Traversal Centrality and the Creative Runway: Novel Primitives for Generative Capacity in Typed Hypergraphs

Standard graph centrality measures—betweenness, closeness, eigenvector, PageRank— answer questions about how a node relates to other nodes. None of them answer the question that matters for generative systems: how long can you keep going from here without repeating yourself? We introduce three metrics for typed cognitive hypergraphs that measure generative capacity rather than relational position. Typed Diameter mea- sures the maximum typed distance between any two nodes—how far the most distant pair of concepts is when traversals must be type-consistent. Traversal Centrality mea- sures the longest non-repeating typed walk from a given node—the creative runway avail- able from that starting point. Maximum Self-Avoiding Typed Walk Length (the Kill Screen) measures the graph’s theoretical generative ceiling—the longest coherent output the architecture can produce before repetition becomes inevitable. We prove that all three metrics are topological invariants of the typed hypergraph (invariant under continuous deformations that preserve type structure), connect them to the cognitive quasicrystal formalism (the Kill Screen is bounded by the patch complexity of the corresponding ape- riodic tiling), and derive falsifiable predictions: freestyle duration correlates with witness dimensionality D, not with vocabulary size or practice hours. The 45-minute empirical kill screen is a measurement of architecture, not endurance. Five falsifiers posted. Keywords: traversal centrality, self-avoiding walk, typed hypergraph, kill screen, gener- ative capacity, cognitive quasicrystal, patch complexity, topological invariant, witness di- mensionality