{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LBRVXKZDXCXCYFC5444HVUPVWF","short_pith_number":"pith:LBRVXKZD","schema_version":"1.0","canonical_sha256":"58635bab23b8ae2c145de7387ad1f5b1673e11f92678d3602c66674d32e73526","source":{"kind":"arxiv","id":"1505.03894","version":2},"attestation_state":"computed","paper":{"title":"The bi-Hamiltonian cohomology of a scalar Poisson pencil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.DG","authors_text":"Guido Carlet, Hessel Posthuma, Sergey Shadrin","submitted_at":"2015-05-14T21:25:54Z","abstract_excerpt":"We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\\hat{F}, d_1,d_2)$ is isomorphic to $\\mathbb{R}$ for $(p,d)=(0,0)$, to $C^\\infty (\\mathbb{R})$ for $(p,d)=(1,1)$, $(2,1)$, $(2,3)$, $(3,3)$, and vanishes otherwise."},"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":"1505.03894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-14T21:25:54Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"bdd524c4dd885bcf4c64c3a0159f90bd268c2e7ca647455d339d70c0ebf22422","abstract_canon_sha256":"c019184e5b1d07f52013d85675b9dc20ad869425a570963eb0f99a211245ff86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.907085Z","signature_b64":"cnP4tIf1w0vM5Zxv954A9UkjP+ZnHmrk3m3WCnZw3w9kI7pMx4MeOM+KXA4h1hO1qKhVDFFQ/56N1lAurBxoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58635bab23b8ae2c145de7387ad1f5b1673e11f92678d3602c66674d32e73526","last_reissued_at":"2026-05-18T00:37:48.906510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.906510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The bi-Hamiltonian cohomology of a scalar Poisson pencil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.DG","authors_text":"Guido Carlet, Hessel Posthuma, Sergey Shadrin","submitted_at":"2015-05-14T21:25:54Z","abstract_excerpt":"We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\\hat{F}, d_1,d_2)$ is isomorphic to $\\mathbb{R}$ for $(p,d)=(0,0)$, to $C^\\infty (\\mathbb{R})$ for $(p,d)=(1,1)$, $(2,1)$, $(2,3)$, $(3,3)$, and vanishes otherwise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03894","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":"1505.03894","created_at":"2026-05-18T00:37:48.906606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03894v2","created_at":"2026-05-18T00:37:48.906606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03894","created_at":"2026-05-18T00:37:48.906606+00:00"},{"alias_kind":"pith_short_12","alias_value":"LBRVXKZDXCXC","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LBRVXKZDXCXCYFC5","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LBRVXKZD","created_at":"2026-05-18T12:29:29.992203+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/LBRVXKZDXCXCYFC5444HVUPVWF","json":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF.json","graph_json":"https://pith.science/api/pith-number/LBRVXKZDXCXCYFC5444HVUPVWF/graph.json","events_json":"https://pith.science/api/pith-number/LBRVXKZDXCXCYFC5444HVUPVWF/events.json","paper":"https://pith.science/paper/LBRVXKZD"},"agent_actions":{"view_html":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF","download_json":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF.json","view_paper":"https://pith.science/paper/LBRVXKZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03894&json=true","fetch_graph":"https://pith.science/api/pith-number/LBRVXKZDXCXCYFC5444HVUPVWF/graph.json","fetch_events":"https://pith.science/api/pith-number/LBRVXKZDXCXCYFC5444HVUPVWF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF/action/storage_attestation","attest_author":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF/action/author_attestation","sign_citation":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF/action/citation_signature","submit_replication":"https://pith.science/pith/LBRVXKZDXCXCYFC5444HVUPVWF/action/replication_record"}},"created_at":"2026-05-18T00:37:48.906606+00:00","updated_at":"2026-05-18T00:37:48.906606+00:00"}