{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ICXZZHISYKIJ74RHXEA6C74P36","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":"7310cc02414811c3d7574c4c6f360d5216fb005df76ca91fbab3b026ef66de0d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-11T08:45:33Z","title_canon_sha256":"894110de97b51f88e9d434bd2937d21d6db36d2e731412cd647aa63b370a08db"},"schema_version":"1.0","source":{"id":"1803.03928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03928","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03928v1","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03928","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"ICXZZHISYKIJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"ICXZZHISYKIJ74RH","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"ICXZZHIS","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:864ee81c8888a4e47f4214e0ab274cd4c07b226994f755629241e2cdf6ef51b6","target":"graph","created_at":"2026-05-18T00:04:13Z","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 conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\\mathbb{k}$ of characteristic $0$. That is, if $\\Phi\\colon G\\longrightarrow G$ is a dominant endomorphism, we prove that one of the following holds: either there exists a non-constant rational function $f\\in \\mathbb{k}(G)$ preserved by $\\Phi$ (i.e., $f\\circ \\Phi = f$), or there exists a point $x\\in G(\\mathbb{k})$ whose $\\Phi$-orbit is Zariski dense in $G$.","authors_text":"Dragos Ghioca, Fei Hu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-11T08:45:33Z","title":"Density of orbits of endomorphisms of commutative linear algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03928","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":"sha256:87d48598ec65aa49cf23271858a863c891e80211860747e793924721e700a007","target":"record","created_at":"2026-05-18T00:04:13Z","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":"7310cc02414811c3d7574c4c6f360d5216fb005df76ca91fbab3b026ef66de0d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-11T08:45:33Z","title_canon_sha256":"894110de97b51f88e9d434bd2937d21d6db36d2e731412cd647aa63b370a08db"},"schema_version":"1.0","source":{"id":"1803.03928","kind":"arxiv","version":1}},"canonical_sha256":"40af9c9d12c2909ff227b901e17f8fdfa72bdd1a1e0241ad32d0040846a274c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40af9c9d12c2909ff227b901e17f8fdfa72bdd1a1e0241ad32d0040846a274c8","first_computed_at":"2026-05-18T00:04:13.145866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:13.145866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GUNnMJO8ODu7Fs70XU7HOegV1bvsZEatl4DevU1/d6fqbYCKKVjVa3714DHYLakTNYbPaDCqTKKUEeEFd5P7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:13.146579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87d48598ec65aa49cf23271858a863c891e80211860747e793924721e700a007","sha256:864ee81c8888a4e47f4214e0ab274cd4c07b226994f755629241e2cdf6ef51b6"],"state_sha256":"a07451fd2fe97fb5b49c9af81e6178f3814973aca11b8c51beed782e3ad08f59"}