The Λ Chain: Dark Energy as the Bulk's Exhaust

An equation-of-state history w(z) as the external, falsifiable test

preprint — not yet on arXiv gr-qc updated 2026-09-09

Abstract. We propose an operational definition of dark energy within the WHD program: the running balance between energy the engine feeds the brane and energy the brane sheds back to the bulk, rather than a bare cosmological constant. A renormalization convention fixes the settled vacuum's energy to exactly zero, so the two contributions — a time-independent constant and a genuinely dynamical, bulk-sourced term — are distinguishable rather than degenerate. The mechanism predicts a specific wall-drain exponent Γ_w governing how fast the loaded brane sheds stored energy, which in turn predicts a specific *shape* for the dark-energy equation-of-state history w(z) — a falsifiable target distinct from a cosmological constant's flat w = −1, testable against current and next-generation large-scale-structure surveys (DESI-class data). This paper depends on the birth-run engine actually existing and behaving as claimed; its quantitative content cannot be finalized ahead of that result.