{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CP6Q5NCTR4EKMMCOEWTDFHG7DU","short_pith_number":"pith:CP6Q5NCT","schema_version":"1.0","canonical_sha256":"13fd0eb4538f08a6304e25a6329cdf1d2eab5f007203f7ce3aaa4ca5613936eb","source":{"kind":"arxiv","id":"1310.8516","version":1},"attestation_state":"computed","paper":{"title":"Non-orientable surfaces in homology cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Daniel Ruberman, Ira M. Gessel, Saso Strle","submitted_at":"2013-10-31T14:21:49Z","abstract_excerpt":"We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \\times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsv\\'ath--Sazb\\'o $d$-invariants or Atiyah--Singer $\\rho$-invariants of $M$. One consequence is that the minimal genus of a smoothly embedded surface in $L(2p,q) \\times I$ is the same as the minimal genus of a surface in $L(2p,q)$. We also consider embeddings of non-orientable surfaces in closed $4$-manifolds."},"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":"1310.8516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-31T14:21:49Z","cross_cats_sorted":[],"title_canon_sha256":"a10295bd1b0c558a8286b72f1a6cce1045365caef431aa79984c072ed6d9890a","abstract_canon_sha256":"2074c7240937e123c2efc22ac0be4f6dab2c93cbdf8c702d319af72f96603e55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.011220Z","signature_b64":"pB6jy6SHH6SWx8ZqrJyD5qv2T2Kr1G0+LMBcmrsgx2qAkJMfegXqG1AxSfymuJ7g1VVpH3T540YiEAxQFAnKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13fd0eb4538f08a6304e25a6329cdf1d2eab5f007203f7ce3aaa4ca5613936eb","last_reissued_at":"2026-05-18T02:03:38.010712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.010712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-orientable surfaces in homology cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Daniel Ruberman, Ira M. Gessel, Saso Strle","submitted_at":"2013-10-31T14:21:49Z","abstract_excerpt":"We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \\times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsv\\'ath--Sazb\\'o $d$-invariants or Atiyah--Singer $\\rho$-invariants of $M$. One consequence is that the minimal genus of a smoothly embedded surface in $L(2p,q) \\times I$ is the same as the minimal genus of a surface in $L(2p,q)$. We also consider embeddings of non-orientable surfaces in closed $4$-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8516","kind":"arxiv","version":1},"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":"1310.8516","created_at":"2026-05-18T02:03:38.010792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8516v1","created_at":"2026-05-18T02:03:38.010792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8516","created_at":"2026-05-18T02:03:38.010792+00:00"},{"alias_kind":"pith_short_12","alias_value":"CP6Q5NCTR4EK","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CP6Q5NCTR4EKMMCO","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CP6Q5NCT","created_at":"2026-05-18T12:27:40.988391+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/CP6Q5NCTR4EKMMCOEWTDFHG7DU","json":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU.json","graph_json":"https://pith.science/api/pith-number/CP6Q5NCTR4EKMMCOEWTDFHG7DU/graph.json","events_json":"https://pith.science/api/pith-number/CP6Q5NCTR4EKMMCOEWTDFHG7DU/events.json","paper":"https://pith.science/paper/CP6Q5NCT"},"agent_actions":{"view_html":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU","download_json":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU.json","view_paper":"https://pith.science/paper/CP6Q5NCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8516&json=true","fetch_graph":"https://pith.science/api/pith-number/CP6Q5NCTR4EKMMCOEWTDFHG7DU/graph.json","fetch_events":"https://pith.science/api/pith-number/CP6Q5NCTR4EKMMCOEWTDFHG7DU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU/action/storage_attestation","attest_author":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU/action/author_attestation","sign_citation":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU/action/citation_signature","submit_replication":"https://pith.science/pith/CP6Q5NCTR4EKMMCOEWTDFHG7DU/action/replication_record"}},"created_at":"2026-05-18T02:03:38.010792+00:00","updated_at":"2026-05-18T02:03:38.010792+00:00"}