{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:K2QGHZ43BZA7E3DS7ZNZSTPJAP","short_pith_number":"pith:K2QGHZ43","schema_version":"1.0","canonical_sha256":"56a063e79b0e41f26c72fe5b994de903fe62dc2315234d346810c0552c70c131","source":{"kind":"arxiv","id":"0802.1905","version":1},"attestation_state":"computed","paper":{"title":"Geometrical aspects of integrable systems","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Emanuele Fiorani","submitted_at":"2008-02-13T20:41:45Z","abstract_excerpt":"We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting."},"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":"0802.1905","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2008-02-13T20:41:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fbbe98db42ff5f001e2b8485bb57ba68d5c4d317123d6423ae6aca14781f4bbb","abstract_canon_sha256":"e5f15b1b288c77273e292bf786db549722e9ea8bb276730c238e4e2e52fe839e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:01.088982Z","signature_b64":"Y98OM4KmqZpe8nROUPozNPUXSEQhsmYtGGSP3ZnWdTe28ImwfchPO6zHuYdWoXIIp5F5WvArUosXhlaZPbA1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56a063e79b0e41f26c72fe5b994de903fe62dc2315234d346810c0552c70c131","last_reissued_at":"2026-05-18T02:16:01.088587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:01.088587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometrical aspects of integrable systems","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Emanuele Fiorani","submitted_at":"2008-02-13T20:41:45Z","abstract_excerpt":"We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1905","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":"0802.1905","created_at":"2026-05-18T02:16:01.088651+00:00"},{"alias_kind":"arxiv_version","alias_value":"0802.1905v1","created_at":"2026-05-18T02:16:01.088651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1905","created_at":"2026-05-18T02:16:01.088651+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2QGHZ43BZA7","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2QGHZ43BZA7E3DS","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2QGHZ43","created_at":"2026-05-18T12:25:57.157939+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/K2QGHZ43BZA7E3DS7ZNZSTPJAP","json":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP.json","graph_json":"https://pith.science/api/pith-number/K2QGHZ43BZA7E3DS7ZNZSTPJAP/graph.json","events_json":"https://pith.science/api/pith-number/K2QGHZ43BZA7E3DS7ZNZSTPJAP/events.json","paper":"https://pith.science/paper/K2QGHZ43"},"agent_actions":{"view_html":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP","download_json":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP.json","view_paper":"https://pith.science/paper/K2QGHZ43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0802.1905&json=true","fetch_graph":"https://pith.science/api/pith-number/K2QGHZ43BZA7E3DS7ZNZSTPJAP/graph.json","fetch_events":"https://pith.science/api/pith-number/K2QGHZ43BZA7E3DS7ZNZSTPJAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP/action/storage_attestation","attest_author":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP/action/author_attestation","sign_citation":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP/action/citation_signature","submit_replication":"https://pith.science/pith/K2QGHZ43BZA7E3DS7ZNZSTPJAP/action/replication_record"}},"created_at":"2026-05-18T02:16:01.088651+00:00","updated_at":"2026-05-18T02:16:01.088651+00:00"}