The Topological Epistemology of Future Creation: A Two-Complex Formalism for Spacetime Continuation

This discussion paper proposes a preliminary two-complex framework for the topological epistemology of future creation. Its object is the construction and revision of possible continuations of historically represented relational spacetime. Events are represented by vertices, couplings by edges, and higher-order primitives by faces, while historically constituted entities are modeled through relational substructures. An assumed ontological relational spacetime is used solely as a formal reference construct, with ultimate ontology suspended. The observer's epistemic capacities and model-reconstruction operators are treated as historically conditioned, and the resulting representations as partial and revisable. Candidate futures are formulated as history-indexed whole-spacetime extensions whose embeddings preserve the represented historical component and its attachments; future-only formulations remain possible with suitable relative data. Dependent types, undercategories, relative cell complexes, homology, and discrete Morse theory supply mathematical resources for comparing extensions and specifying information-preservation requirements. The paper identifies problems of indeterminate future incidence, nonunique reconstruction, epistemic revision, and changing spaces of conceivable possibilities, and provides exact synthetic computations illustrating historical attachment dependence, epistemic revision, and reduction-related information loss, with interfaces to subsequent normative inquiry concerning future creation and justice. Its constructions are provisional, its cases are illustrative, and no empirical forecast or comprehensive ontological generator is claimed.