The UAT/UCP Framework Complete Closure: Lagrangian with η≡κcrit=4. 978, Effective Matter Density Ωmᵉff=0. 3133, Laboratory Geometric Invariant Rgeom=0. 279182 from 8-Coil Frequency Detuning 43. 515°, and Corrected Sound Horizon rd=128. 15 Mpc (vs 141 Mpc Proxy)

This record contains the complete, corrected closure of the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) framework. Main Paper (3 pages, maincorrected. pdf): Derivation of the UAT scalar-tensor action SUAT = ∫√-gMpl²/2 R -1/2 (∂φ) ² -V (φ) -ξ/2 Rφ² + Lm with V (φ) =λ/4 (φ²-η²) ². Three parameters rigidly fixed, not free: η≡κcrit=4. 978 (Ivancho causal coherence limit), φ*=0. 07η=0. 34846 (7% thermal calibration margin at recombination), kearly=0. 967 (quantum brake from laboratory experiment). From kearly=1/ (1-ξφ*²): ξ=-0. 2810, λ=3. 08e-112. Numerical Klein-Gordon integration z=1e9→0 shows frozen field φ (0) =0. 45588 (90. 84% away from η). Freezing does not invalidate amplification because causal membrane integral Mp=∮Ψ8phase·κcrit dt depends on κcrit as structural constant, not on φ (z). Amplification factor A=κcrit×φ× (1-0. 07) =7. 4908 (φ=1. 618034 golden ratio from 8-phase topology) converts BBN Ωb=0. 04182 into Ωmᵉff=0. 3133, matching Planck 2018 0. 315±0. 007 within 0. 55%. Effective Friedmann H²= (3Mpl²) ^-1 kearly (ρm+ρr). Sound Horizon Correction: Early UAT literature used effective proxy rd≈141 Mpc from MCMC Phases 7-9 fitting Pantheon+ (1587 SNe), Planck shift R, and BOSS BAO, giving acoustic shift +5. 85% (lA 296. 3→313. 6). This work provides first-principles integration rd=∫ cs/HUAT (1+z) dz, cs=c/√ (3 (1+Rb) ), with HUAT (z) =H0√ (kearlyΩm (1+z) ³+. . . ), kearly=0. 967, H0=73. 04, yielding rd=128. 15 Mpc (no empirical fcorr factors). With H0=73. 04, DC (z*=1089) =12981 Mpc, lA=πDC/rd=318. 2 (+7. 40%). Both values are temporary proxies pending full CLASS-UAT Boltzmann implementation; 128. 15 Mpc is mathematically correct, 141 Mpc is outdated effective. Supplementary 1 (3 pages, supplementary1. pdf): Laboratory verification of Rgeom=0. 279182. 8 coils physically fixed at 45° spatial positions (complete cancellation R=0, annulled). Frequency detuning 43. 515°=45°×kearly: driving currents In=A sin (wt + nΔφ), Δφ=43. 515°=45°×0. 967, not mechanical rotation. Formula R (N, Δφ) =|Σ e^inΔφ|=|sin (NΔφ/2) /sin (Δφ/2) |=0. 279182 unnormalized (not divided by N). Measured 3. 697 mV /13. 24 mV =0. 2792±0. 0005 within 0. 006%, frequency-independent at 232 Hz and 361. 108 Hz. Appears as 2Rgeom=0. 558364 in Causal Mass Gap Mobs (n) =2Rgeom·Eplanck·κcrit^1/n and boundary action Sboundary. Supplementary 2 (4 pages, supplementary2. pdf): Methodological Guide (5 pitfalls) and growth of structure fσ8 (z) first-order prediction. HUAT (z) modification only, 26 measurements BOSS/eBOSS/DES. χ2UAT=17. 28 (1 free param: 7% margin) vs χ2LCDM=15. 93 (6 params). AIC: 19. 28 vs 27. 93 ΔAIC=-8. 65 weight 98. 7%; BIC: 20. 54 vs 35. 48 ΔBIC=-14. 94 weight 99. 9%; Bayes B≈1755 decisive for UAT. Causal feedback F (z) ∼κcrit=1e-78 membrane stable. Codes: uatₘaincorrected. py (parameter closure, corrected rd=128. 15 Mpc, lA, frozen field, Rgeom frequency vs mechanical clarification) and uatₛupplementary. py (phasor diagram verification and fσ8 Bayesian selection). Requires NumPy, SciPy, Matplotlib. Generates phasors₈coil. png. Files: maincorrected. pdf, supplementary1. pdf, supplementary2. pdf, uatₘaincorrected. py, uatₛupplementary. py, phasors₈coil. png + combined ZIP. Keywords: UAT, UCP, quantum brake, causal coherence, Lagrangian, sound horizon, geometric invariant, Hubble tension ## Contacto Puán, Buenos Aires, Argentina - miguelₚercudani@yahoo. com. ar