{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UAUWM6KBPWFCLXF3UF6NA3EZ4C","short_pith_number":"pith:UAUWM6KB","schema_version":"1.0","canonical_sha256":"a0296679417d8a25dcbba17cd06c99e09d644de5e804f2e8d095c50b62d15747","source":{"kind":"arxiv","id":"1603.09569","version":3},"attestation_state":"computed","paper":{"title":"On Jacobi Inversion Formulae for Telescopic Curves","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Takanori Ayano","submitted_at":"2016-03-31T13:06:45Z","abstract_excerpt":"For a hyperelliptic curve of genus $g$, it is well known that the symmetric products of $g$ points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by $y^r=f(x)$, which are special cases of $(n,s)$ curves, and derived new vanishing properties of the sigma function of the curves $y^r=f(x)$. In this paper we extend the formulae to the telescopic curves proposed by Miura and derive new vanishing properties "},"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":"1603.09569","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2016-03-31T13:06:45Z","cross_cats_sorted":[],"title_canon_sha256":"d7a78ef3488ff7d42267219630fe5c79897cc3745b5173e91220f9ffc3cbb090","abstract_canon_sha256":"7d4c2a69a60a7ef4b911aa205f283e54b29e6d2d7a5270da5dc92598807db524"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.818394Z","signature_b64":"C8mGSrVEqBI1LCRyVc2uMGo+uoxekJarB47UpzEorW4mRKEzJ2xnRinOq24/8FKBPubtvEpob+73zmse91JuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0296679417d8a25dcbba17cd06c99e09d644de5e804f2e8d095c50b62d15747","last_reissued_at":"2026-05-18T01:07:50.817892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.817892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Jacobi Inversion Formulae for Telescopic Curves","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Takanori Ayano","submitted_at":"2016-03-31T13:06:45Z","abstract_excerpt":"For a hyperelliptic curve of genus $g$, it is well known that the symmetric products of $g$ points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by $y^r=f(x)$, which are special cases of $(n,s)$ curves, and derived new vanishing properties of the sigma function of the curves $y^r=f(x)$. In this paper we extend the formulae to the telescopic curves proposed by Miura and derive new vanishing properties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09569","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":"1603.09569","created_at":"2026-05-18T01:07:50.817975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.09569v3","created_at":"2026-05-18T01:07:50.817975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09569","created_at":"2026-05-18T01:07:50.817975+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAUWM6KBPWFC","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAUWM6KBPWFCLXF3","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAUWM6KB","created_at":"2026-05-18T12:30:46.583412+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/UAUWM6KBPWFCLXF3UF6NA3EZ4C","json":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C.json","graph_json":"https://pith.science/api/pith-number/UAUWM6KBPWFCLXF3UF6NA3EZ4C/graph.json","events_json":"https://pith.science/api/pith-number/UAUWM6KBPWFCLXF3UF6NA3EZ4C/events.json","paper":"https://pith.science/paper/UAUWM6KB"},"agent_actions":{"view_html":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C","download_json":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C.json","view_paper":"https://pith.science/paper/UAUWM6KB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.09569&json=true","fetch_graph":"https://pith.science/api/pith-number/UAUWM6KBPWFCLXF3UF6NA3EZ4C/graph.json","fetch_events":"https://pith.science/api/pith-number/UAUWM6KBPWFCLXF3UF6NA3EZ4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C/action/storage_attestation","attest_author":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C/action/author_attestation","sign_citation":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C/action/citation_signature","submit_replication":"https://pith.science/pith/UAUWM6KBPWFCLXF3UF6NA3EZ4C/action/replication_record"}},"created_at":"2026-05-18T01:07:50.817975+00:00","updated_at":"2026-05-18T01:07:50.817975+00:00"}