{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HTUY6T4QVNRGB2BDFIZC2AFRZC","short_pith_number":"pith:HTUY6T4Q","schema_version":"1.0","canonical_sha256":"3ce98f4f90ab6260e8232a322d00b1c88824eeda21f8a0dc633a6d50b7996851","source":{"kind":"arxiv","id":"1601.04238","version":1},"attestation_state":"computed","paper":{"title":"Lines on quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Degtyarev, Al\\.i S\\.inan Sert\\\"oz, Ilia Itenberg","submitted_at":"2016-01-17T02:14:56Z","abstract_excerpt":"We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic."},"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":"1601.04238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-17T02:14:56Z","cross_cats_sorted":[],"title_canon_sha256":"21f750b0aae22daf12195a27eb6d94fa019906c07f9ad374d0f8133dd7679b7e","abstract_canon_sha256":"28d8a6332ea4f4a25b7749f601a7c658cd0e38204aa9214ca478fe10feee3574"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.323346Z","signature_b64":"fH13/uW6BI1Kmig5wX5OJ/eMurRhsotmzPFL11N4oR0sKDfMbzIcPSRKM8zKS+ktunRIOXsAfg91fMwigUh9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ce98f4f90ab6260e8232a322d00b1c88824eeda21f8a0dc633a6d50b7996851","last_reissued_at":"2026-05-18T00:42:13.322804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.322804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lines on quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Degtyarev, Al\\.i S\\.inan Sert\\\"oz, Ilia Itenberg","submitted_at":"2016-01-17T02:14:56Z","abstract_excerpt":"We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04238","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":"1601.04238","created_at":"2026-05-18T00:42:13.322889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.04238v1","created_at":"2026-05-18T00:42:13.322889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04238","created_at":"2026-05-18T00:42:13.322889+00:00"},{"alias_kind":"pith_short_12","alias_value":"HTUY6T4QVNRG","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"HTUY6T4QVNRGB2BD","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"HTUY6T4Q","created_at":"2026-05-18T12:30:22.444734+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/HTUY6T4QVNRGB2BDFIZC2AFRZC","json":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC.json","graph_json":"https://pith.science/api/pith-number/HTUY6T4QVNRGB2BDFIZC2AFRZC/graph.json","events_json":"https://pith.science/api/pith-number/HTUY6T4QVNRGB2BDFIZC2AFRZC/events.json","paper":"https://pith.science/paper/HTUY6T4Q"},"agent_actions":{"view_html":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC","download_json":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC.json","view_paper":"https://pith.science/paper/HTUY6T4Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.04238&json=true","fetch_graph":"https://pith.science/api/pith-number/HTUY6T4QVNRGB2BDFIZC2AFRZC/graph.json","fetch_events":"https://pith.science/api/pith-number/HTUY6T4QVNRGB2BDFIZC2AFRZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC/action/storage_attestation","attest_author":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC/action/author_attestation","sign_citation":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC/action/citation_signature","submit_replication":"https://pith.science/pith/HTUY6T4QVNRGB2BDFIZC2AFRZC/action/replication_record"}},"created_at":"2026-05-18T00:42:13.322889+00:00","updated_at":"2026-05-18T00:42:13.322889+00:00"}