{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H6TJC4QXEGFZK45HJ42MKQHHHQ","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":"fe72a26d8dfee1083b04f6619772815fb8a76438a2fdbfcadaade07b81bfa59f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-20T00:55:28Z","title_canon_sha256":"c5d1a50992987ccafe170b5fa25d87ac2221c362b260e002047d43543c55f49f"},"schema_version":"1.0","source":{"id":"1004.3326","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3326","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3326v3","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3326","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"H6TJC4QXEGFZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H6TJC4QXEGFZK45H","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H6TJC4QX","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:422f8808cab9fb4f1849f492641b2dbaefd2bf1822b28be4e0022a0929cb1277","target":"graph","created_at":"2026-05-18T04:10:09Z","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":"Homologically fibered knots are knots whose exteriors satisfy the same homological conditions as fibered knots. In our previous paper, we observed that for such a knot, higher-order Alexander invariants defined by Cochran, Harvey and Friedl are generally factorized into the part of the Magnus matrix and that of a certain Reidemeister torsion, both of which are known as invariants of homology cylinders over a surface. In this paper, we study more details of the invariants and give some concrete calculations by restricting to the case of the invariants associated with metabelian quotients of the","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":"2010-04-20T00:55:28Z","title":"Factorization formulas and computations of higher-order Alexander invariants for homologically fibered knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3326","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:bbf74a580a2ea547af49b5c7779ca0959806b7988839827b045cebd6b9296c17","target":"record","created_at":"2026-05-18T04:10:09Z","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":"fe72a26d8dfee1083b04f6619772815fb8a76438a2fdbfcadaade07b81bfa59f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-20T00:55:28Z","title_canon_sha256":"c5d1a50992987ccafe170b5fa25d87ac2221c362b260e002047d43543c55f49f"},"schema_version":"1.0","source":{"id":"1004.3326","kind":"arxiv","version":3}},"canonical_sha256":"3fa6917217218b9573a74f34c540e73c0a7a6360e20bbab7a977d4c65635750f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fa6917217218b9573a74f34c540e73c0a7a6360e20bbab7a977d4c65635750f","first_computed_at":"2026-05-18T04:10:09.204751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.204751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnOiFIoAasicTacN3JLAvNeCA8jMzrhgipjBxgN6x5h5WsC//10BJVjaUB+PNgUlJIZUyOE5gsa5imDlbzyYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.205608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3326","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbf74a580a2ea547af49b5c7779ca0959806b7988839827b045cebd6b9296c17","sha256:422f8808cab9fb4f1849f492641b2dbaefd2bf1822b28be4e0022a0929cb1277"],"state_sha256":"09bc569333aa93e454b447f2c5ac04200000530ce936e1b16fffa8610af34764"}