{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OAQFKICHA4DVAFWZNI6GZWIBYU","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":"b6bc4e1c711e73f8150d4805cc9f6d6ec844f71e6bb7f40470a21daa99f6acdb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T07:57:57Z","title_canon_sha256":"f5daaaaab55668f4dd4a547dd59009de1a80f1b89a3bb6f6f43a7808dca88bb2"},"schema_version":"1.0","source":{"id":"1605.05049","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05049","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05049v2","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05049","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"OAQFKICHA4DV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OAQFKICHA4DVAFWZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OAQFKICH","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:8711998573db142943c6f3ca4a8966cda4082b153129fd052308aa5ec253bb9a","target":"graph","created_at":"2026-05-18T00:28:38Z","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 $K$ 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","authors_text":"Tuyen Trung Truong","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T07:57:57Z","title":"Relative dynamical degrees of correspondences over a field of arbitrary characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05049","kind":"arxiv","version":2},"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":"sha256:8731a5ffb099c7fbcd82962ef41d6997c5cf9eee2dd246189e9efacb172c1929","target":"record","created_at":"2026-05-18T00:28:38Z","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":"b6bc4e1c711e73f8150d4805cc9f6d6ec844f71e6bb7f40470a21daa99f6acdb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T07:57:57Z","title_canon_sha256":"f5daaaaab55668f4dd4a547dd59009de1a80f1b89a3bb6f6f43a7808dca88bb2"},"schema_version":"1.0","source":{"id":"1605.05049","kind":"arxiv","version":2}},"canonical_sha256":"702055204707075016d96a3c6cd901c532b1fcbd057e867584c1d686195173ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"702055204707075016d96a3c6cd901c532b1fcbd057e867584c1d686195173ad","first_computed_at":"2026-05-18T00:28:38.152738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:38.152738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQOf9tK5DYIj8T8rDpeWI27/GEpt6TCgWUWBlOoZoeEEyb7cBOLREaW7etBBLKPDpHApOrizZw1xXoAscVInCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:38.153568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05049","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8731a5ffb099c7fbcd82962ef41d6997c5cf9eee2dd246189e9efacb172c1929","sha256:8711998573db142943c6f3ca4a8966cda4082b153129fd052308aa5ec253bb9a"],"state_sha256":"a38a92346160f484a3ea2450c3626d808865b95f8479188cc2bab28e2de98993"}