{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LU5AZXWORALV2JOT2QT4TCQ2D6","short_pith_number":"pith:LU5AZXWO","schema_version":"1.0","canonical_sha256":"5d3a0cdece88175d25d3d427c98a1a1fafa69a3eaa5ea2f3caa1e98026e1e91b","source":{"kind":"arxiv","id":"1201.2338","version":1},"attestation_state":"computed","paper":{"title":"Algebraic varieties with automorphism groups of maximal rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"De-Qi Zhang","submitted_at":"2012-01-11T15:58:14Z","abstract_excerpt":"We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper."},"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":"1201.2338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-11T15:58:14Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"fb2a338e6881c284a45b62e210a003dbc9b319a9517d76a14462e3660986b48b","abstract_canon_sha256":"5b6203c4f277edbe6db9cacbbbc156e9cf5a04a5078f752bf929a15090c0c136"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:15.069519Z","signature_b64":"w0+hqMdTPWIuIAaf7K2Ge9HmpOzSbAie5/caZG1fsGs49Wsw/P49kT9p3LXAY9js6IC3i6DTGdptdnxz7spUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d3a0cdece88175d25d3d427c98a1a1fafa69a3eaa5ea2f3caa1e98026e1e91b","last_reissued_at":"2026-05-18T00:05:15.068909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:15.068909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic varieties with automorphism groups of maximal rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"De-Qi Zhang","submitted_at":"2012-01-11T15:58:14Z","abstract_excerpt":"We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2338","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":"1201.2338","created_at":"2026-05-18T00:05:15.069001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2338v1","created_at":"2026-05-18T00:05:15.069001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2338","created_at":"2026-05-18T00:05:15.069001+00:00"},{"alias_kind":"pith_short_12","alias_value":"LU5AZXWORALV","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LU5AZXWORALV2JOT","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LU5AZXWO","created_at":"2026-05-18T12:27:14.488303+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/LU5AZXWORALV2JOT2QT4TCQ2D6","json":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6.json","graph_json":"https://pith.science/api/pith-number/LU5AZXWORALV2JOT2QT4TCQ2D6/graph.json","events_json":"https://pith.science/api/pith-number/LU5AZXWORALV2JOT2QT4TCQ2D6/events.json","paper":"https://pith.science/paper/LU5AZXWO"},"agent_actions":{"view_html":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6","download_json":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6.json","view_paper":"https://pith.science/paper/LU5AZXWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2338&json=true","fetch_graph":"https://pith.science/api/pith-number/LU5AZXWORALV2JOT2QT4TCQ2D6/graph.json","fetch_events":"https://pith.science/api/pith-number/LU5AZXWORALV2JOT2QT4TCQ2D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6/action/storage_attestation","attest_author":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6/action/author_attestation","sign_citation":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6/action/citation_signature","submit_replication":"https://pith.science/pith/LU5AZXWORALV2JOT2QT4TCQ2D6/action/replication_record"}},"created_at":"2026-05-18T00:05:15.069001+00:00","updated_at":"2026-05-18T00:05:15.069001+00:00"}