{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TO2472NNQ6WIKWSNL7SI7X6XDB","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":"e0e23e8d383553095279e0cbb9276468f51cfe21b2108d71a7d57ac5ffc57917","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-16T14:01:13Z","title_canon_sha256":"5833809863759da74ce612b437406e3b61ae41f92b6feafd420e5a31e7be962f"},"schema_version":"1.0","source":{"id":"1204.3489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3489","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3489v2","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3489","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"TO2472NNQ6WI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TO2472NNQ6WIKWSN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TO2472NN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:78bcdf752e0a33370c632525ff29a7b436133f6c1604b35b92a6132b864885f6","target":"graph","created_at":"2026-05-18T02:24:36Z","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":"We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to $\\sqrt{m^2 + \\xi^2}$ and $\\xi^2 / 2m$, respectively. Higher-order corrections can in principle be computed to any order in the small parameter v/c which is the ratio of typical speeds to the speed of light. Our results imply the dynamics for electronic and positronic states decouple to any order in v/c << 1.\n  To decide whether to get semi- or non-relativis","authors_text":"Martin F\\\"urst, Max Lein","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-16T14:01:13Z","title":"Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3489","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":"sha256:2d675bd19d04243cadbbb581ca6d101d3828fe2d5bfdc0dded5488d14f7fa00e","target":"record","created_at":"2026-05-18T02:24:36Z","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":"e0e23e8d383553095279e0cbb9276468f51cfe21b2108d71a7d57ac5ffc57917","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-16T14:01:13Z","title_canon_sha256":"5833809863759da74ce612b437406e3b61ae41f92b6feafd420e5a31e7be962f"},"schema_version":"1.0","source":{"id":"1204.3489","kind":"arxiv","version":2}},"canonical_sha256":"9bb5cfe9ad87ac855a4d5fe48fdfd7184af728a35dd455b303c5cb6050e5edf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb5cfe9ad87ac855a4d5fe48fdfd7184af728a35dd455b303c5cb6050e5edf3","first_computed_at":"2026-05-18T02:24:36.127765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:36.127765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rP34RDWmObNLiQaIzZShuSowa6qWI2WlOoneXDPrR+/NbvWJeAm9FXi+g2fzMpcGI68w678u29KawK5J20WmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:36.128485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d675bd19d04243cadbbb581ca6d101d3828fe2d5bfdc0dded5488d14f7fa00e","sha256:78bcdf752e0a33370c632525ff29a7b436133f6c1604b35b92a6132b864885f6"],"state_sha256":"9adbfe3858cc3345ebfb9240809643cfdba3298c258cc98d48a4a5468dda9544"}