NP-completeness of three-terminal shortest-path blocking

We prove NP-completeness of undirected, unit-traversal-length three-terminal Blocking Shortest Paths: delete a minimum edge set to increase every pairwise terminal distance by at least one. Hardness holds with unit deletion costs and all three original terminal distances equal to three. A direct Vertex Cover reduction also proves NP-completeness when all terminal distances must remain finite, or increase exactly from three to four. The result classifies the undirected triangle question posed by Stefan Krause in 2005. The classical subdivision identity is credited to Poljak (1974), and the related tripartite attachment mechanism to Khachiyan and coauthors (2008). Historical first priority and continued open status through 2026 are not asserted. This unrefereed research note includes a source and verification archive with the unchanged original proof packet, explicit hash manifests, source-free standard-library Python reproduction, independent adversarial mathematical and computational audits, source-model checks and a bounded priority audit. AI tools were used extensively for construction, verification, adversarial review and writing. Independent AI-agent review is not independent human peer review or journal review; this work has undergone neither. Finite computations supplement the written universal proof and are not formal proof-assistant certification.