{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R4SJ6PRBGQGPT4FY5YL44QDG4U","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":"22f07405410a37c07877f245bbe28db8bc9c0b1de43976d813371daa4156d69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-14T13:54:05Z","title_canon_sha256":"78bac8b240c25b1b250cccfdf9e44acb6e3b96dff1940c2df753970fcf2a120d"},"schema_version":"1.0","source":{"id":"1104.2763","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2763","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2763v3","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2763","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"R4SJ6PRBGQGP","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"R4SJ6PRBGQGPT4FY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"R4SJ6PRB","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:cb6129a7b6d5ae6ab9021d8cd5cc1bb86d45863d22fdcc109baa194a49b74447","target":"graph","created_at":"2026-05-18T02:22:09Z","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"},"paper":{"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","authors_text":"Gwenael Massuyeau, Jean-Baptiste Meilhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-14T13:54:05Z","title":"Equivalence relations for homology cylinders and the core of the Casson invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2763","kind":"arxiv","version":3},"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:c12a0163adc4bf71145735b22a53acb2774466060e8ad6f4a52e16a9946947b6","target":"record","created_at":"2026-05-18T02:22:09Z","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":"22f07405410a37c07877f245bbe28db8bc9c0b1de43976d813371daa4156d69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-14T13:54:05Z","title_canon_sha256":"78bac8b240c25b1b250cccfdf9e44acb6e3b96dff1940c2df753970fcf2a120d"},"schema_version":"1.0","source":{"id":"1104.2763","kind":"arxiv","version":3}},"canonical_sha256":"8f249f3e21340cf9f0b8ee17ce4066e53d27151f52b9569a8eb4ff61f249db3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f249f3e21340cf9f0b8ee17ce4066e53d27151f52b9569a8eb4ff61f249db3d","first_computed_at":"2026-05-18T02:22:09.214413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:09.214413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/X5/gjH59m/AmVqjR+ECP3Sm/RPSD5jguqpBcJT8FrUiZQiEgFuEnwdmcTSLD+AnVKbDfcvO3RhxAHxGWIdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:09.214976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2763","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12a0163adc4bf71145735b22a53acb2774466060e8ad6f4a52e16a9946947b6","sha256:cb6129a7b6d5ae6ab9021d8cd5cc1bb86d45863d22fdcc109baa194a49b74447"],"state_sha256":"f323f02e590644baecf9dbc23f1a57995c78534dce761ff116405e519299e422"}