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Let $f:X\\rightarrow X$ and $g:Y\\rightarrow Y$ be dominant correspondences, and $\\pi :X\\rightarrow Y$ a dominant rational map such that $\\pi \\circ f=g\\circ \\pi$. We define relative dynamical degrees $\\lambda _p(f|\\pi )$ ($p=0,\\ldots ,\\dim (X)-\\dim (Y)$). These degrees measure the relative growth of positive algebraic cycles, satisfy a product formula when $Y$ is smooth and $g$ is a multiple of a rational map, and ar"},"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":"1605.05049","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T07:57:57Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f5daaaaab55668f4dd4a547dd59009de1a80f1b89a3bb6f6f43a7808dca88bb2","abstract_canon_sha256":"b6bc4e1c711e73f8150d4805cc9f6d6ec844f71e6bb7f40470a21daa99f6acdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:38.153568Z","signature_b64":"mQOf9tK5DYIj8T8rDpeWI27/GEpt6TCgWUWBlOoZoeEEyb7cBOLREaW7etBBLKPDpHApOrizZw1xXoAscVInCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"702055204707075016d96a3c6cd901c532b1fcbd057e867584c1d686195173ad","last_reissued_at":"2026-05-18T00:28:38.152738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:38.152738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative dynamical degrees of correspondences over a field of arbitrary characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Tuyen Trung Truong","submitted_at":"2016-05-17T07:57:57Z","abstract_excerpt":"Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\\rightarrow X$ and $g:Y\\rightarrow Y$ be dominant correspondences, and $\\pi :X\\rightarrow Y$ a dominant rational map such that $\\pi \\circ f=g\\circ \\pi$. We define relative dynamical degrees $\\lambda _p(f|\\pi )$ ($p=0,\\ldots ,\\dim (X)-\\dim (Y)$). These degrees measure the relative growth of positive algebraic cycles, satisfy a product formula when $Y$ is smooth and $g$ is a multiple of a rational map, and ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05049","kind":"arxiv","version":2},"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":"1605.05049","created_at":"2026-05-18T00:28:38.152881+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05049v2","created_at":"2026-05-18T00:28:38.152881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05049","created_at":"2026-05-18T00:28:38.152881+00:00"},{"alias_kind":"pith_short_12","alias_value":"OAQFKICHA4DV","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OAQFKICHA4DVAFWZ","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OAQFKICH","created_at":"2026-05-18T12:30:36.002864+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/OAQFKICHA4DVAFWZNI6GZWIBYU","json":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU.json","graph_json":"https://pith.science/api/pith-number/OAQFKICHA4DVAFWZNI6GZWIBYU/graph.json","events_json":"https://pith.science/api/pith-number/OAQFKICHA4DVAFWZNI6GZWIBYU/events.json","paper":"https://pith.science/paper/OAQFKICH"},"agent_actions":{"view_html":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU","download_json":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU.json","view_paper":"https://pith.science/paper/OAQFKICH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05049&json=true","fetch_graph":"https://pith.science/api/pith-number/OAQFKICHA4DVAFWZNI6GZWIBYU/graph.json","fetch_events":"https://pith.science/api/pith-number/OAQFKICHA4DVAFWZNI6GZWIBYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU/action/storage_attestation","attest_author":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU/action/author_attestation","sign_citation":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU/action/citation_signature","submit_replication":"https://pith.science/pith/OAQFKICHA4DVAFWZNI6GZWIBYU/action/replication_record"}},"created_at":"2026-05-18T00:28:38.152881+00:00","updated_at":"2026-05-18T00:28:38.152881+00:00"}