{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:37TYJKV7I2DMJCNQBD2IKT3YIA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a3412ee221f6addf0fd267a60945d5767fea5a9f9ec9cc63569b7d62ebbcfff3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2013-05-20T21:04:57Z","title_canon_sha256":"4bc4532bffbd1cc2c19633323be569728bb93120a5818d00eb4c63ebfaf9e907"},"schema_version":"1.0","source":{"id":"1305.6874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6874","created_at":"2026-05-18T03:08:07Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6874v2","created_at":"2026-05-18T03:08:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6874","created_at":"2026-05-18T03:08:07Z"},{"alias_kind":"pith_short_12","alias_value":"37TYJKV7I2DM","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"37TYJKV7I2DMJCNQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"37TYJKV7","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:755db6685ebb78501fd3856219cf150d5c802919c3d11725d9c16ee22e5c0ad2","target":"graph","created_at":"2026-05-18T03:08:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A mathematical proof is given that Maxwell's equations are an {\\it artifact} of Hodge theory together with the laws of Gauss and Amp\\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms, and valid for any force field -- attractive or repulsive -- generated by a material density and current. In particular, with appropriate sign changes to reflect the attractive nature of the field, they apply to gravitational fields on Minkowski space-time as well.\n  The linearization of the Einstein Field Equations on Minkowksi space-time leads also to a lin","authors_text":"D.H. Sattinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2013-05-20T21:04:57Z","title":"Maxwell's Equations, Hodge Theory, and Gravitation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6874","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4fd783896e10b56fa5c387e9b3126a87771ce545a6eeb5d03c5c8a268f50652f","target":"record","created_at":"2026-05-18T03:08:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a3412ee221f6addf0fd267a60945d5767fea5a9f9ec9cc63569b7d62ebbcfff3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2013-05-20T21:04:57Z","title_canon_sha256":"4bc4532bffbd1cc2c19633323be569728bb93120a5818d00eb4c63ebfaf9e907"},"schema_version":"1.0","source":{"id":"1305.6874","kind":"arxiv","version":2}},"canonical_sha256":"dfe784aabf4686c489b008f4854f784008608fe145fc090e1e974db8fbed784b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe784aabf4686c489b008f4854f784008608fe145fc090e1e974db8fbed784b","first_computed_at":"2026-05-18T03:08:07.123836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:07.123836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwAmoJa2HuPNYN1hCxyh7uA8VgMvfzo2V0guyE8drU/fcIhnLVlKyzARm4gkyypHuBMQvR16JSNfgtnKkMwFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:07.124518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fd783896e10b56fa5c387e9b3126a87771ce545a6eeb5d03c5c8a268f50652f","sha256:755db6685ebb78501fd3856219cf150d5c802919c3d11725d9c16ee22e5c0ad2"],"state_sha256":"001af75930d75f5051f7a30cb6088d37bccaae681b499525eb55dae96dcca988"}