TECHNICAL NOTE — ZENODO DEPOSIT Author: Miguel Ángel Percudani ORCID: 0009-0007-1748-3212 ═══════════════════════════════════════════════════════════════ ABSTRACT ═══════════════════════════════════════════════════════════════ This note presents a first-order calculation of the linear growth rate of cosmic structure, fσ₈(z), within the Unified Applicable Time (UAT) framework. The growth equation is solved using the UAT-modified Hubble expansion history H(z) with the quantum brake parameter k_early = 0.96734, and compared with 26 published measurements from BOSS, eBOSS, DES, and other surveys. RESULTS: χ²(UAT) = 17.28 χ²(ΛCDM) = 17.74 Mean difference in fσ₈(z): ~1.1% (max ~2.0% at z ≈ 1.5) UAT is marginally preferred but the difference is not statistically significant. The framework is competitive with ΛCDM on this observable. KEY THEORETICAL FINDING: A semi-analytical estimation of the causal membrane feedback function F(z) reveals that F(z) ∼ κ_crit = 10⁻⁷⁸. The dynamical factors collapse to order unity in Planck units, isolating κ_crit as the absolute regulator of the system. While negligible for cosmological structure formation at Gpc scales, this identical value is the fundamental constant that sustains the causal membrane at the laboratory scale — defining the Ivancho Limit (η = 4.978), the 8-phase coherence, the thermal offset (3/4), and ultimately Λ itself. The feedback cannot exceed the Ivancho Limit without rupturing the causal membrane and violating the causality of the universe. LIMITATIONS (explicitly acknowledged): • Only the modified H(z) is used; the complete calculation requires a dedicated Boltzmann solver. • Standard codes (CLASS, CAMB) cannot be used without fundamental modifications to their source code. • σ₈(0) is assumed equal for both models. • The F(z) estimation is based on equipartition and slow-roll arguments. This note provides the best prediction achievable with present tools and establishes a falsifiable target for future high-precision surveys (DESI DR2, Euclid). ═══════════════════════════════════════════════════════════════ REFERENCES ═══════════════════════════════════════════════════════════════ UAT Framework: DOI: 10.5281/zenodo.17729221 UCP Constant κ_crit: DOI: 10.5281/zenodo.18210808 Λ First-Principles Resolution: DOI: 10.5281/zenodo.21109424 Methodological Limitations: DOI: 10.5281/zenodo.21317943 ═══════════════════════════════════════════════════════════════ LICENSE ═══════════════════════════════════════════════════════════════ Creative Commons Attribution 4.0 International (CC BY 4.0)