{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LLC6YXFDEDSQA6T57RRUFBTJ46","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":"02d062e12401cc8c1cd440dbd6293f161150b75254f8ac094d55c8637298751a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T06:58:01Z","title_canon_sha256":"0e72fae88ce310735e8f77002c2f1196e2e00599de835aa1c96a60b14a347fc2"},"schema_version":"1.0","source":{"id":"1603.04978","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04978","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04978v3","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04978","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"LLC6YXFDEDSQ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LLC6YXFDEDSQA6T5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LLC6YXFD","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:2584215c4c3b395cdc5f9e369fc3c55955ad426f5046e4ee13ac6db7046ec91e","target":"graph","created_at":"2026-05-18T00:26:30Z","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":"The purpose of this note is to show that $2K$ of any smooth compact complex two ball quotient is very ample, except possibly for four pairs of fake projective planes of minimal type, where $K$ is the canonical line bundle. For the four pairs of fake projective planes, sections of $2K_M$ give an embedding of $M$ except possibly for at most two points on $M$.","authors_text":"Sai-Kee Yeung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T06:58:01Z","title":"Very ampleness of the bicanonical line bundle on compact complex two ball quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04978","kind":"arxiv","version":3},"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:e186f5c99f8b887e2f265b58aef2041a2b989284d259cdb478d2153c68166cf0","target":"record","created_at":"2026-05-18T00:26:30Z","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":"02d062e12401cc8c1cd440dbd6293f161150b75254f8ac094d55c8637298751a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T06:58:01Z","title_canon_sha256":"0e72fae88ce310735e8f77002c2f1196e2e00599de835aa1c96a60b14a347fc2"},"schema_version":"1.0","source":{"id":"1603.04978","kind":"arxiv","version":3}},"canonical_sha256":"5ac5ec5ca320e5007a7dfc63428669e7b8c9b1efe6de7d21b8a6cc88bf788eac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ac5ec5ca320e5007a7dfc63428669e7b8c9b1efe6de7d21b8a6cc88bf788eac","first_computed_at":"2026-05-18T00:26:30.866081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:30.866081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fmHDfRNVon/BApZ1nOwXZ1IXAG3HGSD9Kyfu0116LyTR6b3YRnmnTAt6mpUf37EGdQexekdleTsZCFcL124VCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:30.866627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04978","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e186f5c99f8b887e2f265b58aef2041a2b989284d259cdb478d2153c68166cf0","sha256:2584215c4c3b395cdc5f9e369fc3c55955ad426f5046e4ee13ac6db7046ec91e"],"state_sha256":"c05a790330488cd48b3915ceda12432836dd607cf327f812e4137662dcaafc67"}