Field Collapse in Recursive ECOF Lattices

Abstract The Energy‑Consciousness Observer Framework (ECOF) recasts quantum‑style collapse as an energy‑driven selection process tied to an observer’s identity field 𝕀(t). Extending earlier discrete‑state work, this whitepaper develops a field‑collapse functional that maps any square‑integrable lattice field to a unique, observer‑converged configuration . We prove existence and uniqueness via variational methods, derive a continuum analogue of the Born rule, and demonstrate scale‑invariant collapse dynamics on a recursive lattice. Numerical simulations on grids confirm analytic front‑speed predictions and the linear dependence of metabolic work on the awareness–energy weight . These results generalise ECOF collapse to continuous fields and strengthen the mathematical pillar for subsequent zero‑division and Cantor recursion papers.