{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HMKNF7IWINEJF7IROCINH5OKZL","short_pith_number":"pith:HMKNF7IW","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"},"canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","source":{"kind":"arxiv","id":"1904.06082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06082","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06082v1","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06082","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"HMKNF7IWINEJ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HMKNF7IWINEJF7IR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HMKNF7IW","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HMKNF7IWINEJF7IROCINH5OKZL","target":"record","payload":{"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"},"canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","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"},"source_kind":"arxiv","source_id":"1904.06082","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOkWQdaExto19LKOxhmbSbjpvecaHmI+kM5MTpKCvt5mHP4zgcGNEjhoxkzjNi3GpGggc6JhOgoZIv9+rhBIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:55:40.118670Z"},"content_sha256":"8f6df5a0813befcb1926039c55afb15fbfe8b4c7f911067f6281e8108f031d94","schema_version":"1.0","event_id":"sha256:8f6df5a0813befcb1926039c55afb15fbfe8b4c7f911067f6281e8108f031d94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HMKNF7IWINEJF7IROCINH5OKZL","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hen68PO+GhJCEU0toir2SIS38dMsJdQOj/TOxk7BD7d/uHTmWOMyQI8GW/z6ULFp3Iyvd55zTzc7dTZNoFHuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:55:40.119366Z"},"content_sha256":"b2386c67aa5d5c0184433b82a57f0201ae1f505aca6dc62f4f2ebf18def34e95","schema_version":"1.0","event_id":"sha256:b2386c67aa5d5c0184433b82a57f0201ae1f505aca6dc62f4f2ebf18def34e95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/bundle.json","state_url":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMKNF7IWINEJF7IROCINH5OKZL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T03:55:40Z","links":{"resolver":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL","bundle":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/bundle.json","state":"https://pith.science/pith/HMKNF7IWINEJF7IROCINH5OKZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMKNF7IWINEJF7IROCINH5OKZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HMKNF7IWINEJF7IROCINH5OKZL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"618400a0483c42765f96a611e1bcb440f97ee4d675382477288dc007312d1e59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-12T07:40:49Z","title_canon_sha256":"b10ca6919e86dd93e6a4f1e7fafab96b3edd0b6099766a35ed3b8fe8617319b0"},"schema_version":"1.0","source":{"id":"1904.06082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06082","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06082v1","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06082","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"HMKNF7IWINEJ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HMKNF7IWINEJF7IR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HMKNF7IW","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:b2386c67aa5d5c0184433b82a57f0201ae1f505aca6dc62f4f2ebf18def34e95","target":"graph","created_at":"2026-05-17T23:48:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Adrien Dubouloz (IMB), Charlie Petitjean","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-12T07:40:49Z","title":"Rational real algebraic models of compact differential surfaces with circle actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06082","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8f6df5a0813befcb1926039c55afb15fbfe8b4c7f911067f6281e8108f031d94","target":"record","created_at":"2026-05-17T23:48:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"618400a0483c42765f96a611e1bcb440f97ee4d675382477288dc007312d1e59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-12T07:40:49Z","title_canon_sha256":"b10ca6919e86dd93e6a4f1e7fafab96b3edd0b6099766a35ed3b8fe8617319b0"},"schema_version":"1.0","source":{"id":"1904.06082","kind":"arxiv","version":1}},"canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b14d2fd16434892fd117090d3f5cacadc353c45238d9b86ec1e3c59bfe40802","first_computed_at":"2026-05-17T23:48:44.236963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:44.236963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f2Cpvc/rTTMwtZb0KnM8PpNbYs4fDnIofuqmQpslTCB+lPKSn9mX9fH4gkJqr51edDIklexlNTqNyhpcuY4JDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:44.237671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f6df5a0813befcb1926039c55afb15fbfe8b4c7f911067f6281e8108f031d94","sha256:b2386c67aa5d5c0184433b82a57f0201ae1f505aca6dc62f4f2ebf18def34e95"],"state_sha256":"7317eec6b972c02c780594507c188714c43a661738c74bf4ddc55654a4d3f21c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gz5GL9ngO+MsKGPSrliaqqoHnV0R6IoCPx85E0j1KLruKJzK2uLZH1I4MDUsj6kHRVBvAggcitRsQhEiACD/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:55:40.122156Z","bundle_sha256":"a3ebb0bf64264a8ae5ff309785045a70064b6f328dba68655c151b2820253af7"}}