{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TZTQ5MEGSEFI76SOZ7CQHPSOG5","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":"a84f5fc60c1fe6d5479a41aeb884b03e8cf8a9d4ed20e1b466fb1a83ade0865f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-14T07:12:44Z","title_canon_sha256":"ff95d05fd9827f7bf05eb2b8f6567d7288901cb017c69f2ff91f3af137a5085d"},"schema_version":"1.0","source":{"id":"1501.03261","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03261","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03261v3","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03261","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"TZTQ5MEGSEFI","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"TZTQ5MEGSEFI76SO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"TZTQ5MEG","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:29ccbe38f62b25e5fae78162049cfb1e31c6b544826668200269d27b21c3f3be","target":"graph","created_at":"2026-05-18T00:04:37Z","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":"We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green Griffiths-Lang conjecture claiming that entire curves in complex projective varieties of general type should be contained in a proper subvariety. Using holomorphic foliations theory, we establish a Second Main Theorem following Nevanlinna theory. Finally, with a metric approach, we establish the strong Green-Griffiths-Lang conjecture for Hilbert modular varieties up to finitely many possible exceptions.","authors_text":"Erwan Rousseau (I2M), Fr\\'ed\\'eric Touzet (IRMAR)","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-14T07:12:44Z","title":"Curves in Hilbert modular varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03261","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":"sha256:51df5d6bed97ff6221357dcfb950a38cd8b8d4874770d6dee719849e2b37538d","target":"record","created_at":"2026-05-18T00:04:37Z","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":"a84f5fc60c1fe6d5479a41aeb884b03e8cf8a9d4ed20e1b466fb1a83ade0865f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-14T07:12:44Z","title_canon_sha256":"ff95d05fd9827f7bf05eb2b8f6567d7288901cb017c69f2ff91f3af137a5085d"},"schema_version":"1.0","source":{"id":"1501.03261","kind":"arxiv","version":3}},"canonical_sha256":"9e670eb086910a8ffa4ecfc503be4e377f30a61bd8b680d92de654e29c29f72b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e670eb086910a8ffa4ecfc503be4e377f30a61bd8b680d92de654e29c29f72b","first_computed_at":"2026-05-18T00:04:37.744270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:37.744270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lUg5kMCD+N7Hx4dZka+kHPz/54Eft8ZPack6mMhJ+GP0v5DXnd/pAVh1tGUsC7HrCiwV3GeVUWAfLfm8bcNZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:37.744675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03261","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51df5d6bed97ff6221357dcfb950a38cd8b8d4874770d6dee719849e2b37538d","sha256:29ccbe38f62b25e5fae78162049cfb1e31c6b544826668200269d27b21c3f3be"],"state_sha256":"b975e462837dd496d09b73e29ecbff9fab41311b56f7995db4254554e7ad4e0c"}