The no-signaling principle in quantum mechanics—that local operations on onesubsystem of an entangled pair cannot transmit information to a distant subsystem—has never been structurally proven from independent physical principles. Everyexisting derivation is circular: von Neumann constructed the tensor product for-malism specifically to enforce no-signaling [1], and all subsequent “proofs” deriveno-signaling from a structure that was designed to contain it [2, 3]. We present anon-circular structural proof. Starting from two premises independent of quantumformalism—the relativistic propagation limit c and the experimental record of Belltests, quantum erasers, and which-path experiments—we derive the no-signaling re-sult as a mathematical consequence of the tensor contraction structure. The proofproceeds in four steps: (i) the inscription tensor formalism, which encodes correla-tions in a rank-r tensor whose contraction rules are fixed by the mathematics, notby postulate; (ii) an exhaustive enumeration of all nine measurement configurationsfor an entangled pair, showing that partial contraction yields 12 in every case, in-dependent of the distant party’s choice; (iii) the cross-term kill theorem, provingthat one environmental inscription produces an exact, immediate, and idempotenttransition from quantum to classical probability structure; and (iv) the proof bycontrapositive via which-path and quantum eraser experiments, confirming bothdirections of the theorem against the complete experimental record. Four inde-pendent confirmations—information-theoretic, conservation-law, operational, andsymmetry-based—close every remaining escape route. The proof requires no newphysics, no new axioms, and no ontological commitment beyond what the existingformalism and experimental record already contain. We note that the Entropic Lat-tice Ontology’s fourth spatial degree provides a geometric explanation for why theproof works—the correlation occupies a spatial degree with no three-dimensionaladdress—but this theoretical framework is not required for the proof’s validity