{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S7BWWAQFHC5QJETJPI7B2UE3JB","short_pith_number":"pith:S7BWWAQF","schema_version":"1.0","canonical_sha256":"97c36b020538bb0492697a3e1d509b487163ae7e53271ec4e2849502a22ccf17","source":{"kind":"arxiv","id":"1802.01727","version":3},"attestation_state":"computed","paper":{"title":"Ascent sliceness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"William Rushworth","submitted_at":"2018-02-05T23:16:20Z","abstract_excerpt":"We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $ S^1 \\hookrightarrow \\Sigma_{g} \\times I $, for $ \\Sigma_g $ a closed connected oriented surface of genus $ g $; the virtual knot represented is slice if there exists a pair consisting of a disc $ D $ and an oriented $ 3 $-manifold $ M $, such that $ D \\hookrightarrow M \\times I $, $ \\partial M = \\Sigma_{g} $, and $ \\partial D = S^1 $ (the image of the embedding).\n  This definition of sliceness exemplifies that a cobordism of virtual links is a pair consisting of a surface and a $ "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.01727","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-05T23:16:20Z","cross_cats_sorted":[],"title_canon_sha256":"a944152127556d9c769e2f9fff7f64c351ce8053231de35833d1e2dac3b6e8d5","abstract_canon_sha256":"07d70a2dba226d644ccc4108a3a77cf7436b27d860e842071adaedef06d69db3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:58.803282Z","signature_b64":"taQYJ74hdzDx8AdW5mV4xgctAPMjzQXNyuUi08/YzTkYc6BINes92wTU3oExX8p+QUNVYPCvKzSKsxlwNLhcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97c36b020538bb0492697a3e1d509b487163ae7e53271ec4e2849502a22ccf17","last_reissued_at":"2026-05-17T23:39:58.802731Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:58.802731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ascent sliceness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"William Rushworth","submitted_at":"2018-02-05T23:16:20Z","abstract_excerpt":"We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $ S^1 \\hookrightarrow \\Sigma_{g} \\times I $, for $ \\Sigma_g $ a closed connected oriented surface of genus $ g $; the virtual knot represented is slice if there exists a pair consisting of a disc $ D $ and an oriented $ 3 $-manifold $ M $, such that $ D \\hookrightarrow M \\times I $, $ \\partial M = \\Sigma_{g} $, and $ \\partial D = S^1 $ (the image of the embedding).\n  This definition of sliceness exemplifies that a cobordism of virtual links is a pair consisting of a surface and a $ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01727","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.01727","created_at":"2026-05-17T23:39:58.802808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01727v3","created_at":"2026-05-17T23:39:58.802808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01727","created_at":"2026-05-17T23:39:58.802808+00:00"},{"alias_kind":"pith_short_12","alias_value":"S7BWWAQFHC5Q","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"S7BWWAQFHC5QJETJ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"S7BWWAQF","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB","json":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB.json","graph_json":"https://pith.science/api/pith-number/S7BWWAQFHC5QJETJPI7B2UE3JB/graph.json","events_json":"https://pith.science/api/pith-number/S7BWWAQFHC5QJETJPI7B2UE3JB/events.json","paper":"https://pith.science/paper/S7BWWAQF"},"agent_actions":{"view_html":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB","download_json":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB.json","view_paper":"https://pith.science/paper/S7BWWAQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01727&json=true","fetch_graph":"https://pith.science/api/pith-number/S7BWWAQFHC5QJETJPI7B2UE3JB/graph.json","fetch_events":"https://pith.science/api/pith-number/S7BWWAQFHC5QJETJPI7B2UE3JB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB/action/storage_attestation","attest_author":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB/action/author_attestation","sign_citation":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB/action/citation_signature","submit_replication":"https://pith.science/pith/S7BWWAQFHC5QJETJPI7B2UE3JB/action/replication_record"}},"created_at":"2026-05-17T23:39:58.802808+00:00","updated_at":"2026-05-17T23:39:58.802808+00:00"}