{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CVCV6TB6R6ASU6TO7XDB4O4VZ5","short_pith_number":"pith:CVCV6TB6","schema_version":"1.0","canonical_sha256":"15455f4c3e8f812a7a6efdc61e3b95cf5b48158393c791057a207b8c1fe33afe","source":{"kind":"arxiv","id":"1809.07819","version":1},"attestation_state":"computed","paper":{"title":"The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Allcock, Igor Dolgachev","submitted_at":"2018-09-20T19:39:30Z","abstract_excerpt":"Consider a cubic surface satisfying the mild condition that it may be described in Sylvester's pentahedral form. There is a well-known Enriques or Coble surface S with K3 cover birationally isomorphic to the Hessian surface of this cubic surface. We describe the nef cone and the (-2)-curves of S. In the case of pentahedral parameters (1, 1, 1, 1, nonzero t) we compute the automorphism group of S. For t not 1 it is the semidirect product of the free product (Z/2)*(Z/2)*(Z/2)*(Z/2) by the symmetric group S4. In the special case t=1/16 we study the action of Aut(S) on an invariant smooth rational"},"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":"1809.07819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T19:39:30Z","cross_cats_sorted":[],"title_canon_sha256":"f866d97522dd597a712c7cf84db43323539ce68e990cfa0a1b340dd426a522f8","abstract_canon_sha256":"3d75236a89e44ad9b3e742d177543eb86e138c447390edf0022a4f612006ebe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:13.164670Z","signature_b64":"0GnbjFpq1Rn3vN39TJLrXAIVKNUTHrwQmLG7lBTW24Q74JJw4on3YjGtJZ8TRl8YTWXDi/rtIaSajo++EWv9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15455f4c3e8f812a7a6efdc61e3b95cf5b48158393c791057a207b8c1fe33afe","last_reissued_at":"2026-05-18T00:05:13.164080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:13.164080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Allcock, Igor Dolgachev","submitted_at":"2018-09-20T19:39:30Z","abstract_excerpt":"Consider a cubic surface satisfying the mild condition that it may be described in Sylvester's pentahedral form. There is a well-known Enriques or Coble surface S with K3 cover birationally isomorphic to the Hessian surface of this cubic surface. We describe the nef cone and the (-2)-curves of S. In the case of pentahedral parameters (1, 1, 1, 1, nonzero t) we compute the automorphism group of S. For t not 1 it is the semidirect product of the free product (Z/2)*(Z/2)*(Z/2)*(Z/2) by the symmetric group S4. In the special case t=1/16 we study the action of Aut(S) on an invariant smooth rational"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07819","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":"1809.07819","created_at":"2026-05-18T00:05:13.164180+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.07819v1","created_at":"2026-05-18T00:05:13.164180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07819","created_at":"2026-05-18T00:05:13.164180+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVCV6TB6R6AS","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVCV6TB6R6ASU6TO","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVCV6TB6","created_at":"2026-05-18T12:32:19.392346+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/CVCV6TB6R6ASU6TO7XDB4O4VZ5","json":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5.json","graph_json":"https://pith.science/api/pith-number/CVCV6TB6R6ASU6TO7XDB4O4VZ5/graph.json","events_json":"https://pith.science/api/pith-number/CVCV6TB6R6ASU6TO7XDB4O4VZ5/events.json","paper":"https://pith.science/paper/CVCV6TB6"},"agent_actions":{"view_html":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5","download_json":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5.json","view_paper":"https://pith.science/paper/CVCV6TB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.07819&json=true","fetch_graph":"https://pith.science/api/pith-number/CVCV6TB6R6ASU6TO7XDB4O4VZ5/graph.json","fetch_events":"https://pith.science/api/pith-number/CVCV6TB6R6ASU6TO7XDB4O4VZ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5/action/storage_attestation","attest_author":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5/action/author_attestation","sign_citation":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5/action/citation_signature","submit_replication":"https://pith.science/pith/CVCV6TB6R6ASU6TO7XDB4O4VZ5/action/replication_record"}},"created_at":"2026-05-18T00:05:13.164180+00:00","updated_at":"2026-05-18T00:05:13.164180+00:00"}