Technological Avalanche 2025-2045: Exponential Divergence Analysis With and Without AI Infrastructure

This technical note quantifies the exponential divergence between technological growth trajectories with and without AI infrastructure over the period 2025-2045. Using compound growth modeling with empirically grounded rate assumptions (7% baseline without AI; 15-50% accelerating with AI), the analysis demonstrates that the cumulative gap ratio reaches 1.9x by 2030, 7.2x by 2035, and 1,099x by 2045. The critical window is 2026-2028: the curves appear similar in 2026 (1.15x vs 1.07x, a 7% difference) but diverge rapidly by 2030 (2.65x vs 1.40x, an 89% gap). This is the signature of exponential divergence — by the time the gap is obvious, the window for entry has closed. Section 2 provides the complete quantitative comparison across 10 measurement points (2025-2045) with annual growth rates, cumulative multipliers, and gap ratios. Section 3 details the critical 2026-2030 window with visual analysis. Section 4 maps irreversibility milestones from LOW (2026-2027) through ABSOLUTE (2040-2045). Section 5 establishes 5 projection invariants with explicit falsifiers: if any invariant is falsified, the corresponding projection is void. Section 6 analyzes infrastructure implications including retrofitting cost, opportunity cost, and dependency cost as functions of the gap ratio. The document is prescriptive (defines thresholds and decision points) rather than predictive (claims specific outcomes). Figures include logarithmic-scale divergence plot (2025-2045) and detailed zoom of the critical 2026-2030 window. Prior Art Chain: 10.5281/zenodo.18356012 → 10.5281/zenodo.18393200 → this record.