{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KNG3MKEZARIIE5BPKBDCSZLQCW","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":"7af5b17cb4f690b1bc53e5b25522b26427de1f8452435aeca9e92db2fd49cbc7","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-08-12T09:39:59Z","title_canon_sha256":"fa166c2c41be516421adb17ed6c2cc5a092cf2e6087abcc96222a6fa304c9b9f"},"schema_version":"1.0","source":{"id":"2108.05625","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.05625","created_at":"2026-07-05T08:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"2108.05625v4","created_at":"2026-07-05T08:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.05625","created_at":"2026-07-05T08:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"KNG3MKEZARII","created_at":"2026-07-05T08:13:23Z"},{"alias_kind":"pith_short_16","alias_value":"KNG3MKEZARIIE5BP","created_at":"2026-07-05T08:13:23Z"},{"alias_kind":"pith_short_8","alias_value":"KNG3MKEZ","created_at":"2026-07-05T08:13:23Z"}],"graph_snapshots":[{"event_id":"sha256:0fee1632350eb30275e10baeff589e58c37cf175da2401d354b211567784eb00","target":"graph","created_at":"2026-07-05T08:13:23Z","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/2108.05625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.","authors_text":"Xinyi Yuan","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-08-12T09:39:59Z","title":"Arithmetic bigness and a uniform Bogomolov-type result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.05625","kind":"arxiv","version":4},"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:f13af6ceaff009494f2e2dc847e7324ead2ca1b8a5ae0d02dd93b80bc2394396","target":"record","created_at":"2026-07-05T08:13:23Z","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":"7af5b17cb4f690b1bc53e5b25522b26427de1f8452435aeca9e92db2fd49cbc7","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2021-08-12T09:39:59Z","title_canon_sha256":"fa166c2c41be516421adb17ed6c2cc5a092cf2e6087abcc96222a6fa304c9b9f"},"schema_version":"1.0","source":{"id":"2108.05625","kind":"arxiv","version":4}},"canonical_sha256":"534db62899045082742f504629657015bff68c776ec5799503f298f2df080830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"534db62899045082742f504629657015bff68c776ec5799503f298f2df080830","first_computed_at":"2026-07-05T08:13:23.728223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:13:23.728223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMHKf5J6RPPqPQL+FP6NtfDSdO/WfRJ1wCOEZc+fE7Sq+Jp02gDZUjz/V9EyKt+YqvMZhSU/NYzVhMCrDzYACw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:13:23.728716Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.05625","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f13af6ceaff009494f2e2dc847e7324ead2ca1b8a5ae0d02dd93b80bc2394396","sha256:0fee1632350eb30275e10baeff589e58c37cf175da2401d354b211567784eb00"],"state_sha256":"de4c3b24ab1701c19fc6dc174eed64d90d1b4d5883a480cb3429ca6fd5268497"}