{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YL6TCZY2Y7KSMTFOBWDBQE3Q3Y","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":"1dab6fef828fab7625f0aa63dd41e73a1e8ddc97adc8cf51ec170a39b4954704","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-05T15:32:27Z","title_canon_sha256":"a91719bb2bb4b1fb6ab6e661a4c70ab35178f8b596fe90a50b9aef4eeb7f9ca3"},"schema_version":"1.0","source":{"id":"1412.2029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2029","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2029v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2029","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"YL6TCZY2Y7KS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YL6TCZY2Y7KSMTFO","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YL6TCZY2","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:d6b8830efb85eb5119dc8ed03de84dc32ba7b3e200f67f51f443f13a556f93d7","target":"graph","created_at":"2026-05-18T02:32:05Z","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":"Let $A$ be an abelian variety defined over $\\bar{\\mathbb{Q}}$, and let $\\varphi$ be a dominant endomorphism of $A$ as an algebraic variety. We prove that either there exists a non-constant rational fibration preserved by $\\varphi$, or there exists a point $x\\in A(\\bar{\\mathbb{Q}})$ whose $\\varphi$-orbit is Zariski dense in $A$. This provides a positive answer for abelian varieties of a question raised by Medvedev and the second author (\"nvariant varieties for polynomial dynamical systems\", Ann. of Math. (2) 179 (2014), no. 1, 81-177). We prove also a stronger statement of this result in which ","authors_text":"Dragos Ghioca, Thomas Scanlon","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-05T15:32:27Z","title":"Density of orbits of endomorphisms of abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2029","kind":"arxiv","version":1},"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":"sha256:36971680140b57f4e2ee956011246006443d628faadc4d05cd9b565c07c81f55","target":"record","created_at":"2026-05-18T02:32:05Z","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":"1dab6fef828fab7625f0aa63dd41e73a1e8ddc97adc8cf51ec170a39b4954704","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-05T15:32:27Z","title_canon_sha256":"a91719bb2bb4b1fb6ab6e661a4c70ab35178f8b596fe90a50b9aef4eeb7f9ca3"},"schema_version":"1.0","source":{"id":"1412.2029","kind":"arxiv","version":1}},"canonical_sha256":"c2fd31671ac7d5264cae0d86181370de3e3e5fe867a3ea0643fd7f9561573a54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2fd31671ac7d5264cae0d86181370de3e3e5fe867a3ea0643fd7f9561573a54","first_computed_at":"2026-05-18T02:32:05.526336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:05.526336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPjGn08tI8yCV0SNG+TP+DlfJyVEDRvKl/SC5hxpxAAqRnzLvxWZii9DINa31uxd3HVWk0e7WWo9Su0jQGMmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:05.526774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36971680140b57f4e2ee956011246006443d628faadc4d05cd9b565c07c81f55","sha256:d6b8830efb85eb5119dc8ed03de84dc32ba7b3e200f67f51f443f13a556f93d7"],"state_sha256":"6a75e1a2b9fac5a6307192ee2e878a0d958d4895f39e2488fbf6339866e47692"}