Kernel Analysis of Electron Identity and Global Topology

This note evaluates Wheeler's "One Electron" hypothesis—the proposition that N indistinguishable fermionic excitations can be regarded as a single globally connected worldline. In the Kernel Law framework, physical content is identified with the quotient of micro-history space by the equivalence relation induced by a local observable algebra. We show (i) particle identity labels are eliminated by the SN permutation symmetry and therefore lie entirely in the Kernel, and (ii) global worldline connectivity is a topological functional on history space that does not descend to any element of the local observable algebra under standard locality and finite-access assumptions. Consequently, the "One Electron" hypothesis is empirically empty within local-access quantum field theory: it selects a representative in history space rather than introducing an observable ontology. Includes numerical demonstration showing distinct topologies yield identical local correlators.