{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MGMHNVAK2MLSGF7APKJNIOYEXT","short_pith_number":"pith:MGMHNVAK","schema_version":"1.0","canonical_sha256":"619876d40ad3172317e07a92d43b04bcd73bd1c44522dfcbe6a603e52d725b0a","source":{"kind":"arxiv","id":"1410.6892","version":2},"attestation_state":"computed","paper":{"title":"Metric uniformization of morphisms of Berkovich curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Temkin","submitted_at":"2014-10-25T06:43:29Z","abstract_excerpt":"We show that the metric structure of morphisms $f\\colon Y\\to X$ between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton $\\Gamma=(\\Gamma_Y,\\Gamma_X)$ of $f$, the sets $N_{f,\\ge n}$ of points of $Y$ of multiplicity at least $n$ in the fiber are radial around $\\Gamma_Y$ with the radius changing piecewise monomially along $\\Gamma_Y$. In this case, for any interval $l=[z,y]\\subset Y$ connecting a rigid point $z$ to the skeleton, the restriction $f|_l$ gives rise to a $profile$ piecewise mo"},"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":"1410.6892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-25T06:43:29Z","cross_cats_sorted":[],"title_canon_sha256":"225741ab631ba7a176c920daff80405445465477bd066782c01f70714a2198cc","abstract_canon_sha256":"6253466bdaf27f4f37b8765194035657fdd8e4c4366ba82ffd508584b7ceef16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:47.422983Z","signature_b64":"Driwmnos+/sA6/FD9BEP+GLvGbCd9RKyHbUPq8b7vbxUgcE6eQLsT7q9YoYSvN7Zn+0ifUjfz8mgHB6JjbtHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"619876d40ad3172317e07a92d43b04bcd73bd1c44522dfcbe6a603e52d725b0a","last_reissued_at":"2026-05-18T00:49:47.422335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:47.422335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric uniformization of morphisms of Berkovich curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Temkin","submitted_at":"2014-10-25T06:43:29Z","abstract_excerpt":"We show that the metric structure of morphisms $f\\colon Y\\to X$ between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton $\\Gamma=(\\Gamma_Y,\\Gamma_X)$ of $f$, the sets $N_{f,\\ge n}$ of points of $Y$ of multiplicity at least $n$ in the fiber are radial around $\\Gamma_Y$ with the radius changing piecewise monomially along $\\Gamma_Y$. In this case, for any interval $l=[z,y]\\subset Y$ connecting a rigid point $z$ to the skeleton, the restriction $f|_l$ gives rise to a $profile$ piecewise mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6892","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":"1410.6892","created_at":"2026-05-18T00:49:47.422438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6892v2","created_at":"2026-05-18T00:49:47.422438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6892","created_at":"2026-05-18T00:49:47.422438+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGMHNVAK2MLS","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGMHNVAK2MLSGF7A","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGMHNVAK","created_at":"2026-05-18T12:28:38.356838+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/MGMHNVAK2MLSGF7APKJNIOYEXT","json":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT.json","graph_json":"https://pith.science/api/pith-number/MGMHNVAK2MLSGF7APKJNIOYEXT/graph.json","events_json":"https://pith.science/api/pith-number/MGMHNVAK2MLSGF7APKJNIOYEXT/events.json","paper":"https://pith.science/paper/MGMHNVAK"},"agent_actions":{"view_html":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT","download_json":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT.json","view_paper":"https://pith.science/paper/MGMHNVAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6892&json=true","fetch_graph":"https://pith.science/api/pith-number/MGMHNVAK2MLSGF7APKJNIOYEXT/graph.json","fetch_events":"https://pith.science/api/pith-number/MGMHNVAK2MLSGF7APKJNIOYEXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT/action/storage_attestation","attest_author":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT/action/author_attestation","sign_citation":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT/action/citation_signature","submit_replication":"https://pith.science/pith/MGMHNVAK2MLSGF7APKJNIOYEXT/action/replication_record"}},"created_at":"2026-05-18T00:49:47.422438+00:00","updated_at":"2026-05-18T00:49:47.422438+00:00"}