The Nested Causal Pursuit of the Born Rule: Boundary Flux, Enclosure Refinement, and the Point of Rest with Quantum Theory

The Nested Causal Pursuit of the Born Rule makes explicit the measurement bridge contained in Nested Causality while retaining established quantum mechanics, quantum field theory, and Standard Model interactions as lawful interior dynamics. Zero Infinity is used as an empty reference architecture of countably infinite depth and scale: physical states can also be described as departures from that reference without being replaced by the description. A single accounting cut prevents the same supported departure from being counted again at each enclosing scale. The paper derives the Born measure from enclosure-refinement invariance. Standard quantum theory supplies mutually exclusive record channels and their conserved quadratic loads. Requiring a coarse record and every physically equivalent refinement of that record to carry the same total measure yields an additive functional equation. Continuity and nonnegativity force linearity in quadratic load, producing p(i) = Tr(rho P_i), with the argument extended to generalized measurements through a larger system-apparatus enclosure. A complementary first-passage construction gives the boundary process a testable form. Reference-equivalent, recursively memoryless residual capacities on parallel record channels produce exponential crossings and the same Born weights. A Weibull deformation yields p_i proportional to w_i^alpha and shows exactly where alternatives diverge: every alpha other than one violates refinement invariance. The accompanying Python program reproduces these predictions numerically and reports the refinement defects. The result is a derivation of the Born measure within the combined Nested Causality and established quantum framework. It does not independently derive Hilbert space, unitary evolution, or a complete apparatus-specific boundary instrument. It identifies the remaining calculation: derive the capacity coordinate and completely positive record map of a specified apparatus from its interactions and enclosing geometry.