{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FFCDT45ODR64PEGQRMT27GHTOI","short_pith_number":"pith:FFCDT45O","schema_version":"1.0","canonical_sha256":"294439f3ae1c7dc790d08b27af98f372139eb485be349d1dbe3e03109d9157e2","source":{"kind":"arxiv","id":"1602.05614","version":2},"attestation_state":"computed","paper":{"title":"Rationality of dynamical canonical height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Dragos Ghioca, Laura DeMarco","submitted_at":"2016-02-17T22:17:33Z","abstract_excerpt":"We present a dynamical proof of the well-known fact that the Neron-Tate canonical height (and its local counterpart) takes rational values at points of an elliptic curve over a function field k of transcendence degree 1 over an algebraically closed field K of characteristic 0. More generally, we investigate the mechanism for which the local canonical height for a rational function f defined over k can take irrational values (at points in a local completion of k), providing examples in all degrees greater than 1. Building on Kiwi's classification of non-archimedean Julia sets for quadratic maps"},"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":"1602.05614","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-17T22:17:33Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"e6e7b3c49d967e16dfdaff8894e86af0e70763201111a0206f5c37221eab242e","abstract_canon_sha256":"6f64f8c99ce8796ee2f27716cc92e43b215706a8fb58d52eb26fdbb764fa2a22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:51.025926Z","signature_b64":"LhEOupP8Z8zyyC1Nk0ogANSBWG6McgmW64B8BvV5zyzmJ0LcVya66UBfFHfBTVeCxJ2kaE1wNaet/Nyx1BemCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"294439f3ae1c7dc790d08b27af98f372139eb485be349d1dbe3e03109d9157e2","last_reissued_at":"2026-05-18T00:47:51.025267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:51.025267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rationality of dynamical canonical height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Dragos Ghioca, Laura DeMarco","submitted_at":"2016-02-17T22:17:33Z","abstract_excerpt":"We present a dynamical proof of the well-known fact that the Neron-Tate canonical height (and its local counterpart) takes rational values at points of an elliptic curve over a function field k of transcendence degree 1 over an algebraically closed field K of characteristic 0. More generally, we investigate the mechanism for which the local canonical height for a rational function f defined over k can take irrational values (at points in a local completion of k), providing examples in all degrees greater than 1. Building on Kiwi's classification of non-archimedean Julia sets for quadratic maps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05614","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":"1602.05614","created_at":"2026-05-18T00:47:51.025397+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05614v2","created_at":"2026-05-18T00:47:51.025397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05614","created_at":"2026-05-18T00:47:51.025397+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFCDT45ODR64","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFCDT45ODR64PEGQ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFCDT45O","created_at":"2026-05-18T12:30:15.759754+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/FFCDT45ODR64PEGQRMT27GHTOI","json":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI.json","graph_json":"https://pith.science/api/pith-number/FFCDT45ODR64PEGQRMT27GHTOI/graph.json","events_json":"https://pith.science/api/pith-number/FFCDT45ODR64PEGQRMT27GHTOI/events.json","paper":"https://pith.science/paper/FFCDT45O"},"agent_actions":{"view_html":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI","download_json":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI.json","view_paper":"https://pith.science/paper/FFCDT45O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05614&json=true","fetch_graph":"https://pith.science/api/pith-number/FFCDT45ODR64PEGQRMT27GHTOI/graph.json","fetch_events":"https://pith.science/api/pith-number/FFCDT45ODR64PEGQRMT27GHTOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI/action/storage_attestation","attest_author":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI/action/author_attestation","sign_citation":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI/action/citation_signature","submit_replication":"https://pith.science/pith/FFCDT45ODR64PEGQRMT27GHTOI/action/replication_record"}},"created_at":"2026-05-18T00:47:51.025397+00:00","updated_at":"2026-05-18T00:47:51.025397+00:00"}