Inter-local coherence refers to the structural and epistemological conditions under which independently produced observational sequences can jointly support unified scientific inference. Contemporary scientific practice routinely integrates data from distributed instruments, laboratories, and methodological environments. Although each observational locality maintains internal methodological coherence, their outputs rarely share ordering conventions, transformation pipelines, or operational definitions. As a result, heterogeneous observational sequences may not be structurally compatible before modelling begins. This preprint develops a methodological framework for analyzing the structural compatibility of independent observational sequences. A distinction is introduced between local coherence—the internal stability of an observational locality—and inter-local coherence, the supra-local condition required for cross-local evidential integration. The paper formalizes the methodological requirements for inter-local coherence, including ordering compatibility, transformation stability, semantic alignment, structural trend non-contradiction, and integrability into a global evidential architecture. Case studies from cosmology, climate science, particle physics, and biomedical research illustrate how structural divergences emerge during fixation, ordering, transformation, and operational definition. These divergences often remain invisible at the modelling stage, leading to unacknowledged harmonization assumptions and sensitivity to locality-specific preprocessing pipelines. The framework presented here is methodological rather than metaphysical. It clarifies the epistemic preconditions under which heterogeneous observational lineages can function as coherent scientific evidence. The preprint concludes with a discussion of implications for scientific objectivity, distributed epistemology, and future directions for formal criteria, empirical audits of observational pipelines, and domain-specific assessments of inter-local coherence. Version: 1.0 (Preprint)Author: Alexey A. NekludoffAffiliation: AstraVerge InstituteDocument Date: 11 November 2025Release Date (Zenodo): 2025-12–05