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We let $f:X\\times\\mathbb{A}^N\\dashrightarrow X\\times \\mathbb{A}^N$ be the rational endomorphism given by $(x,y)\\mapsto (g(x), A(x)y)$. We prove that if the determinant of $A$ is nonzero"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.03931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-11T10:13:56Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"23908a72d816d862c12fdad678f1c15f5660ad56d3f039e2ceee2fff99aa2aad","abstract_canon_sha256":"b7acc5f2565d26fe62deb9518a73cc30acec3df8b10145393674d1f161a6304c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.431975Z","signature_b64":"mUgx0KSw5BSSM38r3xj28GQNV7YsnSyVCjU4PfzIoyinHPmRTbDi86UfQTQms5rti6cfWYgQm7EvgW/sqngWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d84873f32382ae72a296b5906f4df6349f16526191546aef857fa06fe7a763a","last_reissued_at":"2026-05-18T00:21:33.431366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.431366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic dynamics of skew-linear self-maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Dragos Ghioca, Junyi Xie","submitted_at":"2018-03-11T10:13:56Z","abstract_excerpt":"Let $X$ be a variety defined over an algebraically closed field $k$ of characteristic $0$, let $N\\in\\mathbb{N}$, let $g:X\\dashrightarrow X$ be a dominant rational self-map, and let $A:\\mathbb{A}^N\\to \\mathbb{A}^N$ be a linear transformation defined over $k(X)$, i.e., for a Zariski open dense subset $U\\subset X$, we have that for $x\\in U(k)$, the specialization $A(x)$ is an $N$-by-$N$ matrix with entries in $k$. We let $f:X\\times\\mathbb{A}^N\\dashrightarrow X\\times \\mathbb{A}^N$ be the rational endomorphism given by $(x,y)\\mapsto (g(x), A(x)y)$. We prove that if the determinant of $A$ is nonzero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03931","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.03931","created_at":"2026-05-18T00:21:33.431458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03931v1","created_at":"2026-05-18T00:21:33.431458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03931","created_at":"2026-05-18T00:21:33.431458+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWCIOPZSHAVO","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWCIOPZSHAVOOKRJ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWCIOPZS","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN","json":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN.json","graph_json":"https://pith.science/api/pith-number/DWCIOPZSHAVOOKRJNNMQN5G7MN/graph.json","events_json":"https://pith.science/api/pith-number/DWCIOPZSHAVOOKRJNNMQN5G7MN/events.json","paper":"https://pith.science/paper/DWCIOPZS"},"agent_actions":{"view_html":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN","download_json":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN.json","view_paper":"https://pith.science/paper/DWCIOPZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03931&json=true","fetch_graph":"https://pith.science/api/pith-number/DWCIOPZSHAVOOKRJNNMQN5G7MN/graph.json","fetch_events":"https://pith.science/api/pith-number/DWCIOPZSHAVOOKRJNNMQN5G7MN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN/action/storage_attestation","attest_author":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN/action/author_attestation","sign_citation":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN/action/citation_signature","submit_replication":"https://pith.science/pith/DWCIOPZSHAVOOKRJNNMQN5G7MN/action/replication_record"}},"created_at":"2026-05-18T00:21:33.431458+00:00","updated_at":"2026-05-18T00:21:33.431458+00:00"}