{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JDHIPRXJWT6ODG6H6I5LD453XC","short_pith_number":"pith:JDHIPRXJ","schema_version":"1.0","canonical_sha256":"48ce87c6e9b4fce19bc7f23ab1f3bbb88d3ab9693e4d90911276fd6689147068","source":{"kind":"arxiv","id":"1609.07438","version":2},"attestation_state":"computed","paper":{"title":"Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Angel Ballesteros, Juan Carlos Marrero, Zohreh Ravanpak","submitted_at":"2016-09-23T17:18:40Z","abstract_excerpt":"Given a Lie-Poisson completely integrable bi-Hamiltonian system on $\\mathbb{R}^n$, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group $G_\\eta$ of dimension $n$, where $\\eta \\in \\mathbb{R}$ is the deformation parameter. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures on $G_\\eta$ that underly the dynamics of the deformed system and by making use of the group law on $G_\\eta$, one may obtain two completely integrabl"},"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":"1609.07438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-09-23T17:18:40Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d97a6d313959fdeabbd13422eafa50ec9ac2f5667f7ecc8c7012c9cf775827c6","abstract_canon_sha256":"97b088ecc9c0b92969cac2ebdc9db64e2667e667a0febba9bff643cbe41d92bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.114989Z","signature_b64":"MkqbLz0g6VvVH00X5xxcjVGXufNGxRs4aCeOhoSfySQ67IBf4BOyHmRETdumFRs5jZEcbDgYFIIeX1lp906UBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48ce87c6e9b4fce19bc7f23ab1f3bbb88d3ab9693e4d90911276fd6689147068","last_reissued_at":"2026-05-18T00:48:54.114262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.114262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Angel Ballesteros, Juan Carlos Marrero, Zohreh Ravanpak","submitted_at":"2016-09-23T17:18:40Z","abstract_excerpt":"Given a Lie-Poisson completely integrable bi-Hamiltonian system on $\\mathbb{R}^n$, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group $G_\\eta$ of dimension $n$, where $\\eta \\in \\mathbb{R}$ is the deformation parameter. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures on $G_\\eta$ that underly the dynamics of the deformed system and by making use of the group law on $G_\\eta$, one may obtain two completely integrabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07438","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":""},"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":"1609.07438","created_at":"2026-05-18T00:48:54.114397+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07438v2","created_at":"2026-05-18T00:48:54.114397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07438","created_at":"2026-05-18T00:48:54.114397+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDHIPRXJWT6O","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDHIPRXJWT6ODG6H","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDHIPRXJ","created_at":"2026-05-18T12:30:25.849896+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/JDHIPRXJWT6ODG6H6I5LD453XC","json":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC.json","graph_json":"https://pith.science/api/pith-number/JDHIPRXJWT6ODG6H6I5LD453XC/graph.json","events_json":"https://pith.science/api/pith-number/JDHIPRXJWT6ODG6H6I5LD453XC/events.json","paper":"https://pith.science/paper/JDHIPRXJ"},"agent_actions":{"view_html":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC","download_json":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC.json","view_paper":"https://pith.science/paper/JDHIPRXJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07438&json=true","fetch_graph":"https://pith.science/api/pith-number/JDHIPRXJWT6ODG6H6I5LD453XC/graph.json","fetch_events":"https://pith.science/api/pith-number/JDHIPRXJWT6ODG6H6I5LD453XC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC/action/storage_attestation","attest_author":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC/action/author_attestation","sign_citation":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC/action/citation_signature","submit_replication":"https://pith.science/pith/JDHIPRXJWT6ODG6H6I5LD453XC/action/replication_record"}},"created_at":"2026-05-18T00:48:54.114397+00:00","updated_at":"2026-05-18T00:48:54.114397+00:00"}