{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AX3C2BUHNP7GESRFXMGWPGA2QI","short_pith_number":"pith:AX3C2BUH","schema_version":"1.0","canonical_sha256":"05f62d06876bfe624a25bb0d67981a822c93978f00828cc4f7c172683f853eed","source":{"kind":"arxiv","id":"1606.00598","version":3},"attestation_state":"computed","paper":{"title":"On upper bounds of arithmetic degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Yohsuke Matsuzawa","submitted_at":"2016-06-02T09:43:46Z","abstract_excerpt":"Let $X$ be a smooth projective variety over $ \\overline{\\mathbb Q}$, and $f:X -rightarrow X$ be a dominant rational map. Let $\\delta_{f}$ be the first dynamical degree of $f$ and $h_{X}:X( \\overline{\\mathbb Q})\\to [1,\\infty)$ be a Weil height function on $X$ associated with an ample divisor on $X$. We prove several inequalities which give upper bounds of the sequence $(h_X (f^n(P)))_{n\\geq0}$ where $P$ is a point of $X( \\overline{\\mathbb Q})$ whose forward orbit by $f$ is well-defined. As a corollary, we prove that the upper arithmetic degree is less than or equal to the first dynamical degree"},"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":"1606.00598","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T09:43:46Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"19642f2e2064844c7680a8261de7a1415dbf08d84b6caffa32eaa33c909198fd","abstract_canon_sha256":"41ce8523043b03312aa9cfbc3d407a49878f1789af4bf745fe5662fefedab7f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:02.487843Z","signature_b64":"OaoohRHmSeHB58bnlwI/Z185qayrJZcYbKkQ2sdA/i432+gVf+THGGtEQtBi1G/iLpFpEyrNI/Ocn8+Qgdi9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05f62d06876bfe624a25bb0d67981a822c93978f00828cc4f7c172683f853eed","last_reissued_at":"2026-05-18T00:24:02.487404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:02.487404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On upper bounds of arithmetic degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Yohsuke Matsuzawa","submitted_at":"2016-06-02T09:43:46Z","abstract_excerpt":"Let $X$ be a smooth projective variety over $ \\overline{\\mathbb Q}$, and $f:X -rightarrow X$ be a dominant rational map. Let $\\delta_{f}$ be the first dynamical degree of $f$ and $h_{X}:X( \\overline{\\mathbb Q})\\to [1,\\infty)$ be a Weil height function on $X$ associated with an ample divisor on $X$. We prove several inequalities which give upper bounds of the sequence $(h_X (f^n(P)))_{n\\geq0}$ where $P$ is a point of $X( \\overline{\\mathbb Q})$ whose forward orbit by $f$ is well-defined. As a corollary, we prove that the upper arithmetic degree is less than or equal to the first dynamical degree"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00598","kind":"arxiv","version":3},"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":"1606.00598","created_at":"2026-05-18T00:24:02.487471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00598v3","created_at":"2026-05-18T00:24:02.487471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00598","created_at":"2026-05-18T00:24:02.487471+00:00"},{"alias_kind":"pith_short_12","alias_value":"AX3C2BUHNP7G","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AX3C2BUHNP7GESRF","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AX3C2BUH","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.11188","citing_title":"Higher arithmetic degrees of dominant rational self-maps","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI","json":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI.json","graph_json":"https://pith.science/api/pith-number/AX3C2BUHNP7GESRFXMGWPGA2QI/graph.json","events_json":"https://pith.science/api/pith-number/AX3C2BUHNP7GESRFXMGWPGA2QI/events.json","paper":"https://pith.science/paper/AX3C2BUH"},"agent_actions":{"view_html":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI","download_json":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI.json","view_paper":"https://pith.science/paper/AX3C2BUH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00598&json=true","fetch_graph":"https://pith.science/api/pith-number/AX3C2BUHNP7GESRFXMGWPGA2QI/graph.json","fetch_events":"https://pith.science/api/pith-number/AX3C2BUHNP7GESRFXMGWPGA2QI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI/action/storage_attestation","attest_author":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI/action/author_attestation","sign_citation":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI/action/citation_signature","submit_replication":"https://pith.science/pith/AX3C2BUHNP7GESRFXMGWPGA2QI/action/replication_record"}},"created_at":"2026-05-18T00:24:02.487471+00:00","updated_at":"2026-05-18T00:24:02.487471+00:00"}