{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:II2PKJX5366KVUT2L5ZQQUCHWD","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":"11641b9e1d43ac05bc9ff8c7a65a5215502b2dd742b1a11f4f45d015a6c3700a","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-05-28T04:55:48Z","title_canon_sha256":"259f5884543269b8f268f1929da00c46c1eecfc3784c2b046c44acdd2fc0592c"},"schema_version":"1.0","source":{"id":"2105.13587","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.13587","created_at":"2026-07-05T11:21:28Z"},{"alias_kind":"arxiv_version","alias_value":"2105.13587v9","created_at":"2026-07-05T11:21:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.13587","created_at":"2026-07-05T11:21:28Z"},{"alias_kind":"pith_short_12","alias_value":"II2PKJX5366K","created_at":"2026-07-05T11:21:28Z"},{"alias_kind":"pith_short_16","alias_value":"II2PKJX5366KVUT2","created_at":"2026-07-05T11:21:28Z"},{"alias_kind":"pith_short_8","alias_value":"II2PKJX5","created_at":"2026-07-05T11:21:28Z"}],"graph_snapshots":[{"event_id":"sha256:a6ef75beb304c4ca150b67c0ab38f16dd7bb8e9ad293ec467e3cd468da5a3987","target":"graph","created_at":"2026-07-05T11:21:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.13587/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider their intersection theory, volume theory, and height theory, and apply these to study heights of algebraic points of quasi-projective varieties.","authors_text":"Shou-Wu Zhang, Xinyi Yuan","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-05-28T04:55:48Z","title":"Adelic line bundles on quasi-projective varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.13587","kind":"arxiv","version":9},"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":"sha256:9d840aea45c6a409918d85517536338c225fb2aeac0334054a55a9e5e04d7ee7","target":"record","created_at":"2026-07-05T11:21:28Z","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":"11641b9e1d43ac05bc9ff8c7a65a5215502b2dd742b1a11f4f45d015a6c3700a","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-05-28T04:55:48Z","title_canon_sha256":"259f5884543269b8f268f1929da00c46c1eecfc3784c2b046c44acdd2fc0592c"},"schema_version":"1.0","source":{"id":"2105.13587","kind":"arxiv","version":9}},"canonical_sha256":"4234f526fddfbcaad27a5f73085047b0e2b1eed9ede0fef57d24b8d66edd1cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4234f526fddfbcaad27a5f73085047b0e2b1eed9ede0fef57d24b8d66edd1cd7","first_computed_at":"2026-07-05T11:21:28.048709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:28.048709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vmqNynYX8ffuRt1rdkfN8yGcSkufjfRRelvpq4yHSaNefotSdjyzQY4WUvlZCB/VFVKMNXpmS8MzdbwU8sO2CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:28.049201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.13587","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d840aea45c6a409918d85517536338c225fb2aeac0334054a55a9e5e04d7ee7","sha256:a6ef75beb304c4ca150b67c0ab38f16dd7bb8e9ad293ec467e3cd468da5a3987"],"state_sha256":"fa57f2db2f069fb2f4469d7bf28c36b501575b957adaba91fa7ff6de6aa8046a"}