{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NB4AUS6GVLHKJAVJFTX3WIO3QO","short_pith_number":"pith:NB4AUS6G","schema_version":"1.0","canonical_sha256":"68780a4bc6aacea482a92cefbb21db839a648e95c300c6a055cc69c6cdd7d4f9","source":{"kind":"arxiv","id":"1103.0672","version":2},"attestation_state":"computed","paper":{"title":"Symplectic Microgeometry II: Generating functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Alan Weinstein, Alberto S. Cattaneo, Benoit Dherin","submitted_at":"2011-03-03T12:44:24Z","abstract_excerpt":"We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics."},"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":"1103.0672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-03-03T12:44:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b447cf59568fca07a61daa6b04ca92c5faf3884d8129dd2fbd96639ea9a2d8f7","abstract_canon_sha256":"c96578b41ffc54b449c2bcae9510d6c6f456b80f762bcd3caaba883b8993fe28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:47:24.362782Z","signature_b64":"ZD0yG7fr2c/dXB1wM17QFt5GotV/UN4++UArYBzHnhXInB314maEPcRZShEBHiq/3bHWJ3BWRj4eTXMzoj2WDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68780a4bc6aacea482a92cefbb21db839a648e95c300c6a055cc69c6cdd7d4f9","last_reissued_at":"2026-07-05T00:47:24.362397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:47:24.362397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic Microgeometry II: Generating functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Alan Weinstein, Alberto S. Cattaneo, Benoit Dherin","submitted_at":"2011-03-03T12:44:24Z","abstract_excerpt":"We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0672","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1103.0672/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1103.0672","created_at":"2026-07-05T00:47:24.362446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.0672v2","created_at":"2026-07-05T00:47:24.362446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0672","created_at":"2026-07-05T00:47:24.362446+00:00"},{"alias_kind":"pith_short_12","alias_value":"NB4AUS6GVLHK","created_at":"2026-07-05T00:47:24.362446+00:00"},{"alias_kind":"pith_short_16","alias_value":"NB4AUS6GVLHKJAVJ","created_at":"2026-07-05T00:47:24.362446+00:00"},{"alias_kind":"pith_short_8","alias_value":"NB4AUS6G","created_at":"2026-07-05T00:47:24.362446+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/NB4AUS6GVLHKJAVJFTX3WIO3QO","json":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO.json","graph_json":"https://pith.science/api/pith-number/NB4AUS6GVLHKJAVJFTX3WIO3QO/graph.json","events_json":"https://pith.science/api/pith-number/NB4AUS6GVLHKJAVJFTX3WIO3QO/events.json","paper":"https://pith.science/paper/NB4AUS6G"},"agent_actions":{"view_html":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO","download_json":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO.json","view_paper":"https://pith.science/paper/NB4AUS6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.0672&json=true","fetch_graph":"https://pith.science/api/pith-number/NB4AUS6GVLHKJAVJFTX3WIO3QO/graph.json","fetch_events":"https://pith.science/api/pith-number/NB4AUS6GVLHKJAVJFTX3WIO3QO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO/action/storage_attestation","attest_author":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO/action/author_attestation","sign_citation":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO/action/citation_signature","submit_replication":"https://pith.science/pith/NB4AUS6GVLHKJAVJFTX3WIO3QO/action/replication_record"}},"created_at":"2026-07-05T00:47:24.362446+00:00","updated_at":"2026-07-05T00:47:24.362446+00:00"}