Human History in Complexes

Human history is encountered through incomplete sources, contested identities, heterogeneous durations, changing relations, and transformations in the conditions of further action. This expanded article develops a theoretical and computational approach to these problems through finite cell complexes and their historically situated interpretations, incorporating earlier event–coupling–primitive and CW-spacetime formalisms. Its starting point is the open-source History Complex within The Science Infrastructures (https://github.com/huangwanhong-maker/The-Science-Infrastructures). In that implementation, occasions define vertices, repeated appearances of beings define worldline edges, and ties sustained across meetings define attached two-cells; a refined carrier resolves participant-specific presences and signed relations. The paper reconstructs these definitions, derives elementary topological and gauge-theoretic properties, and distinguishes documentary assertions, formal invariants, probabilistic reconstructions, and claims about historical processes. It then places the implementation in dialogue with earlier investigations of generative relational history, evolving constraints, heterogeneous value circulation, future-creation topology, knowledge translation, historical warrant, and epistemic justice. These connections motivate an exploratory extension in which histories are studied at multiple resolutions, interpreters are themselves historically situated, and permissible continuations are separated from observed trajectories without presupposing a universal privileged time. Original vector figures illustrate the record-to-complex pipeline, temporal lenses, signed triangles, multi-resolution histories, a continuation landscape, and the distinction between semantic translation and topological attachment. A synthetic example is worked through algebraically; a repository case is discussed with explicit evidential restrictions. The resulting programme treats topology as a disciplined means of questioning historical records, while distinguishing evidence, generated structure, the grammar of admissible transformations, and realized history. Six theoretical appendices develop the topological, temporal, gauge-theoretic, grammatical and epistemic foundations.