{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PBP4POAXDWXDR67E6PJX7TOUCF","short_pith_number":"pith:PBP4POAX","schema_version":"1.0","canonical_sha256":"785fc7b8171dae38fbe4f3d37fcdd4117d3133ee5f705afe39085d43a4125b4c","source":{"kind":"arxiv","id":"1808.00038","version":2},"attestation_state":"computed","paper":{"title":"Formal Barycenter Spaces with Weights: The Euler Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.AT","authors_text":"Sadok Kallel","submitted_at":"2018-07-31T19:32:35Z","abstract_excerpt":"We compute the Euler characteristic with compact supports $\\chi_c$ of the formal barycenter spaces with weights of a finite CW complex, connected or not. This reduces to the topological Euler characteristic $\\chi$ when the weights of the singular points are less than one. As foresighted by A. Malchiodi, our formula is related to the Leray-Schauder degree for mean field equations on a compact Riemann surface obtained by C.C. Chen and C.S. Lin."},"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":"1808.00038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-07-31T19:32:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9dd591e2ed43962038464f221073da447cc0b38af16eb6f56fed8e1183c96231","abstract_canon_sha256":"ebd8ab939ed8729760c1a3936d2475d97355cfcf6ab4b32041138f1ff489a5ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:39.400200Z","signature_b64":"kZN0vuWlH5q3rjmXEdw+UNMFhw3x1SuGGv5p6MmPCnSpYkW9MtciJqkY5h6uX7CWGy3lNDRCtoJ5Brs/3DXuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"785fc7b8171dae38fbe4f3d37fcdd4117d3133ee5f705afe39085d43a4125b4c","last_reissued_at":"2026-05-17T23:54:39.399643Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:39.399643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formal Barycenter Spaces with Weights: The Euler Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.AT","authors_text":"Sadok Kallel","submitted_at":"2018-07-31T19:32:35Z","abstract_excerpt":"We compute the Euler characteristic with compact supports $\\chi_c$ of the formal barycenter spaces with weights of a finite CW complex, connected or not. This reduces to the topological Euler characteristic $\\chi$ when the weights of the singular points are less than one. As foresighted by A. Malchiodi, our formula is related to the Leray-Schauder degree for mean field equations on a compact Riemann surface obtained by C.C. Chen and C.S. Lin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00038","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":"1808.00038","created_at":"2026-05-17T23:54:39.399741+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.00038v2","created_at":"2026-05-17T23:54:39.399741+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00038","created_at":"2026-05-17T23:54:39.399741+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBP4POAXDWXD","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBP4POAXDWXDR67E","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBP4POAX","created_at":"2026-05-18T12:32:43.782077+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/PBP4POAXDWXDR67E6PJX7TOUCF","json":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF.json","graph_json":"https://pith.science/api/pith-number/PBP4POAXDWXDR67E6PJX7TOUCF/graph.json","events_json":"https://pith.science/api/pith-number/PBP4POAXDWXDR67E6PJX7TOUCF/events.json","paper":"https://pith.science/paper/PBP4POAX"},"agent_actions":{"view_html":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF","download_json":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF.json","view_paper":"https://pith.science/paper/PBP4POAX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.00038&json=true","fetch_graph":"https://pith.science/api/pith-number/PBP4POAXDWXDR67E6PJX7TOUCF/graph.json","fetch_events":"https://pith.science/api/pith-number/PBP4POAXDWXDR67E6PJX7TOUCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF/action/storage_attestation","attest_author":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF/action/author_attestation","sign_citation":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF/action/citation_signature","submit_replication":"https://pith.science/pith/PBP4POAXDWXDR67E6PJX7TOUCF/action/replication_record"}},"created_at":"2026-05-17T23:54:39.399741+00:00","updated_at":"2026-05-17T23:54:39.399741+00:00"}