{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XTGTTIUNCTYDPAMBSQCRLVS6AL","short_pith_number":"pith:XTGTTIUN","schema_version":"1.0","canonical_sha256":"bccd39a28d14f0378181940515d65e02d8bd909e7cd0842ba6638549fe3d4f5a","source":{"kind":"arxiv","id":"1712.00694","version":1},"attestation_state":"computed","paper":{"title":"The sigma function for trigonal cyclic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AG","authors_text":"Emma Previato, Jiryo Komeda, Shigeki Matsutani","submitted_at":"2017-12-03T02:00:56Z","abstract_excerpt":"A recent generalization of the \"Kleinian sigma function\" involves the choice of a point $P$ of a Riemann surface $X$, namely a \"pointed curve\" $(X, P)$. This paper concludes our explicit calculation of the sigma function for curves cyclic trigonal at $P$. We exhibit the Riemann constant for a Weierstrass semigroup at $P$ with minimal set of generators $\\{3, 2r+s,2s+r\\}$, $r<s$, equivalently, non-symmetric, we construct a basis of $H^1(X, \\mathbb{C})$ and a fundamental 2-differential on $X\\times X$, we give the order of vanishing for sigma on Wirtinger strata of the Jacobian of $X$, and a solut"},"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":"1712.00694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-03T02:00:56Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"c786d929f30cebe035e28e858cea014d129855489ab5848fc72378551aed9348","abstract_canon_sha256":"30a63a8e843c822e1d1f72d5129224429d5724c5918979d38c99ef8ad7594bc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:15.737093Z","signature_b64":"uk5bm3G2LTpf6Wwy8pleQRhQWBYZ6B54sza0bdq5N3HMzcLOL/WA3WhGOTRrpJg7EsFw5Et6m7ue5PUFxhQTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bccd39a28d14f0378181940515d65e02d8bd909e7cd0842ba6638549fe3d4f5a","last_reissued_at":"2026-05-18T00:08:15.736655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:15.736655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The sigma function for trigonal cyclic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AG","authors_text":"Emma Previato, Jiryo Komeda, Shigeki Matsutani","submitted_at":"2017-12-03T02:00:56Z","abstract_excerpt":"A recent generalization of the \"Kleinian sigma function\" involves the choice of a point $P$ of a Riemann surface $X$, namely a \"pointed curve\" $(X, P)$. This paper concludes our explicit calculation of the sigma function for curves cyclic trigonal at $P$. We exhibit the Riemann constant for a Weierstrass semigroup at $P$ with minimal set of generators $\\{3, 2r+s,2s+r\\}$, $r<s$, equivalently, non-symmetric, we construct a basis of $H^1(X, \\mathbb{C})$ and a fundamental 2-differential on $X\\times X$, we give the order of vanishing for sigma on Wirtinger strata of the Jacobian of $X$, and a solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00694","kind":"arxiv","version":1},"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":"1712.00694","created_at":"2026-05-18T00:08:15.736720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00694v1","created_at":"2026-05-18T00:08:15.736720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00694","created_at":"2026-05-18T00:08:15.736720+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTGTTIUNCTYD","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTGTTIUNCTYDPAMB","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTGTTIUN","created_at":"2026-05-18T12:31:56.362134+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/XTGTTIUNCTYDPAMBSQCRLVS6AL","json":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL.json","graph_json":"https://pith.science/api/pith-number/XTGTTIUNCTYDPAMBSQCRLVS6AL/graph.json","events_json":"https://pith.science/api/pith-number/XTGTTIUNCTYDPAMBSQCRLVS6AL/events.json","paper":"https://pith.science/paper/XTGTTIUN"},"agent_actions":{"view_html":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL","download_json":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL.json","view_paper":"https://pith.science/paper/XTGTTIUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00694&json=true","fetch_graph":"https://pith.science/api/pith-number/XTGTTIUNCTYDPAMBSQCRLVS6AL/graph.json","fetch_events":"https://pith.science/api/pith-number/XTGTTIUNCTYDPAMBSQCRLVS6AL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL/action/storage_attestation","attest_author":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL/action/author_attestation","sign_citation":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL/action/citation_signature","submit_replication":"https://pith.science/pith/XTGTTIUNCTYDPAMBSQCRLVS6AL/action/replication_record"}},"created_at":"2026-05-18T00:08:15.736720+00:00","updated_at":"2026-05-18T00:08:15.736720+00:00"}