{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HMKNF7IWINEJF7IROCINH5OKZL","short_pith_number":"pith:HMKNF7IW","schema_version":"1.0","canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","source":{"kind":"arxiv","id":"1904.06082","version":1},"attestation_state":"computed","paper":{"title":"Rational real algebraic models of compact differential surfaces with circle actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), Charlie Petitjean","submitted_at":"2019-04-12T07:40:49Z","abstract_excerpt":"We give an algebro-geometric classification of smooth real affine algebraic surfaces endowed with an effective action of the real algebraic circle group $\\mathbb{S}^1$ up to equivariant isomorphisms. As an application, we show that every compact differentiable surface endowed with an action of the circle $S^1$ admits a unique smooth rational real quasi-projective model up to $\\mathbb{S}^1$-equivariant birational diffeomorphism."},"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":"1904.06082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-12T07:40:49Z","cross_cats_sorted":[],"title_canon_sha256":"b10ca6919e86dd93e6a4f1e7fafab96b3edd0b6099766a35ed3b8fe8617319b0","abstract_canon_sha256":"618400a0483c42765f96a611e1bcb440f97ee4d675382477288dc007312d1e59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:44.237671Z","signature_b64":"f2Cpvc/rTTMwtZb0KnM8PpNbYs4fDnIofuqmQpslTCB+lPKSn9mX9fH4gkJqr51edDIklexlNTqNyhpcuY4JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","last_reissued_at":"2026-05-17T23:48:44.236963Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:44.236963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational real algebraic models of compact differential surfaces with circle actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), Charlie Petitjean","submitted_at":"2019-04-12T07:40:49Z","abstract_excerpt":"We give an algebro-geometric classification of smooth real affine algebraic surfaces endowed with an effective action of the real algebraic circle group $\\mathbb{S}^1$ up to equivariant isomorphisms. As an application, we show that every compact differentiable surface endowed with an action of the circle $S^1$ admits a unique smooth rational real quasi-projective model up to $\\mathbb{S}^1$-equivariant birational diffeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06082","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":"1904.06082","created_at":"2026-05-17T23:48:44.237069+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.06082v1","created_at":"2026-05-17T23:48:44.237069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06082","created_at":"2026-05-17T23:48:44.237069+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMKNF7IWINEJ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMKNF7IWINEJF7IR","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMKNF7IW","created_at":"2026-05-18T12:33:18.533446+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/HMKNF7IWINEJF7IROCINH5OKZL","json":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL.json","graph_json":"https://pith.science/api/pith-number/HMKNF7IWINEJF7IROCINH5OKZL/graph.json","events_json":"https://pith.science/api/pith-number/HMKNF7IWINEJF7IROCINH5OKZL/events.json","paper":"https://pith.science/paper/HMKNF7IW"},"agent_actions":{"view_html":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL","download_json":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL.json","view_paper":"https://pith.science/paper/HMKNF7IW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.06082&json=true","fetch_graph":"https://pith.science/api/pith-number/HMKNF7IWINEJF7IROCINH5OKZL/graph.json","fetch_events":"https://pith.science/api/pith-number/HMKNF7IWINEJF7IROCINH5OKZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/action/storage_attestation","attest_author":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/action/author_attestation","sign_citation":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/action/citation_signature","submit_replication":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/action/replication_record"}},"created_at":"2026-05-17T23:48:44.237069+00:00","updated_at":"2026-05-17T23:48:44.237069+00:00"}