Dark Energy Is Not Constant: A First-Principles Derivation of w(z) from the IPN Cycle Architecture

This working paper derives the dark energy equation of state w(z) from first principles using the ASTOE (All Systems Theory of Everything) framework. Beginning from the IPN cycle architecture and the boundary coupling constant δ = 1/3699, the derivation produces a structured w(z) curve with zero free parameters beyond the observed w₀. The paper predicts seven measurable slope changes at specific redshifts (z ≈ 0.15, 0.35, 0.60, 0.90, 1.30, 2.00, 3.50), corresponding to IPN evaluation cycle boundaries — a pattern no known scalar field model produces. Submitted as a priority record ahead of DESI DR3.