditional derivation of the leading even-order structure of the per-event APS spectral-asymmetry shift, Delta eta_APS^(a) = C_a (Delta M_tr^(a) / m_eta)^2 + O((Delta M_tr / m_eta)^4), from the Bismut-Freed first-variation identity under the explicit spectral-symmetry assumption J D_0 J^-1 = -D_0, J V J^-1 = +V, together with pole-dominance estimates of the channel-dependent coefficients C_a giving C_He ~ 0.3, C_alpha ~ 0.1, C_beta ~ 0.03, and C_a >= 0 for coherent trace-channel-building transitions. (iv) A computation of the present-day adiabatic ratio Theta_dot_H / (H Theta_H) ~ 4 x 10^-4, yielding a predicted deviation from a pure cosmological constant of |w_eff + 1| ~ 2 x 10^-4 (with a factor-of-several theoretical uncertainty band, Section 9.1) -- consistent with current Planck+DESI bounds and potentially detectable by next-generation surveys. Fluctuations across the N_cell independent horizon domains are suppressed on the l=0 projection by a factor sqrt(N_eff) / N_cell ~ 10^-40, giving a coherent horizon-phase signal-to-noise ratio ~ 10^39. Within the present phenomenological Scale-4 ansatz, the dark-energy problem is reduced to a sharply defined operator problem: compute the trace-channel spectral-asymmetry shift per weak or hadronic event. UTI v2.6 itself derives only the nuclear-scale scalar eta and makes no claim to a derivation of G or any modification of macroscopic general relativity; the horizon-sector phase variable introduced here is a new phenomenological ingredient motivated by the trace-channel impedance interpretation, and its ultraviolet completion is left for future work.

NOTE

This paper essentially replaces Dark Energy from Topological Decay - https://zenodo.org/records/19391183