Recalibration of the UAT/UCP Acoustic Horizon: From the Empirical Approximation r_d ≈ 141 Mpc to the Exact Value r_d = 128.15 Mpc

This Zenodo repository contains the formal technical note that corrects the UAT/UCP acoustic horizon value. Previous UAT/UCP analyses used r_d ≈ 141 Mpc as an effective value. That value came from an empirical scaling relation and an external calibration baseline, not from the exact sound-horizon integral. This update replaces that approximation with a direct integration of the sound-horizon equation from z_rec = 1089 to z_max = 20000, using: the stable scalar-field branch phi(z_rec) ≈ 0 baryon density from BBN photon density from COBE/FIRAS H0 = 73.04 km/s/Mpc from SH0ES pure Python integration without CLASS, CAMB, or LCDM libraries The corrected result is: r_d = 128.15 Mpc This is not a new free parameter. It is a numerical correction of the same physical integral that the earlier approximation avoided. IMPORTANT: The upload of this new update on the corresponding platform supersedes Note 7 in the predecessor upload. Earlier technical documents that used r_d ≈ 141 Mpc are retained as Supplementary 2 for historical reference. All previous BAO fits based on 141 Mpc should be recalculated. The note includes the field equations used to obtain the corrected result and documents the limitations of the current calculation. ## Contacto Puán, Buenos Aires, Argentina - [email protected]