{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:PAXWDZQRAAP7VYBVVPTPXLSCDC","short_pith_number":"pith:PAXWDZQR","schema_version":"1.0","canonical_sha256":"782f61e611001ffae035abe6fbae42189b470ffc90cdac535529f7d957f134f1","source":{"kind":"arxiv","id":"2312.10546","version":2},"attestation_state":"computed","paper":{"title":"Locally flat simple spheres in $\\mathbb{C} P^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anthony Conway, Patrick Orson","submitted_at":"2023-12-16T22:08:15Z","abstract_excerpt":"The fundamental group of the complement of a locally flat surface in a $4$-manifold is called the knot group of the surface. In this article we prove that two locally flat $2$-spheres in $\\mathbb{C} P^2$ with knot group $\\mathbb{Z}_2$ are ambiently isotopic if they are homologous. This combines with work of Tristram and Lee-Wilczy\\'{n}ski, as well as the classification of $\\mathbb{Z}$-surfaces, to complete a proof of the statement: a class $d \\in H_2(\\mathbb{C} P^2) \\cong \\mathbb{Z}$ is represented by a locally flat $2$-sphere with abelian knot group if and only if $|d| \\in \\lbrace 0,1,2\\rbrac"},"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":"2312.10546","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-12-16T22:08:15Z","cross_cats_sorted":[],"title_canon_sha256":"bf2573d82cec2f2e76c5d478ad7d772d669b932e0f6db603e3fa8c775a6830f8","abstract_canon_sha256":"3cbdb7f8a8941008e40ec80639bd49894ac92dd95ef429f7bcaad1ae95562f07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:21:25.328847Z","signature_b64":"tyfm44Ks1Kf9iXwHNY/viJmKU1/sL4pU3ykuPg7RQ7V2XU8kKqv4fRJfT0sB01e1ubacL9gJu0SjzCEx86llDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"782f61e611001ffae035abe6fbae42189b470ffc90cdac535529f7d957f134f1","last_reissued_at":"2026-07-05T09:21:25.328344Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:21:25.328344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally flat simple spheres in $\\mathbb{C} P^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anthony Conway, Patrick Orson","submitted_at":"2023-12-16T22:08:15Z","abstract_excerpt":"The fundamental group of the complement of a locally flat surface in a $4$-manifold is called the knot group of the surface. In this article we prove that two locally flat $2$-spheres in $\\mathbb{C} P^2$ with knot group $\\mathbb{Z}_2$ are ambiently isotopic if they are homologous. This combines with work of Tristram and Lee-Wilczy\\'{n}ski, as well as the classification of $\\mathbb{Z}$-surfaces, to complete a proof of the statement: a class $d \\in H_2(\\mathbb{C} P^2) \\cong \\mathbb{Z}$ is represented by a locally flat $2$-sphere with abelian knot group if and only if $|d| \\in \\lbrace 0,1,2\\rbrac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.10546","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.10546/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2312.10546","created_at":"2026-07-05T09:21:25.328402+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.10546v2","created_at":"2026-07-05T09:21:25.328402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.10546","created_at":"2026-07-05T09:21:25.328402+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAXWDZQRAAP7","created_at":"2026-07-05T09:21:25.328402+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAXWDZQRAAP7VYBV","created_at":"2026-07-05T09:21:25.328402+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAXWDZQR","created_at":"2026-07-05T09:21:25.328402+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.20030","citing_title":"FAEDKV: Infinite-Window Fourier Transform for Unbiased KV Cache Compression","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC","json":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC.json","graph_json":"https://pith.science/api/pith-number/PAXWDZQRAAP7VYBVVPTPXLSCDC/graph.json","events_json":"https://pith.science/api/pith-number/PAXWDZQRAAP7VYBVVPTPXLSCDC/events.json","paper":"https://pith.science/paper/PAXWDZQR"},"agent_actions":{"view_html":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC","download_json":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC.json","view_paper":"https://pith.science/paper/PAXWDZQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.10546&json=true","fetch_graph":"https://pith.science/api/pith-number/PAXWDZQRAAP7VYBVVPTPXLSCDC/graph.json","fetch_events":"https://pith.science/api/pith-number/PAXWDZQRAAP7VYBVVPTPXLSCDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC/action/storage_attestation","attest_author":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC/action/author_attestation","sign_citation":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC/action/citation_signature","submit_replication":"https://pith.science/pith/PAXWDZQRAAP7VYBVVPTPXLSCDC/action/replication_record"}},"created_at":"2026-07-05T09:21:25.328402+00:00","updated_at":"2026-07-05T09:21:25.328402+00:00"}