Electrons as Emergent Projection Events: B-Chem Framework for Subatomic Quantum Chemistry Beyond Particle Ontology

Classical and quantum chemistry routinely treat electrons as permanently existing particles whose number and spatial distribution define chemical structure and reactivity. At the same time, quantum field theory, polarization theory, and modern electronic-structure methods demonstrate that many experimentally observed charge phenomena occur without literal particle transport or permanent localization. In this work, I introduce the Bansal-Chem (B-Chem) framework, a projection-based formulation in which the chemically relevant electron is not a primitive particle but an emergent, geometry-and field-constrained projection event. The electron is modeled as a structured B-fiber object with stratified components-real, complex, dual (nilpotent), and hypercomplex-corresponding respectively to charge density, phase coherence, transient/tunneling behavior, and spin-relativistic structure. Standard electron models used across chemistry and condensed-matter physics are shown to arise as operational projections of this single underlying object, selected by experimental context and environmental coupling. Avogadro's number and Faraday relations are reinterpreted as projection-scaling constants rather than as evidence of permanent microscopic particle inventories. Measurement-induced collapse and decoherence are reformulated as contextual projection and dynamical suppression of inaccessible fiber components, without modifying Schrödinger or Standard Model dynamics. The framework is fully compatible with quantum electrodynamics and density functional theory, while providing a unified structural explanation for the coexistence of particles, waves, densities, quasiparticles, and effective electrons in chemical theory. B-Chem thus offers a geometry-and field-driven ontology for electrons that preserves established calculations while clarifying their conceptual foundations.