Topological Signatures of Knowledge Diffusion Along Historical Human Movement Networks: A Computational Framework and an Invitation to the Social Sciences

Repeated directed human movement along fixed corridors produces measurable diffusion effects in knowledge, biology, language, environment, and material culture that no individual participant observes and no single source records. This paper proposes a framework, a methodology, and a set of computational instruments for recovering those effects, and it advances a specific, falsifiable claim for others to test: that the directed topological structure of a historical movement network predicts its observed spatiotemporal diffusion better than geographic proximity, undirected network distance, or directed shortest-path distance, and that circuit-structured systems are separable from convergence-structured systems by a measurable spectral signature. The proposal models historical human movement networks as time-evolving directed simplicial complexes and characterizes them with two distinct operators: directed path homology for topology and a directed, non-reversible diffusion generator for dynamics; the paper specifies why the two cannot be the same operator. It introduces a dual-layer evidence model that separates what the network structurally transmitted, recoverable from topology, from what the traveler's narrative reports, recoverable from text, and formalizes the gap between the layers as a directed Hausdorff distance. A three-zone epistemological architecture, adapted from prior work on epistemic frontier mapping, locates the framework's proper domain in the zone of structural transmission that operated beneath any participant's awareness and above any single source's evidentiary reach. A computational pipeline is specified rather than executed: CNN-based feature extraction from archival sources, GPU-accelerated corpus-scale pattern detection, ArcGIS spatial integration, and diffusion modeling on the resulting complex. Ten movement systems spanning six continents and sixty millennia, from the Aboriginal Australian Songlines to the twentieth-century "Hippie Trail," are positioned within the framework as candidate test cases, with the Camino de Santiago developed as a worked proof-of-concept design. The paper is offered as part thought experiment and part toolkit: an argument that the structural knowledge latent in historical evidence is formally characterizable and computationally recoverable, and an invitation to historians, anthropologists, linguists, geneticists, and other social scientists to bring these instruments to bear on their own evidence.