Topological Void Analysis A Mathematical Framework for Systematic Technical Innovation Discovery in Knowledge Spaces

• URL: http://arxiv.org/abs/2607.00005v1
• Date: Mon, 20 Apr 2026 06:41:39 GMT
• Title: Topological Void Analysis A Mathematical Framework for Systematic Technical Innovation Discovery in Knowledge Spaces
• Abstract summary: We present Topological Void Analysis (TVA), a mathematical framework that defines topological voids as triads in a dense-sparse hybrid embedding space.<n>TVA generates 2,128 invention candidates across 96 targets; 90% survive automated quality filtering, yielding 191 REVISE and 1 APPROVE verdict from four-specialist adversarial review.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Identifying where to innovate in a dense technical domain - such as operating systems or hardware/software co-design - is fundamentally a search problem in a high-dimensional knowledge space. Existing approaches rely on keyword search, citation proximity, or human intuition, none of which formalise the notion of an unexplored region that is simultaneously relevant to a target goal and absent from prior art. We present Topological Void Analysis (TVA), a mathematical framework that defines topological voids as triads (A, B, C) in a dense-sparse hybrid embedding space. A void requires three conditions: (i) both concepts A and B are 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 ~140k indexed documents, TVA generates 2,128 invention candidates across 96 targets; 90% survive automated quality filtering, yielding 191 REVISE and 1 APPROVE verdict from four-specialist adversarial review (0.05% end-to-end). Two case studies demonstrate the framework surfaces non-obvious connective tissue rather than merely obvious related pairs.

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