New 'Topological Void' Math Spots Hidden Innovation Gaps in Tech

Identifying where to innovate in dense technical domains – like operating systems or hardware/software co-design – has traditionally relied on keyword search, citation proximity, or human intuition, none of which formalize the concept of an unexplored region that is both relevant to a target goal and absent from prior art. Kris Pan's Topological Void Analysis (TVA) addresses this by mathematically defining topological voids as triads (A, B, C) in a dense-sparse hybrid embedding space. A void requires three conditions: (i) concepts A and B are each semantically cohesive with domain anchor C; (ii) their pairwise similarity falls within a calibrated marginality band – avoiding both obvious combinations and unrelated noise; and (iii) they share a sparse lexical bridge while the geodesic midpoint on the embedding hypersphere is unoccupied.

Applied to a corpus of ~140,000 indexed documents across 96 target domains, TVA generated 2,128 invention candidates. Automated quality filtering retained 90% of these, which were then subjected to a four-specialist adversarial review process. The review yielded 191 "REVISE" verdicts and a single "APPROVE" – representing a 0.05% end-to-end discovery rate. Two case studies demonstrated that the framework surfaces non-obvious connective tissue—genuinely novel combinations—rather than merely obvious related pairs. TVA offers a systematic, replicable method for R&D teams to uncover blind spots in crowded technical landscapes, potentially accelerating innovation pipelines in areas where prior art is dense and incremental improvement dominates.