{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QN2OQHPTUWNGBQRN57ETN6Q4FZ","short_pith_number":"pith:QN2OQHPT","canonical_record":{"source":{"id":"1212.3511","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b","abstract_canon_sha256":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295"},"schema_version":"1.0"},"canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","source":{"kind":"arxiv","id":"1212.3511","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3511v5","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"pith_short_12","alias_value":"QN2OQHPTUWNG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QN2OQHPTUWNGBQRN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QN2OQHPT","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QN2OQHPTUWNGBQRN57ETN6Q4FZ","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3511","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b","abstract_canon_sha256":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295"},"schema_version":"1.0"},"canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:35.042129Z","signature_b64":"7KkHzrb+GDnsxP9JQOQT6HfSYxuRutEPHH8DflcjgCN8Wz23wwS3Bdrd8NYCAv5m6Ei/iMFCefG0zPxlUygyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","last_reissued_at":"2026-05-18T00:59:35.041443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:35.041443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3511","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sooCMox5BVFdXJEKt487OjrnSt/fZ0xfAne7VLKY9KtH9losW9fIruKejrAfdsy7isJOPuZp5//jFBMQLbbEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:33:46.445240Z"},"content_sha256":"57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d","schema_version":"1.0","event_id":"sha256:57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QN2OQHPTUWNGBQRN57ETN6Q4FZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"64 lines on smooth quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Matthias Schuett, Slawomir Rams","submitted_at":"2012-12-14T16:20:31Z","abstract_excerpt":"Let k be a field of characteristic other than 2,3. We prove that there are no geometrically smooth quartic surfaces in IP^3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on a smooth quartic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3511","kind":"arxiv","version":5},"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":"2026-05-18T00:59:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSBVLPxjlc5WKOw8OVYhR1zNvzSTztUFI7EKXQr6OvHmNLwaNWN8uBTjNE24hS8LYqbYwoxPyr5+gDgIVgbwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:33:46.445598Z"},"content_sha256":"e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb","schema_version":"1.0","event_id":"sha256:e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/bundle.json","state_url":"https://pith.science/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/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":"2026-06-02T11:33:46Z","links":{"resolver":"https://pith.science/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ","bundle":"https://pith.science/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/bundle.json","state":"https://pith.science/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QN2OQHPTUWNGBQRN57ETN6Q4FZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QN2OQHPTUWNGBQRN57ETN6Q4FZ","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":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b"},"schema_version":"1.0","source":{"id":"1212.3511","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3511v5","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"pith_short_12","alias_value":"QN2OQHPTUWNG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QN2OQHPTUWNGBQRN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QN2OQHPT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb","target":"graph","created_at":"2026-05-18T00:59:35Z","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":"Let k be a field of characteristic other than 2,3. We prove that there are no geometrically smooth quartic surfaces in IP^3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on a smooth quartic.","authors_text":"Matthias Schuett, Slawomir Rams","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title":"64 lines on smooth quartic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3511","kind":"arxiv","version":5},"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":"sha256:57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d","target":"record","created_at":"2026-05-18T00:59:35Z","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":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b"},"schema_version":"1.0","source":{"id":"1212.3511","kind":"arxiv","version":5}},"canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","first_computed_at":"2026-05-18T00:59:35.041443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:35.041443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KkHzrb+GDnsxP9JQOQT6HfSYxuRutEPHH8DflcjgCN8Wz23wwS3Bdrd8NYCAv5m6Ei/iMFCefG0zPxlUygyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:35.042129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3511","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d","sha256:e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb"],"state_sha256":"02b9bfee195748358299a42c1782a37f8e5656abad3b562ef8e597ca52bc53e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHza3+aMN0fnwG1Hy4G9WRGLGuJY10V05MxkWs9ioLlcahzcVO+O5GRqm8vZOQkSAS2L/mc5Pe06o1YtHjGmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:33:46.447504Z","bundle_sha256":"d941591c3802eba54b9f23ddb3511d4e841cfd1dd8b712a35011af238574c67e"}}