{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NPLN5ADPP2LEMGTVT3522WOSKO","short_pith_number":"pith:NPLN5ADP","canonical_record":{"source":{"id":"2309.12192","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-21T15:58:53Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"61bee34529365251a0c3d898a11e8efa924f0b0b13a5eff7d33e15eaa8e0d455","abstract_canon_sha256":"fdb1e76f2857c15a55821eaacfa209860a358ba46287cf21180e52ac442e2ad0"},"schema_version":"1.0"},"canonical_sha256":"6bd6de806f7e96461a759efbad59d2538773460c6ff4d0be3a6a33faeb53d8cc","source":{"kind":"arxiv","id":"2309.12192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12192","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12192v2","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12192","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"NPLN5ADPP2LE","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"NPLN5ADPP2LEMGTV","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"NPLN5ADP","created_at":"2026-06-19T16:11:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NPLN5ADPP2LEMGTVT3522WOSKO","target":"record","payload":{"canonical_record":{"source":{"id":"2309.12192","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-21T15:58:53Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"61bee34529365251a0c3d898a11e8efa924f0b0b13a5eff7d33e15eaa8e0d455","abstract_canon_sha256":"fdb1e76f2857c15a55821eaacfa209860a358ba46287cf21180e52ac442e2ad0"},"schema_version":"1.0"},"canonical_sha256":"6bd6de806f7e96461a759efbad59d2538773460c6ff4d0be3a6a33faeb53d8cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:07.759018Z","signature_b64":"sLNibKPTs4QmrEKd+EqXvSBlPbPp3CQ67PQnh1Wx+CRnMEeVJxTdDJa2KNLmI7tLDBz/CIOV5vAM4ojtU8VyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bd6de806f7e96461a759efbad59d2538773460c6ff4d0be3a6a33faeb53d8cc","last_reissued_at":"2026-06-19T16:11:07.758601Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:07.758601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.12192","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5xuIu7aEhcLz9qw9nOClfTxKeCIE/LBmCFoIO2qeO4rSRWAzt7+7f4Etrj4hPqFgzfkeorR9drD2gtqLeACoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:45:50.541693Z"},"content_sha256":"43d0152aad5ffcba41a9311a4bea7f275b8c72ac06879006753063fa62bb6d3f","schema_version":"1.0","event_id":"sha256:43d0152aad5ffcba41a9311a4bea7f275b8c72ac06879006753063fa62bb6d3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NPLN5ADPP2LEMGTVT3522WOSKO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real versus complex plane curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Giulio Bresciani","submitted_at":"2023-09-21T15:58:53Z","abstract_excerpt":"We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree.\n  More generally, we prove that a plane curve $C$ over an algebraically closed field $K$ of characteristic $0$ with field of moduli $k_{C}\\subset K$ is defined by a polynomial with coefficients in $k'$, where $k'/k_{C}$ is an extension with $[k':k_{C}]\\le 3$ and $[k':k_{C}]\\mid \\operatorname{deg} C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12192","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/2309.12192/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"siU7kZU1ALVk7W/ntv2/3Wgx5hvDT0iVpXabE/iR7QsclJ37Jcx4Fcvo4zQr1IfTQ+go5T9wWQFjhkZ8yZQOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:45:50.542180Z"},"content_sha256":"3bc2d2865b5e0815489b4f9f9b5e2cba14ddaeebb84b7ab9158feee4426e035f","schema_version":"1.0","event_id":"sha256:3bc2d2865b5e0815489b4f9f9b5e2cba14ddaeebb84b7ab9158feee4426e035f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPLN5ADPP2LEMGTVT3522WOSKO/bundle.json","state_url":"https://pith.science/pith/NPLN5ADPP2LEMGTVT3522WOSKO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPLN5ADPP2LEMGTVT3522WOSKO/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":"2026-08-04T14:45:50Z","links":{"resolver":"https://pith.science/pith/NPLN5ADPP2LEMGTVT3522WOSKO","bundle":"https://pith.science/pith/NPLN5ADPP2LEMGTVT3522WOSKO/bundle.json","state":"https://pith.science/pith/NPLN5ADPP2LEMGTVT3522WOSKO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPLN5ADPP2LEMGTVT3522WOSKO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NPLN5ADPP2LEMGTVT3522WOSKO","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":"fdb1e76f2857c15a55821eaacfa209860a358ba46287cf21180e52ac442e2ad0","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-21T15:58:53Z","title_canon_sha256":"61bee34529365251a0c3d898a11e8efa924f0b0b13a5eff7d33e15eaa8e0d455"},"schema_version":"1.0","source":{"id":"2309.12192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12192","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12192v2","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12192","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"NPLN5ADPP2LE","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"NPLN5ADPP2LEMGTV","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"NPLN5ADP","created_at":"2026-06-19T16:11:07Z"}],"graph_snapshots":[{"event_id":"sha256:3bc2d2865b5e0815489b4f9f9b5e2cba14ddaeebb84b7ab9158feee4426e035f","target":"graph","created_at":"2026-06-19T16:11:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.12192/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree.\n  More generally, we prove that a plane curve $C$ over an algebraically closed field $K$ of characteristic $0$ with field of moduli $k_{C}\\subset K$ is defined by a polynomial with coefficients in $k'$, where $k'/k_{C}$ is an extension with $[k':k_{C}]\\le 3$ and $[k':k_{C}]\\mid \\operatorname{deg} C$.","authors_text":"Giulio Bresciani","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-21T15:58:53Z","title":"Real versus complex plane curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12192","kind":"arxiv","version":2},"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":"sha256:43d0152aad5ffcba41a9311a4bea7f275b8c72ac06879006753063fa62bb6d3f","target":"record","created_at":"2026-06-19T16:11:07Z","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":"fdb1e76f2857c15a55821eaacfa209860a358ba46287cf21180e52ac442e2ad0","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-21T15:58:53Z","title_canon_sha256":"61bee34529365251a0c3d898a11e8efa924f0b0b13a5eff7d33e15eaa8e0d455"},"schema_version":"1.0","source":{"id":"2309.12192","kind":"arxiv","version":2}},"canonical_sha256":"6bd6de806f7e96461a759efbad59d2538773460c6ff4d0be3a6a33faeb53d8cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bd6de806f7e96461a759efbad59d2538773460c6ff4d0be3a6a33faeb53d8cc","first_computed_at":"2026-06-19T16:11:07.758601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:07.758601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sLNibKPTs4QmrEKd+EqXvSBlPbPp3CQ67PQnh1Wx+CRnMEeVJxTdDJa2KNLmI7tLDBz/CIOV5vAM4ojtU8VyBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:07.759018Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.12192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43d0152aad5ffcba41a9311a4bea7f275b8c72ac06879006753063fa62bb6d3f","sha256:3bc2d2865b5e0815489b4f9f9b5e2cba14ddaeebb84b7ab9158feee4426e035f"],"state_sha256":"73691dba67854a8013754ffb7155c5c828b3aea83a9040cd04c3cbfacd1ce3ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LAl5UAu801ADGbZHNbiPaQQqUILs/UvwwHsrMLDulg/ewvU7SpbGzVmmlFFM/1xxiYu37OFyG/eFP+3c/i++Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T14:45:50.545720Z","bundle_sha256":"058c46345512702971ba176518a91f39582a84680c0b004035c90a8ec7e0083d"}}