{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZIWLKAVJSWCSOJLHYIGBZLUPWN","short_pith_number":"pith:ZIWLKAVJ","schema_version":"1.0","canonical_sha256":"ca2cb502a99585272567c20c1cae8fb370943b077f1eab1c893bfdc5e1a054b3","source":{"kind":"arxiv","id":"1309.5243","version":2},"attestation_state":"computed","paper":{"title":"Algorithms for Mumford curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Qingchun Ren, Ralph Morrison","submitted_at":"2013-09-20T12:08:18Z","abstract_excerpt":"Mumford showed that Schottky subgroups of $PGL(2,K)$ give rise to certain curves, now called Mumford curves, over a non-Archimedean field K. Such curves are foundational to subjects dealing with non-Archimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step is finding a good set of generators for a Schottky group, a problem solved in this paper. This result allows us to design and implement algorithms for tasks such as: approximating the period matrices "},"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":"1309.5243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-20T12:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"a9a5fc9fc12b689fb38056702ff378ad802da4b5de1e9c40ce8f383479dd3984","abstract_canon_sha256":"9f9fd82a310ad20c5adf455cd2a9967b7f4a808e50e1de6c8cc8bf43184d160c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:11.159120Z","signature_b64":"1LsgRWrzZqoH8AHKyJQ0hPnvSsa8D9F9PrVaQ0lBFDRVEQICa9TK/N4IhAZ2xDTUfL3cSST7i2uUilRotew9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca2cb502a99585272567c20c1cae8fb370943b077f1eab1c893bfdc5e1a054b3","last_reissued_at":"2026-05-18T03:12:11.158287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:11.158287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms for Mumford curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Qingchun Ren, Ralph Morrison","submitted_at":"2013-09-20T12:08:18Z","abstract_excerpt":"Mumford showed that Schottky subgroups of $PGL(2,K)$ give rise to certain curves, now called Mumford curves, over a non-Archimedean field K. Such curves are foundational to subjects dealing with non-Archimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step is finding a good set of generators for a Schottky group, a problem solved in this paper. This result allows us to design and implement algorithms for tasks such as: approximating the period matrices "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5243","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":"1309.5243","created_at":"2026-05-18T03:12:11.158440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5243v2","created_at":"2026-05-18T03:12:11.158440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5243","created_at":"2026-05-18T03:12:11.158440+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZIWLKAVJSWCS","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZIWLKAVJSWCSOJLH","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZIWLKAVJ","created_at":"2026-05-18T12:28:09.283467+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/ZIWLKAVJSWCSOJLHYIGBZLUPWN","json":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN.json","graph_json":"https://pith.science/api/pith-number/ZIWLKAVJSWCSOJLHYIGBZLUPWN/graph.json","events_json":"https://pith.science/api/pith-number/ZIWLKAVJSWCSOJLHYIGBZLUPWN/events.json","paper":"https://pith.science/paper/ZIWLKAVJ"},"agent_actions":{"view_html":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN","download_json":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN.json","view_paper":"https://pith.science/paper/ZIWLKAVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5243&json=true","fetch_graph":"https://pith.science/api/pith-number/ZIWLKAVJSWCSOJLHYIGBZLUPWN/graph.json","fetch_events":"https://pith.science/api/pith-number/ZIWLKAVJSWCSOJLHYIGBZLUPWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN/action/storage_attestation","attest_author":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN/action/author_attestation","sign_citation":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN/action/citation_signature","submit_replication":"https://pith.science/pith/ZIWLKAVJSWCSOJLHYIGBZLUPWN/action/replication_record"}},"created_at":"2026-05-18T03:12:11.158440+00:00","updated_at":"2026-05-18T03:12:11.158440+00:00"}