{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:DJA57EP4SZQBTJCMVJJY5JYZES","short_pith_number":"pith:DJA57EP4","schema_version":"1.0","canonical_sha256":"1a41df91fc966019a44caa538ea719248bd790ddc7ae65da981d413735638c8a","source":{"kind":"arxiv","id":"math-ph/0203012","version":1},"attestation_state":"computed","paper":{"title":"A variational principle for actions on symmetric symplectic spaces","license":"","headline":"","cross_cats":["math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"A. Ozorio de Almeida, Pedro de M. Rios","submitted_at":"2002-03-08T23:57:39Z","abstract_excerpt":"We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly."},"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":"math-ph/0203012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-03-08T23:57:39Z","cross_cats_sorted":["math.MP","math.SG"],"title_canon_sha256":"c68239dd52c326aa2a8acbb0b490f0f79e6e578eb2acecc296bfda25fb758442","abstract_canon_sha256":"4c8618d07b0d2e07c0d1558e09ec80209078214055dc25fb454fd6a6f755b0de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:27.809731Z","signature_b64":"XuHC2kT1yM4ydxSj95GqwKYqqOu7L1KJ4kmE3iIykDM07tZD7wAWhSs86kxJNAPAvKr5tKFXdO2XYXR+t24oAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a41df91fc966019a44caa538ea719248bd790ddc7ae65da981d413735638c8a","last_reissued_at":"2026-05-18T02:37:27.809246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:27.809246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A variational principle for actions on symmetric symplectic spaces","license":"","headline":"","cross_cats":["math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"A. Ozorio de Almeida, Pedro de M. Rios","submitted_at":"2002-03-08T23:57:39Z","abstract_excerpt":"We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0203012","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":"math-ph/0203012","created_at":"2026-05-18T02:37:27.809311+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0203012v1","created_at":"2026-05-18T02:37:27.809311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0203012","created_at":"2026-05-18T02:37:27.809311+00:00"},{"alias_kind":"pith_short_12","alias_value":"DJA57EP4SZQB","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"DJA57EP4SZQBTJCM","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"DJA57EP4","created_at":"2026-05-18T12:25:50.845339+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/DJA57EP4SZQBTJCMVJJY5JYZES","json":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES.json","graph_json":"https://pith.science/api/pith-number/DJA57EP4SZQBTJCMVJJY5JYZES/graph.json","events_json":"https://pith.science/api/pith-number/DJA57EP4SZQBTJCMVJJY5JYZES/events.json","paper":"https://pith.science/paper/DJA57EP4"},"agent_actions":{"view_html":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES","download_json":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES.json","view_paper":"https://pith.science/paper/DJA57EP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0203012&json=true","fetch_graph":"https://pith.science/api/pith-number/DJA57EP4SZQBTJCMVJJY5JYZES/graph.json","fetch_events":"https://pith.science/api/pith-number/DJA57EP4SZQBTJCMVJJY5JYZES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES/action/storage_attestation","attest_author":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES/action/author_attestation","sign_citation":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES/action/citation_signature","submit_replication":"https://pith.science/pith/DJA57EP4SZQBTJCMVJJY5JYZES/action/replication_record"}},"created_at":"2026-05-18T02:37:27.809311+00:00","updated_at":"2026-05-18T02:37:27.809311+00:00"}