Chronometric Closure Paper VI: Existence and Non-Circularity of the Chronometric History Measure

Chronometric Closure Paper VI addresses a foundational burden left open by Closure Paper V: the existence and non-circularity of the chronometric history measure dnu_gamma. The paper develops dnu_gamma as a restricted chronometric transition measure arising from a refinement-consistent limit of finite-rank admissible record-transition histories. Its anti-circularity principle is explicit: record-transition order => dnu_gamma => Delta T_chi, not background time dt => dnu_gamma => Delta T_chi. The main mathematical result is a conditional existence theorem showing that, under admissible directed refinements, positive non-dt-based transition weights, refinement consistency, bounded or controlled integrand variation, and a vanishing refinement-defect envelope, the finite accumulated chronometric sums form a Cauchy net and converge to a finite chronometric interval. The paper does not claim a universal path-space measure or a Radon measure. Instead, it establishes a more conservative restricted transition measure for admissible finite-rank chronometric histories.