{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:EKKEI6R7GVHDR5IN64HQU7AP4D","short_pith_number":"pith:EKKEI6R7","canonical_record":{"source":{"id":"math/0103186","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-03-27T18:56:43Z","cross_cats_sorted":[],"title_canon_sha256":"ed69b25bedcf7b63359490923005d1305e3d42a687cdb77d3f3d0c1bffa404bc","abstract_canon_sha256":"9b35dc9b38fda9c41cb9a1ef0fd50a5830a93c780ac606ffc2f3af59e751e9d9"},"schema_version":"1.0"},"canonical_sha256":"2294447a3f354e38f50df70f0a7c0fe0f3a6be82f9fed8a44556ae3ab80330cb","source":{"kind":"arxiv","id":"math/0103186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103186","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103186v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103186","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"EKKEI6R7GVHD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"EKKEI6R7GVHDR5IN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"EKKEI6R7","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:EKKEI6R7GVHDR5IN64HQU7AP4D","target":"record","payload":{"canonical_record":{"source":{"id":"math/0103186","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-03-27T18:56:43Z","cross_cats_sorted":[],"title_canon_sha256":"ed69b25bedcf7b63359490923005d1305e3d42a687cdb77d3f3d0c1bffa404bc","abstract_canon_sha256":"9b35dc9b38fda9c41cb9a1ef0fd50a5830a93c780ac606ffc2f3af59e751e9d9"},"schema_version":"1.0"},"canonical_sha256":"2294447a3f354e38f50df70f0a7c0fe0f3a6be82f9fed8a44556ae3ab80330cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.869326Z","signature_b64":"e+uXzZPtkm3rKVl1kXZdyf/FB/bMJPW8q1FWdbzf0B3zTZVPo2kP5GxfqwwtPbVRk0B4RPp5IacuEbdsoogbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2294447a3f354e38f50df70f0a7c0fe0f3a6be82f9fed8a44556ae3ab80330cb","last_reissued_at":"2026-05-18T01:05:37.868829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.868829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0103186","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SMW5NR1hP+LeM8iWEAjF69Oqz0LHuWsA9aEsePj9XCzO13o0pVPzJBxKsYIuGwb8Db8I8e3M/bDXuzTP54ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:41:05.889988Z"},"content_sha256":"620165b678f08c3e60e0f18e3f7e5d341e3f873cf5326a2e19b515bec78132b0","schema_version":"1.0","event_id":"sha256:620165b678f08c3e60e0f18e3f7e5d341e3f873cf5326a2e19b515bec78132b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:EKKEI6R7GVHDR5IN64HQU7AP4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Birational automorphisms of quartic Hessian surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor V. Dolgachev (Univ. of Michigan), Jonghae Keum (KIAS)","submitted_at":"2001-03-27T18:56:43Z","abstract_excerpt":"We find generators of the group of birational automorphisms of the\n Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16. The latter embeds naturally in the even unimodular lattice $II^{1,25}$ of rank 26 and signature $(1,25)$ as the orthogonal complement of a root sublattice of rank 10. Our generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of S. Kond$\\bar {\\roman o}$. We shall explain how our generators are relate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103186","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIEQFmFuA9fEJPNcOmu8srF0NYUpysY218Vv5V4pTbv0XRPZkUxkGnq+N4r498T9XFF7wAXhDYqXkRBIuhj/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:41:05.890782Z"},"content_sha256":"efb5a5bd53a043b732e3ea90b3bf91eca4bb2af6bb07fcf347717afe409a1128","schema_version":"1.0","event_id":"sha256:efb5a5bd53a043b732e3ea90b3bf91eca4bb2af6bb07fcf347717afe409a1128"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/bundle.json","state_url":"https://pith.science/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/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":"2026-08-13T05:41:05Z","links":{"resolver":"https://pith.science/pith/EKKEI6R7GVHDR5IN64HQU7AP4D","bundle":"https://pith.science/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/bundle.json","state":"https://pith.science/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKKEI6R7GVHDR5IN64HQU7AP4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:EKKEI6R7GVHDR5IN64HQU7AP4D","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":"9b35dc9b38fda9c41cb9a1ef0fd50a5830a93c780ac606ffc2f3af59e751e9d9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-27T18:56:43Z","title_canon_sha256":"ed69b25bedcf7b63359490923005d1305e3d42a687cdb77d3f3d0c1bffa404bc"},"schema_version":"1.0","source":{"id":"math/0103186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103186","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103186v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103186","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"EKKEI6R7GVHD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"EKKEI6R7GVHDR5IN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"EKKEI6R7","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:efb5a5bd53a043b732e3ea90b3bf91eca4bb2af6bb07fcf347717afe409a1128","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"We find generators of the group of birational automorphisms of the\n Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16. The latter embeds naturally in the even unimodular lattice $II^{1,25}$ of rank 26 and signature $(1,25)$ as the orthogonal complement of a root sublattice of rank 10. Our generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of S. Kond$\\bar {\\roman o}$. We shall explain how our generators are relate","authors_text":"Igor V. Dolgachev (Univ. of Michigan), Jonghae Keum (KIAS)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-03-27T18:56:43Z","title":"Birational automorphisms of quartic Hessian surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103186","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":"sha256:620165b678f08c3e60e0f18e3f7e5d341e3f873cf5326a2e19b515bec78132b0","target":"record","created_at":"2026-05-18T01:05:37Z","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":"9b35dc9b38fda9c41cb9a1ef0fd50a5830a93c780ac606ffc2f3af59e751e9d9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-27T18:56:43Z","title_canon_sha256":"ed69b25bedcf7b63359490923005d1305e3d42a687cdb77d3f3d0c1bffa404bc"},"schema_version":"1.0","source":{"id":"math/0103186","kind":"arxiv","version":1}},"canonical_sha256":"2294447a3f354e38f50df70f0a7c0fe0f3a6be82f9fed8a44556ae3ab80330cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2294447a3f354e38f50df70f0a7c0fe0f3a6be82f9fed8a44556ae3ab80330cb","first_computed_at":"2026-05-18T01:05:37.868829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.868829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e+uXzZPtkm3rKVl1kXZdyf/FB/bMJPW8q1FWdbzf0B3zTZVPo2kP5GxfqwwtPbVRk0B4RPp5IacuEbdsoogbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.869326Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0103186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:620165b678f08c3e60e0f18e3f7e5d341e3f873cf5326a2e19b515bec78132b0","sha256:efb5a5bd53a043b732e3ea90b3bf91eca4bb2af6bb07fcf347717afe409a1128"],"state_sha256":"5db71e762965e1e0ea0feb5995653371b51958906e7f48fbd659485c8a8a28f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3vghPnGQ67iUg5Zikof8D2R1LQ7AqgCQ6p0k46s7joi2MiGuRG/3vBEdaC9gL5yHfEwrQ7u5i7/prWnZuAbBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:41:05.897043Z","bundle_sha256":"ad4d7955fee106fbe3d6596c3f4929afa038b6a589f62b14aa0ea1e6324a55bd"}}