The Heuristic Convergence Theorem: When Partial Perspectives Assemble the Invisible Whole

This paper introduces the Heuristic Convergence Theorem, a proposal situated at the intersection of symbolic systems, distributed cognition, and epistemic simulation. It investigates whether agents operating under conditions of partial knowledge—symbolic fragments, domain constraints, and local heuristics—can collectively approximate a coherent structure without global access to truth. Rather than imposing deductive closure, the approach explores convergence as a runtime phenomenon: a pattern of increasing semantic compression, structural alignment, and epistemic viability. Using symbolic simulation, we observe that convergence is not enforced, but emergent. Distributed agents exchange and mutate representations in bounded space, and through iterative cycles, a semantic field of coherence emerges asymptotically. This model does not claim universality, nor does it suggest a formal proof in the classical sense. It demonstrates a form of structural survival: that symbolic agreement may arise from incompleteness, and that what persists under distortion may become a valid epistemic signature. We draw connections to Cub³, an architecture that models epistemic tension through projection geometry. There, constructs are evaluated across orthogonal domains—computation, mathematics, and physics—each offering a distorted shadow of the whole. This metaphor aligns with our theorem: partial views projected from distinct heuristics can converge, not by resolving contradiction, but by structurally surviving it. The work proposes no final answers. It offers a simulated field where epistemic agents learn to converge under symbolic pressure—and where convergence itself becomes a kind of computable truth.