{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KF4ZHMJTJRTVNCNLLWJ6N4IJJQ","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":"56d9e32ceaa48873b95f37cf342739148e542d242d1401ae4e504d3b6cbc2876","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-03-25T14:38:37Z","title_canon_sha256":"b594727ced50d74f86e44e0887c7ea05172c075f0f2f8b5003c807335c50be3d"},"schema_version":"1.0","source":{"id":"1303.6143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6143","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6143v2","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6143","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"KF4ZHMJTJRTV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KF4ZHMJTJRTVNCNL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KF4ZHMJT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:4210e953313fd458008d0606a5d6c92471ddeb011d015dccc52aab6f8e100fec","target":"graph","created_at":"2026-05-18T03:15:57Z","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":"Conservation of energy and momentum in the classical theory of radiating electrons has been a challenging problem since its inception. We propose a formulation of classical electrodynamics in Hamiltonian form that satisfies the Maxwell equations and the Lorentz force. The radiated field is represented with eigenfunctions using the Gel'fand $\\beta$-transform. The electron Hamiltonian is the standard one coupling the particles with the propagating fields. The dynamics conserves energy and excludes self-acceleration. A complete Hamiltonian formulation results from adding electrostatic action-at-a","authors_text":"Fabrice Doveil (PIIM), Fr\\'ed\\'eric Andr\\'e, Nikita M. Ryskin, Pierre Bernardi (PIIM), Yves Elskens (PIIM)","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-03-25T14:38:37Z","title":"Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6143","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:a519adaedc4ed8436fb8046fd522f0c706ae5ddb592e033025b45ba7e1cde726","target":"record","created_at":"2026-05-18T03:15:57Z","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":"56d9e32ceaa48873b95f37cf342739148e542d242d1401ae4e504d3b6cbc2876","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-03-25T14:38:37Z","title_canon_sha256":"b594727ced50d74f86e44e0887c7ea05172c075f0f2f8b5003c807335c50be3d"},"schema_version":"1.0","source":{"id":"1303.6143","kind":"arxiv","version":2}},"canonical_sha256":"517993b1334c675689ab5d93e6f1094c208795036fb6d0d95e6e0401a919d648","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517993b1334c675689ab5d93e6f1094c208795036fb6d0d95e6e0401a919d648","first_computed_at":"2026-05-18T03:15:57.493028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.493028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NUBs4RqAJ6fi/kx/DpRCQuxnzq6TVo/xiRqxLfYpZnGuV9klb+6AnCjlDpKSoi0O5H+5tpviFOVB5wDVORYADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.494109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a519adaedc4ed8436fb8046fd522f0c706ae5ddb592e033025b45ba7e1cde726","sha256:4210e953313fd458008d0606a5d6c92471ddeb011d015dccc52aab6f8e100fec"],"state_sha256":"ab3445d869d836f91fabdb23a62707e4ad086e05c78d6090146e62effdf68d19"}