{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BROQPXYHFDE7OKUHNFKK5KSSOQ","short_pith_number":"pith:BROQPXYH","schema_version":"1.0","canonical_sha256":"0c5d07df0728c9f72a876954aeaa527433b395cb79fabc635bbc43bab5f441dd","source":{"kind":"arxiv","id":"1212.1955","version":1},"attestation_state":"computed","paper":{"title":"Canonical equations of Hamilton with beautiful symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"physics.class-ph","authors_text":"Guo Liang, Qi Guo","submitted_at":"2012-12-10T03:00:07Z","abstract_excerpt":"The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.1955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-12-10T03:00:07Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"df3ad3c56a83b6d309eba623249dfa70d39f0538efc56a0035d99c853eb2bf44","abstract_canon_sha256":"cf18bea6f166388f6d02daf8f4ca971d268e59009c0e0cb889cb94bcfdde7ed7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:54.647135Z","signature_b64":"qFxsqqe0RX4Z+8y4WkJWahbuUM8Qx24pXAcQ22gTSGZiTbLl4ElUzPjblBotNUVhttj/qKGFH9AHwyzpgUXHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c5d07df0728c9f72a876954aeaa527433b395cb79fabc635bbc43bab5f441dd","last_reissued_at":"2026-05-18T03:38:54.646643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:54.646643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical equations of Hamilton with beautiful symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"physics.class-ph","authors_text":"Guo Liang, Qi Guo","submitted_at":"2012-12-10T03:00:07Z","abstract_excerpt":"The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1955","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.1955","created_at":"2026-05-18T03:38:54.646728+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1955v1","created_at":"2026-05-18T03:38:54.646728+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1955","created_at":"2026-05-18T03:38:54.646728+00:00"},{"alias_kind":"pith_short_12","alias_value":"BROQPXYHFDE7","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BROQPXYHFDE7OKUH","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BROQPXYH","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ","json":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ.json","graph_json":"https://pith.science/api/pith-number/BROQPXYHFDE7OKUHNFKK5KSSOQ/graph.json","events_json":"https://pith.science/api/pith-number/BROQPXYHFDE7OKUHNFKK5KSSOQ/events.json","paper":"https://pith.science/paper/BROQPXYH"},"agent_actions":{"view_html":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ","download_json":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ.json","view_paper":"https://pith.science/paper/BROQPXYH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1955&json=true","fetch_graph":"https://pith.science/api/pith-number/BROQPXYHFDE7OKUHNFKK5KSSOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BROQPXYHFDE7OKUHNFKK5KSSOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ/action/storage_attestation","attest_author":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ/action/author_attestation","sign_citation":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ/action/citation_signature","submit_replication":"https://pith.science/pith/BROQPXYHFDE7OKUHNFKK5KSSOQ/action/replication_record"}},"created_at":"2026-05-18T03:38:54.646728+00:00","updated_at":"2026-05-18T03:38:54.646728+00:00"}