{"paper":{"title":"What Current Flows Through a Resistor?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Bob Eisenberg, Huaxiong Huang, Nathan Gold, Zilong Song","submitted_at":"2018-05-13T03:57:06Z","abstract_excerpt":"Our digital technology depends on mathematics to compute current flow and design its devices. Mathematics describes current flow by an idealization, Kirchhoff's current law. All the electrons that flow into a node flow out. This idealization describes real circuits only when stray capacitances are included in the circuit design. Motivated by Maxwell's equations, we propose that current in Kirchhoff's law be defined as \\[{\\varepsilon }_{\\mathrm{0\\ \\ }}\\frac{\\mathrm{\\partial }\\boldsymbol{\\mathrm{E}}}{\\mathrm{\\partial }t}\\ \\mathrm{+}\\mathrm{\\ }\\mathrm{\\ }\\widetilde{\\boldsymbol{\\mathrm{J}}},\\] the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04814","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}