Path-Dependent Knowledge Substrates (PDKS)

Path-Dependent Knowledge Substrates (PDKS) by Adam Bishop, XOps360 LLC. A formal framework proving that digital authority is a convergence property of structural architecture, not an emergent property of content quality. PDKS demonstrates that search engines, recommendation algorithms, and AI citation systems implicitly assume first-order Markov models for authority, and that this assumption is formally wrong. Three mechanisms break it: path-dependent interpretation, path-dependent trust formation, and path-dependent ranking accumulation. The framework uses the Banach Fixed-Point Theorem to prove that a properly architected knowledge substrate guarantees authority convergence to a unique fixed point. The contraction condition q = alpha + beta * L_F < 1 provides a testable engineering criterion. Published as a 6-part blog series on xops360.com. Author ORCID: 0009-0000-4569-3726.