Interacting Multiplicities and Multiscale Organization in OFT: Operational Identities, Multifractal Diagnostics, and Conditional Matching to Covariant Sources and Stress

This research preprint develops a calculation framework for matching interacting multiplicities and multiscale organization to covariant physical response within the OFT/Q-interaction programme. A scale-dependent registry distinguishes particle, sector and channel multiplicities and retains orientation, connected moments, source responses, exchange currents and finite-range scaling diagnostics. Typed identity cards and explicit sector projections separate parent descriptors from benchmark and auxiliary maps. Measure spectra and field-increment spectra are treated with distinct normalization and embedding rules. The manuscript provides exact and selected-model results: dependency-preserving field and metric variations; multichannel auxiliary elimination; Gaussian and joint-lognormal fourth-moment closures; a finite-cutoff heavy-tail example; constructive dependence counterexamples; and a solved multifractal cascade with finite-resolution rare-event probabilities. An alternative two-scalar covariant benchmark has positive kinetic coefficients and metric-subluminal characteristics in its stated homogeneous domain. Both benchmark actions are checked through all ten independent inverse-metric variations, including the volume contribution to the Hilbert stress. The accompanying source and standard-library Python script make the displayed algebraic, statistical and tensor checks reproducible. These calculations do not constitute a microscopic derivation of OFT or a black-hole simulation. The physical parent map, full source/transport matching and nonlinear future-trapping calculation remain explicit research requirements. This is Paper IV of the developed sequence, manuscript version 0.4.