{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RTGASGZJRA3M3TVYK6PGYN2WZ4","short_pith_number":"pith:RTGASGZJ","schema_version":"1.0","canonical_sha256":"8ccc091b298836cdceb8579e6c3756cf3e87b183b461b0271d74cf9187e4560c","source":{"kind":"arxiv","id":"1907.01207","version":4},"attestation_state":"computed","paper":{"title":"Curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Christian Liedtke, Frank Gounelas, Xi Chen","submitted_at":"2019-07-02T07:33:26Z","abstract_excerpt":"We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation theory of curves on K3 surfaces. Regeneration, a process opposite to specialisation, which preserves the geometric genus and does not require the class of the curve to extend, and the marked point trick, which allows a controlled degeneration of rational curves to integral ones in c"},"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":"1907.01207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-02T07:33:26Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e9ad7e6cc28089036fcbe7760d7ebd40a930978f022caefa210e7f0fe018d820","abstract_canon_sha256":"a34b27dbcce51df87cc2351e5073f3d4c019b0c01672bac82286136ffa909386"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:12:29.270232Z","signature_b64":"Sh8XifRAHErfpkNa/fgqvJZax3VWVLWCWv85Tn31WbbiWB0W5D5Z1DPLcNxGoZDKCqSFeOsrD958FHR1g0LFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ccc091b298836cdceb8579e6c3756cf3e87b183b461b0271d74cf9187e4560c","last_reissued_at":"2026-07-05T06:12:29.269685Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:12:29.269685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Christian Liedtke, Frank Gounelas, Xi Chen","submitted_at":"2019-07-02T07:33:26Z","abstract_excerpt":"We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation theory of curves on K3 surfaces. Regeneration, a process opposite to specialisation, which preserves the geometric genus and does not require the class of the curve to extend, and the marked point trick, which allows a controlled degeneration of rational curves to integral ones in c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01207","kind":"arxiv","version":4},"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/1907.01207/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.01207","created_at":"2026-07-05T06:12:29.269767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01207v4","created_at":"2026-07-05T06:12:29.269767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01207","created_at":"2026-07-05T06:12:29.269767+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTGASGZJRA3M","created_at":"2026-07-05T06:12:29.269767+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTGASGZJRA3M3TVY","created_at":"2026-07-05T06:12:29.269767+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTGASGZJ","created_at":"2026-07-05T06:12:29.269767+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.01909","citing_title":"On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4","json":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4.json","graph_json":"https://pith.science/api/pith-number/RTGASGZJRA3M3TVYK6PGYN2WZ4/graph.json","events_json":"https://pith.science/api/pith-number/RTGASGZJRA3M3TVYK6PGYN2WZ4/events.json","paper":"https://pith.science/paper/RTGASGZJ"},"agent_actions":{"view_html":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4","download_json":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4.json","view_paper":"https://pith.science/paper/RTGASGZJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01207&json=true","fetch_graph":"https://pith.science/api/pith-number/RTGASGZJRA3M3TVYK6PGYN2WZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/RTGASGZJRA3M3TVYK6PGYN2WZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4/action/storage_attestation","attest_author":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4/action/author_attestation","sign_citation":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4/action/citation_signature","submit_replication":"https://pith.science/pith/RTGASGZJRA3M3TVYK6PGYN2WZ4/action/replication_record"}},"created_at":"2026-07-05T06:12:29.269767+00:00","updated_at":"2026-07-05T06:12:29.269767+00:00"}