{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:R4SJ6PRBGQGPT4FY5YL44QDG4U","short_pith_number":"pith:R4SJ6PRB","schema_version":"1.0","canonical_sha256":"8f249f3e21340cf9f0b8ee17ce4066e53d27151f52b9569a8eb4ff61f249db3d","source":{"kind":"arxiv","id":"1104.2763","version":3},"attestation_state":"computed","paper":{"title":"Equivalence relations for homology cylinders and the core of the Casson invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Jean-Baptiste Meilhan","submitted_at":"2011-04-14T13:54:05Z","abstract_excerpt":"Let R be a compact oriented surface of genus g with one boundary component. Homology cylinders over R form a monoid IC into which the Torelli group I of R embeds by the mapping cylinder construction. Two homology cylinders M and M' are said to be Y_k-equivalent if M' is obtained from M by \"twisting\" an arbitrary surface S in M with a homeomorphim belonging to the k-th term of the lower central series of the Torelli group of S. The J_k-equivalence relation on IC is defined in a similar way using the k-th term of the Johnson filtration. In this paper, we characterize the Y_3-equivalence with thr"},"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":"1104.2763","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-14T13:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"78bac8b240c25b1b250cccfdf9e44acb6e3b96dff1940c2df753970fcf2a120d","abstract_canon_sha256":"22f07405410a37c07877f245bbe28db8bc9c0b1de43976d813371daa4156d69f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:09.214976Z","signature_b64":"0/X5/gjH59m/AmVqjR+ECP3Sm/RPSD5jguqpBcJT8FrUiZQiEgFuEnwdmcTSLD+AnVKbDfcvO3RhxAHxGWIdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f249f3e21340cf9f0b8ee17ce4066e53d27151f52b9569a8eb4ff61f249db3d","last_reissued_at":"2026-05-18T02:22:09.214413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:09.214413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence relations for homology cylinders and the core of the Casson invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Jean-Baptiste Meilhan","submitted_at":"2011-04-14T13:54:05Z","abstract_excerpt":"Let R be a compact oriented surface of genus g with one boundary component. Homology cylinders over R form a monoid IC into which the Torelli group I of R embeds by the mapping cylinder construction. Two homology cylinders M and M' are said to be Y_k-equivalent if M' is obtained from M by \"twisting\" an arbitrary surface S in M with a homeomorphim belonging to the k-th term of the lower central series of the Torelli group of S. The J_k-equivalence relation on IC is defined in a similar way using the k-th term of the Johnson filtration. In this paper, we characterize the Y_3-equivalence with thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2763","kind":"arxiv","version":3},"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":"1104.2763","created_at":"2026-05-18T02:22:09.214494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2763v3","created_at":"2026-05-18T02:22:09.214494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2763","created_at":"2026-05-18T02:22:09.214494+00:00"},{"alias_kind":"pith_short_12","alias_value":"R4SJ6PRBGQGP","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"R4SJ6PRBGQGPT4FY","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"R4SJ6PRB","created_at":"2026-05-18T12:26:41.206345+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/R4SJ6PRBGQGPT4FY5YL44QDG4U","json":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U.json","graph_json":"https://pith.science/api/pith-number/R4SJ6PRBGQGPT4FY5YL44QDG4U/graph.json","events_json":"https://pith.science/api/pith-number/R4SJ6PRBGQGPT4FY5YL44QDG4U/events.json","paper":"https://pith.science/paper/R4SJ6PRB"},"agent_actions":{"view_html":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U","download_json":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U.json","view_paper":"https://pith.science/paper/R4SJ6PRB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2763&json=true","fetch_graph":"https://pith.science/api/pith-number/R4SJ6PRBGQGPT4FY5YL44QDG4U/graph.json","fetch_events":"https://pith.science/api/pith-number/R4SJ6PRBGQGPT4FY5YL44QDG4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U/action/storage_attestation","attest_author":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U/action/author_attestation","sign_citation":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U/action/citation_signature","submit_replication":"https://pith.science/pith/R4SJ6PRBGQGPT4FY5YL44QDG4U/action/replication_record"}},"created_at":"2026-05-18T02:22:09.214494+00:00","updated_at":"2026-05-18T02:22:09.214494+00:00"}