{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:C3HXWJKICAN3F2D6QEI6R3G5RT","short_pith_number":"pith:C3HXWJKI","canonical_record":{"source":{"id":"math/0211463","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2002-11-29T18:18:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"930bf2963e0040e99f19a0146db73bb86bbf2b2a6df559441b74af5619c05d15","abstract_canon_sha256":"9d7e2d62bb1e598ad5fced37c39951fc75a48e3ed30733bc75c4d7245358f96b"},"schema_version":"1.0"},"canonical_sha256":"16cf7b2548101bb2e87e8111e8ecdd8cd33f630e45d084fdfcf3b0c56061857e","source":{"kind":"arxiv","id":"math/0211463","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211463","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211463v4","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211463","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"C3HXWJKICAN3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"C3HXWJKICAN3F2D6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"C3HXWJKI","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:C3HXWJKICAN3F2D6QEI6R3G5RT","target":"record","payload":{"canonical_record":{"source":{"id":"math/0211463","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2002-11-29T18:18:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"930bf2963e0040e99f19a0146db73bb86bbf2b2a6df559441b74af5619c05d15","abstract_canon_sha256":"9d7e2d62bb1e598ad5fced37c39951fc75a48e3ed30733bc75c4d7245358f96b"},"schema_version":"1.0"},"canonical_sha256":"16cf7b2548101bb2e87e8111e8ecdd8cd33f630e45d084fdfcf3b0c56061857e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.310218Z","signature_b64":"oQVt93qLmDWrHDSj8kgsfql6y2ewGp1UJ/IQ6EntMuCSnGyRLo0goHvAzTg2mi/+wn4d0BDKbx3v3cBOYziBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16cf7b2548101bb2e87e8111e8ecdd8cd33f630e45d084fdfcf3b0c56061857e","last_reissued_at":"2026-05-18T01:38:29.309536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.309536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0211463","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1G321TI709QkVP2EQ1zGn920LWFSW3cczV+5IT708H3HTqBX2Vse9FFh15kWt3l5B5KkOs0UGsm8l5fn8kbgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:06:11.326109Z"},"content_sha256":"75795393762941a39d7d6f2667f41caeb3b7603089f579708252bc684374d3dd","schema_version":"1.0","event_id":"sha256:75795393762941a39d7d6f2667f41caeb3b7603089f579708252bc684374d3dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:C3HXWJKICAN3F2D6QEI6R3G5RT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bi-Hamiltonian partially integrable systems","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"G.Giachetta, G.Sardanashvily, L.Mangiarotti","submitted_at":"2002-11-29T18:18:35Z","abstract_excerpt":"Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211463","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCI+BzcZWaQRR3V2J5OXj2L3KmG6php+8VdkG9LzHF5l8Lv1KH7EPd5xIpmP7jGFjDOYXUMxpEEH87ux788FCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:06:11.326764Z"},"content_sha256":"26dbd18a450168ab82786782ef0b43148f6a40adac6c5ae1bba3c63fb0e7a9f8","schema_version":"1.0","event_id":"sha256:26dbd18a450168ab82786782ef0b43148f6a40adac6c5ae1bba3c63fb0e7a9f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/bundle.json","state_url":"https://pith.science/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T00:06:11Z","links":{"resolver":"https://pith.science/pith/C3HXWJKICAN3F2D6QEI6R3G5RT","bundle":"https://pith.science/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/bundle.json","state":"https://pith.science/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3HXWJKICAN3F2D6QEI6R3G5RT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:C3HXWJKICAN3F2D6QEI6R3G5RT","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":"9d7e2d62bb1e598ad5fced37c39951fc75a48e3ed30733bc75c4d7245358f96b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DS","submitted_at":"2002-11-29T18:18:35Z","title_canon_sha256":"930bf2963e0040e99f19a0146db73bb86bbf2b2a6df559441b74af5619c05d15"},"schema_version":"1.0","source":{"id":"math/0211463","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211463","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211463v4","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211463","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"C3HXWJKICAN3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"C3HXWJKICAN3F2D6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"C3HXWJKI","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:26dbd18a450168ab82786782ef0b43148f6a40adac6c5ae1bba3c63fb0e7a9f8","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems.","authors_text":"G.Giachetta, G.Sardanashvily, L.Mangiarotti","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2002-11-29T18:18:35Z","title":"Bi-Hamiltonian partially integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211463","kind":"arxiv","version":4},"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":"sha256:75795393762941a39d7d6f2667f41caeb3b7603089f579708252bc684374d3dd","target":"record","created_at":"2026-05-18T01:38:29Z","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":"9d7e2d62bb1e598ad5fced37c39951fc75a48e3ed30733bc75c4d7245358f96b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DS","submitted_at":"2002-11-29T18:18:35Z","title_canon_sha256":"930bf2963e0040e99f19a0146db73bb86bbf2b2a6df559441b74af5619c05d15"},"schema_version":"1.0","source":{"id":"math/0211463","kind":"arxiv","version":4}},"canonical_sha256":"16cf7b2548101bb2e87e8111e8ecdd8cd33f630e45d084fdfcf3b0c56061857e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16cf7b2548101bb2e87e8111e8ecdd8cd33f630e45d084fdfcf3b0c56061857e","first_computed_at":"2026-05-18T01:38:29.309536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.309536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oQVt93qLmDWrHDSj8kgsfql6y2ewGp1UJ/IQ6EntMuCSnGyRLo0goHvAzTg2mi/+wn4d0BDKbx3v3cBOYziBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.310218Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211463","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75795393762941a39d7d6f2667f41caeb3b7603089f579708252bc684374d3dd","sha256:26dbd18a450168ab82786782ef0b43148f6a40adac6c5ae1bba3c63fb0e7a9f8"],"state_sha256":"587950efb1a1f02e7eb4d6661d7aaa605446e573ba2eb851fedc9929ab475e7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9P+BMfTQWJWHMPk3XcGiCiCOaOZXV44PQZHM3uOS9b1eUKPaH0/zeEzVU7wTwNRl6w6DfiMQrqhonhUjuSheCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:06:11.330485Z","bundle_sha256":"36aaad6889129deb688dfae6af2e361beb2bbc113d9b6f91d6f20565a1fc6dc3"}}