{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UWKGMBQIT42NKZ2DX2CT4XJH7S","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":"a1bc1b0aecab9bf588c7f576c2ac65dad06f4489bf8dea7262caa7b0eb6a6033","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-01T08:37:57Z","title_canon_sha256":"81fbd53795da1196eb994312d3600c0b703955f9a9664f0a4e2f17b353d56c83"},"schema_version":"1.0","source":{"id":"1807.00293","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00293","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00293v5","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00293","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_12","alias_value":"UWKGMBQIT42N","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_16","alias_value":"UWKGMBQIT42NKZ2D","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_8","alias_value":"UWKGMBQI","created_at":"2026-05-20T00:02:00Z"}],"graph_snapshots":[{"event_id":"sha256:b468cd0c729af2e1cbd1086dbd4150d4005fd73b0a61991837f9f263aed50bb5","target":"graph","created_at":"2026-05-20T00:02:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.00293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If the group of a 2-knot group $K$ has an abelian normal subgroup of rank $\\geq1$ which is not finitely generated then either $K$ has no minimal Seifert hypersurface or $K$ is topologically equivalent to Example 10 of Ralph Fox's``{\\it A quick trip through knot theory}\".","authors_text":"Jonathan A. Hillman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-01T08:37:57Z","title":"Rank 1 abelian normal subgroups of 2-knot groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00293","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":"sha256:231c3bb4ee5e99f3739180c297a6d18c5c58f54ff927968275e515b094c27258","target":"record","created_at":"2026-05-20T00:02:00Z","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":"a1bc1b0aecab9bf588c7f576c2ac65dad06f4489bf8dea7262caa7b0eb6a6033","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-01T08:37:57Z","title_canon_sha256":"81fbd53795da1196eb994312d3600c0b703955f9a9664f0a4e2f17b353d56c83"},"schema_version":"1.0","source":{"id":"1807.00293","kind":"arxiv","version":5}},"canonical_sha256":"a5946606089f34d56743be853e5d27fc8b9d1a3646579a27b229db410c7020fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5946606089f34d56743be853e5d27fc8b9d1a3646579a27b229db410c7020fd","first_computed_at":"2026-05-20T00:02:00.718919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:00.718919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rSmPUaB8L5nwNHGot9qBrWg3iAmxfnIo0RsA8crIN+8xE6H3fC1ssxr0vkW/Eg71d+cREhqQlvvQVGtw7q7yCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:00.719844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00293","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:231c3bb4ee5e99f3739180c297a6d18c5c58f54ff927968275e515b094c27258","sha256:b468cd0c729af2e1cbd1086dbd4150d4005fd73b0a61991837f9f263aed50bb5"],"state_sha256":"4972c75aed4ba18b29014d38fd64af6458c7bccce8d128af2ef38160bf099c30"}