{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:W65RHE5X7CIT2ZP4AEWTZ6YCUA","short_pith_number":"pith:W65RHE5X","schema_version":"1.0","canonical_sha256":"b7bb1393b7f8913d65fc012d3cfb02a009f3b3926bf06fcc6f802476f6f08acc","source":{"kind":"arxiv","id":"1312.0848","version":3},"attestation_state":"computed","paper":{"title":"$G$-minimality and invariant negative spheres in $G$-Hirzebruch surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weimin Chen","submitted_at":"2013-12-03T15:19:41Z","abstract_excerpt":"In this paper a study of $G$-minimality, i.e., minimality of four-manifolds equipped with an action of a finite group $G$, is initiated. We focus on cyclic actions on $CP^2\\# \\overline{CP^2}$, and our work shows that even in this simple setting, the comparison of $G$-minimality in the various categories, i.e., locally linear, smooth, and symplectic, is already delicate and interesting. For example, we show that if a symplectic $Z_n$-action on $CP^2\\# \\overline{CP^2}$ has an invariant locally linear topological $(-1)$-sphere, then it must admit an invariant symplectic $(-1)$-sphere, provided th"},"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":"1312.0848","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T15:19:41Z","cross_cats_sorted":[],"title_canon_sha256":"7291da07527764c0270f8b1a7e98ca62ff6008a61753272a8d50238f70da8bb8","abstract_canon_sha256":"ff57fc6b7e1da91da3184f2d7208b05f4cf453bc47a8799cc8957bd92128e5fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:09.628996Z","signature_b64":"EgTGhjXgtbkP5S5NSlXuzr7NX7mQp40JG4rocEQRSxvZvIPBm/n+D6rOh07oGEj9fZp4xU4oLrghbFAUxyY5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7bb1393b7f8913d65fc012d3cfb02a009f3b3926bf06fcc6f802476f6f08acc","last_reissued_at":"2026-05-18T01:53:09.628515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:09.628515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$G$-minimality and invariant negative spheres in $G$-Hirzebruch surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weimin Chen","submitted_at":"2013-12-03T15:19:41Z","abstract_excerpt":"In this paper a study of $G$-minimality, i.e., minimality of four-manifolds equipped with an action of a finite group $G$, is initiated. We focus on cyclic actions on $CP^2\\# \\overline{CP^2}$, and our work shows that even in this simple setting, the comparison of $G$-minimality in the various categories, i.e., locally linear, smooth, and symplectic, is already delicate and interesting. For example, we show that if a symplectic $Z_n$-action on $CP^2\\# \\overline{CP^2}$ has an invariant locally linear topological $(-1)$-sphere, then it must admit an invariant symplectic $(-1)$-sphere, provided th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0848","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":"1312.0848","created_at":"2026-05-18T01:53:09.628589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0848v3","created_at":"2026-05-18T01:53:09.628589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0848","created_at":"2026-05-18T01:53:09.628589+00:00"},{"alias_kind":"pith_short_12","alias_value":"W65RHE5X7CIT","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"W65RHE5X7CIT2ZP4","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"W65RHE5X","created_at":"2026-05-18T12:28:04.890932+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/W65RHE5X7CIT2ZP4AEWTZ6YCUA","json":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA.json","graph_json":"https://pith.science/api/pith-number/W65RHE5X7CIT2ZP4AEWTZ6YCUA/graph.json","events_json":"https://pith.science/api/pith-number/W65RHE5X7CIT2ZP4AEWTZ6YCUA/events.json","paper":"https://pith.science/paper/W65RHE5X"},"agent_actions":{"view_html":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA","download_json":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA.json","view_paper":"https://pith.science/paper/W65RHE5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0848&json=true","fetch_graph":"https://pith.science/api/pith-number/W65RHE5X7CIT2ZP4AEWTZ6YCUA/graph.json","fetch_events":"https://pith.science/api/pith-number/W65RHE5X7CIT2ZP4AEWTZ6YCUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA/action/storage_attestation","attest_author":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA/action/author_attestation","sign_citation":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA/action/citation_signature","submit_replication":"https://pith.science/pith/W65RHE5X7CIT2ZP4AEWTZ6YCUA/action/replication_record"}},"created_at":"2026-05-18T01:53:09.628589+00:00","updated_at":"2026-05-18T01:53:09.628589+00:00"}