{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S6ZC6TUVA3W6GUCYR3BCVWLPHN","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":"ff7dbbdc0020e517cea8d3a2839ef71e8bd9f5b65e3db7b8a79118ddb0c2adc7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-02-10T19:39:12Z","title_canon_sha256":"50b82517e513f11e1a24a555d4b1c3d8425e0f833b547452cd43fd8329ce3c5c"},"schema_version":"1.0","source":{"id":"1802.03645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03645","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03645v2","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03645","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"S6ZC6TUVA3W6","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S6ZC6TUVA3W6GUCY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S6ZC6TUV","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:a0f991bcc233e84270d128c996eaf8bbc38bc8e11c76620ecbafc6cd4239642b","target":"graph","created_at":"2026-05-18T00:23:44Z","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":"In this survey paper we present results about link diagrams in Seifert manifolds using arrow diagrams, starting with link diagrams in $F\\times S^1$ and $N\\hat{\\times}S^1$, where $F$ is an orientable and $N$ an unorientable surface. Reidemeister moves for such arrow diagrams make the study of link invariants possible. Transitions between arrow diagrams and alternative diagrams are presented. We recall results about %the knot group presentation for lens spaces and the Kauffman bracket and HOMFLYPT skein modules of some Seifert manifolds using arrow diagrams, namely lens spaces, a product of a di","authors_text":"Bo\\v{s}tjan Gabrov\\v{s}ek, Maciej Mroczkowski","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-02-10T19:39:12Z","title":"Link diagrams in Seifert manifolds and applications to skein modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03645","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":"sha256:0158a34064c7f9df18963d2b2edb12b54f4a3923f0cf3e83211403c61338172b","target":"record","created_at":"2026-05-18T00:23:44Z","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":"ff7dbbdc0020e517cea8d3a2839ef71e8bd9f5b65e3db7b8a79118ddb0c2adc7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-02-10T19:39:12Z","title_canon_sha256":"50b82517e513f11e1a24a555d4b1c3d8425e0f833b547452cd43fd8329ce3c5c"},"schema_version":"1.0","source":{"id":"1802.03645","kind":"arxiv","version":2}},"canonical_sha256":"97b22f4e9506ede350588ec22ad96f3b75b060aaccddd6117c7f790a7762ad17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97b22f4e9506ede350588ec22ad96f3b75b060aaccddd6117c7f790a7762ad17","first_computed_at":"2026-05-18T00:23:44.657480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:44.657480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dCXsl/l2DnSAg/EmzAC5+zWHByt1iNh80JYvsU0tK2CXcjKzwc971SdLzwvxhxQLHxgGmbMr6z9TNoffL3lmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:44.657960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0158a34064c7f9df18963d2b2edb12b54f4a3923f0cf3e83211403c61338172b","sha256:a0f991bcc233e84270d128c996eaf8bbc38bc8e11c76620ecbafc6cd4239642b"],"state_sha256":"d2359af54547f6ffd7a99b31d4f4f362e874c428b44c26242b31b8cdc953f64f"}