{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:K4SBBSUTOFZFTZ37F74GDX3ZMW","short_pith_number":"pith:K4SBBSUT","canonical_record":{"source":{"id":"0704.3163","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-04-24T11:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"ca435d60c7a7385aeeb306c4b5338f2cf11cde4025d5c685f49e6fe41620b652","abstract_canon_sha256":"ea41c6c34867a6c4a8aff2b6cee5ff0e7727e7d3a2f35217cfded0666ff62e16"},"schema_version":"1.0"},"canonical_sha256":"572410ca93717259e77f2ff861df7965b7ea59bace164e4eff30737d30d9748b","source":{"kind":"arxiv","id":"0704.3163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3163","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3163v1","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3163","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"K4SBBSUTOFZF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K4SBBSUTOFZFTZ37","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K4SBBSUT","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:K4SBBSUTOFZFTZ37F74GDX3ZMW","target":"record","payload":{"canonical_record":{"source":{"id":"0704.3163","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-04-24T11:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"ca435d60c7a7385aeeb306c4b5338f2cf11cde4025d5c685f49e6fe41620b652","abstract_canon_sha256":"ea41c6c34867a6c4a8aff2b6cee5ff0e7727e7d3a2f35217cfded0666ff62e16"},"schema_version":"1.0"},"canonical_sha256":"572410ca93717259e77f2ff861df7965b7ea59bace164e4eff30737d30d9748b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:46.604513Z","signature_b64":"Kk0JvBlTn0ProlT/U4Nd+E7MbQ63GrxveDhcw3LxmCeUBGgBeM4jb4uK0WgWqXVVtewMvB6KZ1PpZWLMLUBWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"572410ca93717259e77f2ff861df7965b7ea59bace164e4eff30737d30d9748b","last_reissued_at":"2026-05-18T04:40:46.603979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:46.603979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.3163","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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ax8FIBv84b/wMIpbsxhp60aTZ1pxSP7rR1vaULWjSmnkSkc3QrXZZjHXuE9IVH8r58uyikabq5gPTjYbRByAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:23.024972Z"},"content_sha256":"7fea37159a286e9824a08201499c21e4174c54b2082aae0cd1b3c371f5dd3b95","schema_version":"1.0","event_id":"sha256:7fea37159a286e9824a08201499c21e4174c54b2082aae0cd1b3c371f5dd3b95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:K4SBBSUTOFZFTZ37F74GDX3ZMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Severi varieties and self rational maps of K3 surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Dedieu","submitted_at":"2007-04-24T11:15:22Z","abstract_excerpt":"Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and degree lying on some K3 surface. We also establish a number of numerical constraints satisfied by such non trivial rational maps, that is of topological degree >1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3163","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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mx/ZrSSKgjrawZNp/rHY1Ygplw01IOa2AaSgrODR6G2WgFOmzI6L+UCN1vxu6YVNXZ8Fyp2fH7zmQhqt3HEaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:23.025700Z"},"content_sha256":"834eae821c20441aac7326dd8cabca3a8769fbd20f5a1947607646e2964aa617","schema_version":"1.0","event_id":"sha256:834eae821c20441aac7326dd8cabca3a8769fbd20f5a1947607646e2964aa617"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/bundle.json","state_url":"https://pith.science/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/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":"2026-06-07T17:20:23Z","links":{"resolver":"https://pith.science/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW","bundle":"https://pith.science/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/bundle.json","state":"https://pith.science/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K4SBBSUTOFZFTZ37F74GDX3ZMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:K4SBBSUTOFZFTZ37F74GDX3ZMW","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":"ea41c6c34867a6c4a8aff2b6cee5ff0e7727e7d3a2f35217cfded0666ff62e16","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-04-24T11:15:22Z","title_canon_sha256":"ca435d60c7a7385aeeb306c4b5338f2cf11cde4025d5c685f49e6fe41620b652"},"schema_version":"1.0","source":{"id":"0704.3163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3163","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3163v1","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3163","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"K4SBBSUTOFZF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K4SBBSUTOFZFTZ37","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K4SBBSUT","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:834eae821c20441aac7326dd8cabca3a8769fbd20f5a1947607646e2964aa617","target":"graph","created_at":"2026-05-18T04:40:46Z","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":"Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and degree lying on some K3 surface. We also establish a number of numerical constraints satisfied by such non trivial rational maps, that is of topological degree >1.","authors_text":"Thomas Dedieu","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-04-24T11:15:22Z","title":"Severi varieties and self rational maps of K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3163","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":"sha256:7fea37159a286e9824a08201499c21e4174c54b2082aae0cd1b3c371f5dd3b95","target":"record","created_at":"2026-05-18T04:40:46Z","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":"ea41c6c34867a6c4a8aff2b6cee5ff0e7727e7d3a2f35217cfded0666ff62e16","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-04-24T11:15:22Z","title_canon_sha256":"ca435d60c7a7385aeeb306c4b5338f2cf11cde4025d5c685f49e6fe41620b652"},"schema_version":"1.0","source":{"id":"0704.3163","kind":"arxiv","version":1}},"canonical_sha256":"572410ca93717259e77f2ff861df7965b7ea59bace164e4eff30737d30d9748b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"572410ca93717259e77f2ff861df7965b7ea59bace164e4eff30737d30d9748b","first_computed_at":"2026-05-18T04:40:46.603979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.603979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kk0JvBlTn0ProlT/U4Nd+E7MbQ63GrxveDhcw3LxmCeUBGgBeM4jb4uK0WgWqXVVtewMvB6KZ1PpZWLMLUBWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.604513Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fea37159a286e9824a08201499c21e4174c54b2082aae0cd1b3c371f5dd3b95","sha256:834eae821c20441aac7326dd8cabca3a8769fbd20f5a1947607646e2964aa617"],"state_sha256":"e26460d00d1c8eda7e6f1f7ce85bdf6c7bced2ac16c1e9bd2d8454426d394001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wE44KLfP6h8jCx23U4T/c6UnW+2FE38T0b7kJo3YGdibOICkoago/gKwgTUJsyDRSzADXr8paVEkmlmCGY+lCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:20:23.029340Z","bundle_sha256":"d1ff6b3a9f6e0a065836c91b9de96714a2066f3798379b3f6cc6fd300d302900"}}