{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:DJA57EP4SZQBTJCMVJJY5JYZES","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":"4c8618d07b0d2e07c0d1558e09ec80209078214055dc25fb454fd6a6f755b0de","cross_cats_sorted":["math.MP","math.SG"],"license":"","primary_cat":"math-ph","submitted_at":"2002-03-08T23:57:39Z","title_canon_sha256":"c68239dd52c326aa2a8acbb0b490f0f79e6e578eb2acecc296bfda25fb758442"},"schema_version":"1.0","source":{"id":"math-ph/0203012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0203012","created_at":"2026-05-18T02:37:27Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0203012v1","created_at":"2026-05-18T02:37:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0203012","created_at":"2026-05-18T02:37:27Z"},{"alias_kind":"pith_short_12","alias_value":"DJA57EP4SZQB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"DJA57EP4SZQBTJCM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"DJA57EP4","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:84a27f68d404aefa849bea483fa56abc4cf57ef68f5d360f107c8af8af3af8f3","target":"graph","created_at":"2026-05-18T02:37:27Z","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 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.","authors_text":"A. Ozorio de Almeida, Pedro de M. Rios","cross_cats":["math.MP","math.SG"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-03-08T23:57:39Z","title":"A variational principle for actions on symmetric symplectic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0203012","kind":"arxiv","version":1},"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":"sha256:3a26adcbd0b881697e9d5257882521ed5d153d1e163f59247504022a0a396a50","target":"record","created_at":"2026-05-18T02:37:27Z","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":"4c8618d07b0d2e07c0d1558e09ec80209078214055dc25fb454fd6a6f755b0de","cross_cats_sorted":["math.MP","math.SG"],"license":"","primary_cat":"math-ph","submitted_at":"2002-03-08T23:57:39Z","title_canon_sha256":"c68239dd52c326aa2a8acbb0b490f0f79e6e578eb2acecc296bfda25fb758442"},"schema_version":"1.0","source":{"id":"math-ph/0203012","kind":"arxiv","version":1}},"canonical_sha256":"1a41df91fc966019a44caa538ea719248bd790ddc7ae65da981d413735638c8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a41df91fc966019a44caa538ea719248bd790ddc7ae65da981d413735638c8a","first_computed_at":"2026-05-18T02:37:27.809246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:27.809246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XuHC2kT1yM4ydxSj95GqwKYqqOu7L1KJ4kmE3iIykDM07tZD7wAWhSs86kxJNAPAvKr5tKFXdO2XYXR+t24oAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:27.809731Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0203012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a26adcbd0b881697e9d5257882521ed5d153d1e163f59247504022a0a396a50","sha256:84a27f68d404aefa849bea483fa56abc4cf57ef68f5d360f107c8af8af3af8f3"],"state_sha256":"ae8bdaf95ee41d9e5969ee30707ffd1e00df70728c41c9c757848917a808ad67"}