{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VGPYTUH7LXL7HPFT3OEKJ2ZDCX","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":"3162e3e8b807b5d50d9fd92908603cc5ba553f4a8819b93b616ff132dc824fb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-24T11:58:14Z","title_canon_sha256":"f2ed2951f97ab7e664ad6406656d4427d271c35a4ec176d9737b9e73424ecd3c"},"schema_version":"1.0","source":{"id":"1708.07365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07365","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07365v2","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07365","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"VGPYTUH7LXL7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VGPYTUH7LXL7HPFT","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VGPYTUH7","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:f5346522db9f58bf7175f8d3730ad0c38f0b99a6fc7da25c624b40e48ed18c79","target":"graph","created_at":"2026-05-18T00:33:58Z","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":"In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for stably odd free knots. Some additional results on knot sliceness and cobordism are given.","authors_text":"Denis Fedoseev, Vassily Manturov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-24T11:58:14Z","title":"Cobordisms of graphs. A sliceness criterion for stably odd knots and related results on cobordisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07365","kind":"arxiv","version":2},"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":"sha256:39415922a882db56621d67eac7286dbf14c7842be66cdc6522be8ac49719c68c","target":"record","created_at":"2026-05-18T00:33:58Z","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":"3162e3e8b807b5d50d9fd92908603cc5ba553f4a8819b93b616ff132dc824fb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-24T11:58:14Z","title_canon_sha256":"f2ed2951f97ab7e664ad6406656d4427d271c35a4ec176d9737b9e73424ecd3c"},"schema_version":"1.0","source":{"id":"1708.07365","kind":"arxiv","version":2}},"canonical_sha256":"a99f89d0ff5dd7f3bcb3db88a4eb2315f9a13b7e393560619449a51cf1e96747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a99f89d0ff5dd7f3bcb3db88a4eb2315f9a13b7e393560619449a51cf1e96747","first_computed_at":"2026-05-18T00:33:58.556745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:58.556745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNiYTU1P/EaUs/c6CkWouDMS7c87xvaYTipsm5M73Pfks7oXyrPFmUxjvS8jmOscA0mFuV7y3hXGROGnHXqeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:58.557395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39415922a882db56621d67eac7286dbf14c7842be66cdc6522be8ac49719c68c","sha256:f5346522db9f58bf7175f8d3730ad0c38f0b99a6fc7da25c624b40e48ed18c79"],"state_sha256":"75cb06ee1549ef92ccacf46243aefb17703663a77dd1730d5576e7a71d8f707f"}