{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:Y5AS72JO7KFHAXUWYKOVSRJZW4","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":"e9471bf478e4623cb45bef53d2e44025b964256f552295f1785f20d4c3162a16","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-07-25T09:07:52Z","title_canon_sha256":"7e533409f51621cc574381a104ef18085237ee9cb16f852bd7332f97941811c8"},"schema_version":"1.0","source":{"id":"0807.4034","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4034","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4034v5","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4034","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"Y5AS72JO7KFH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"Y5AS72JO7KFHAXUW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"Y5AS72JO","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:91a581f0a498bff161f03ca9ae97641013d71b9c91af3cf5c4a601f4c0c1eb36","target":"graph","created_at":"2026-05-18T03:17:44Z","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":"Sutured manifolds defined by Gabai are useful in the geometrical study of knots and 3-dimensional manifolds. On the other hand, homology cylinders are in an important position in the recent theory of homology cobordisms of surfaces and finite-type invariants. We study a relationship between them by focusing on sutured manifolds associated with a special class of knots which we call {\\it homologically fibered knots}. Then we use invariants of homology cylinders to give applications to knot theory such as fibering obstructions, Reidemeister torsions and handle numbers of homologically fibered kn","authors_text":"Hiroshi Goda, Takuya Sakasai","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-07-25T09:07:52Z","title":"Homology cylinders and sutured manifolds for homologically fibered knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4034","kind":"arxiv","version":5},"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":"sha256:87bf4e940e27bfeae1f0a951c0b88b4065e531b576aa679c5822acd815ed12f5","target":"record","created_at":"2026-05-18T03:17:44Z","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":"e9471bf478e4623cb45bef53d2e44025b964256f552295f1785f20d4c3162a16","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-07-25T09:07:52Z","title_canon_sha256":"7e533409f51621cc574381a104ef18085237ee9cb16f852bd7332f97941811c8"},"schema_version":"1.0","source":{"id":"0807.4034","kind":"arxiv","version":5}},"canonical_sha256":"c7412fe92efa8a705e96c29d594539b734b134488020b7bed8f2cde0bf1edc46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7412fe92efa8a705e96c29d594539b734b134488020b7bed8f2cde0bf1edc46","first_computed_at":"2026-05-18T03:17:44.997830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.997830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dGDCNawlyjWUXAcwCudLFTweyHsEeBFFR4XFRqTAEBJOQ3w5SUaSfQf52Ut+Es6qHdEhDmznMQ+5UHkSVNDJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.998417Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.4034","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87bf4e940e27bfeae1f0a951c0b88b4065e531b576aa679c5822acd815ed12f5","sha256:91a581f0a498bff161f03ca9ae97641013d71b9c91af3cf5c4a601f4c0c1eb36"],"state_sha256":"e41c001eda4586bab20edecb9abf69b31e589636b9530179c78737ac1c6e07c9"}