{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SP3X6DRGQYRWCAM5ZNUS2CKAGH","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":"ca0daf340c42338dc73801cbf5e9729ea3778e6d5ff8e2985d1632befbb54b53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-24T07:11:56Z","title_canon_sha256":"0a263cf51e3e678745d45b90c30e0781c22172844bad5b3fc97f73261eb31b3e"},"schema_version":"1.0","source":{"id":"2105.11123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11123","created_at":"2026-07-05T03:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11123v2","created_at":"2026-07-05T03:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11123","created_at":"2026-07-05T03:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"SP3X6DRGQYRW","created_at":"2026-07-05T03:27:02Z"},{"alias_kind":"pith_short_16","alias_value":"SP3X6DRGQYRWCAM5","created_at":"2026-07-05T03:27:02Z"},{"alias_kind":"pith_short_8","alias_value":"SP3X6DRG","created_at":"2026-07-05T03:27:02Z"}],"graph_snapshots":[{"event_id":"sha256:14ff734a1c3d2f51c04b2eb66e6546bd7903f1a90a2b25a9db75be0cc98a9363","target":"graph","created_at":"2026-07-05T03:27:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.11123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We state and prove that a certain class of smooth functions said to be BH-separable is a meagre subset for the Fr\\'echet topology. Because these functions are the only admissible Hamiltonians for Arnold-Liouville systems admitting a bi-Hamiltonian structure, we get that, generically, Arnold-Liouville systems cannot be bi-Hamiltonian. At the end of the paper, we determine, both as a concrete representation of our general result and as an illustrative list, which polynomial Hamiltonians $H$ of the form $H(x,y)=xy+ax^3+bx^2y+cxy^2+dy^3$ are BH-separable.","authors_text":"Hassan Boualem, Robert Brouzet","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-24T07:11:56Z","title":"Generically, Arnold-Liouville Systems Cannot be Bi-Hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11123","kind":"arxiv","version":2},"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":"sha256:7b13b5481612fda06b35330f014b36b16c1014680dbe6246e20ab09e3be35287","target":"record","created_at":"2026-07-05T03:27:02Z","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":"ca0daf340c42338dc73801cbf5e9729ea3778e6d5ff8e2985d1632befbb54b53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-24T07:11:56Z","title_canon_sha256":"0a263cf51e3e678745d45b90c30e0781c22172844bad5b3fc97f73261eb31b3e"},"schema_version":"1.0","source":{"id":"2105.11123","kind":"arxiv","version":2}},"canonical_sha256":"93f77f0e26862361019dcb692d094031c69179934ed474a770c177fde3ebddc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93f77f0e26862361019dcb692d094031c69179934ed474a770c177fde3ebddc0","first_computed_at":"2026-07-05T03:27:02.815753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:27:02.815753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XJHWYsvrl01ZShp2YIP+4zPBuANgya54lTwEjQfL7fXhpPgQ2HWARd1oUfYpWb8jN1F3XRyGlSOxt+WgWn7LAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:27:02.816126Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.11123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b13b5481612fda06b35330f014b36b16c1014680dbe6246e20ab09e3be35287","sha256:14ff734a1c3d2f51c04b2eb66e6546bd7903f1a90a2b25a9db75be0cc98a9363"],"state_sha256":"16d32524f4a257cf299e27af2ae94f3e5b2cce81ae7a7d4165202fc8b0ea7a4f"}