{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IFJZ6VMOL7BDIDWZHN2KKZW33Y","short_pith_number":"pith:IFJZ6VMO","schema_version":"1.0","canonical_sha256":"41539f558e5fc2340ed93b74a566dbde308e7262c6a137b1bb509f3a867ad67c","source":{"kind":"arxiv","id":"1305.3201","version":3},"attestation_state":"computed","paper":{"title":"Periods of second kind differentials of (n,s)-curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.CV","authors_text":"J. C. Eilbeck, K. Eilers, V. Z. Enolski","submitted_at":"2013-05-14T16:27:23Z","abstract_excerpt":"For elliptic curves, expressions for the periods of elliptic integrals of the second kind in terms of theta-constants, have been known since the middle of the 19th century. In this paper we consider the problem of generalizing these results to curves of higher genera, in particular to a special class of algebraic curves, the so-called $(n,s)$-curves. It is shown that the representations required can be obtained by the comparison of two equivalent expressions for the projective connection, one due to Fay-Wirtinger and the other from Klein-Weierstrass. As a principle example, we consider the cas"},"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":"1305.3201","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-14T16:27:23Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"6fde94e3daf1f3e65e39643643cab9fff3c93718a4fc72ec0362f39ad36acd9d","abstract_canon_sha256":"d735749f5e711a1b168e40e72914e38a90fd558d57eb072caf49f1add0eac0af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:06.972278Z","signature_b64":"+DWEA2y+qXPu0rMGqBLzSkgfRJ0ldlvrxlqK2avuhD2I1O9wUYXUT2hTcmC2MUe5QB4REDptMQR6INHSrYnIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41539f558e5fc2340ed93b74a566dbde308e7262c6a137b1bb509f3a867ad67c","last_reissued_at":"2026-05-18T02:44:06.971807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:06.971807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of second kind differentials of (n,s)-curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.CV","authors_text":"J. C. Eilbeck, K. Eilers, V. Z. Enolski","submitted_at":"2013-05-14T16:27:23Z","abstract_excerpt":"For elliptic curves, expressions for the periods of elliptic integrals of the second kind in terms of theta-constants, have been known since the middle of the 19th century. In this paper we consider the problem of generalizing these results to curves of higher genera, in particular to a special class of algebraic curves, the so-called $(n,s)$-curves. It is shown that the representations required can be obtained by the comparison of two equivalent expressions for the projective connection, one due to Fay-Wirtinger and the other from Klein-Weierstrass. As a principle example, we consider the cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3201","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":"1305.3201","created_at":"2026-05-18T02:44:06.971886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3201v3","created_at":"2026-05-18T02:44:06.971886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3201","created_at":"2026-05-18T02:44:06.971886+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFJZ6VMOL7BD","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFJZ6VMOL7BDIDWZ","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFJZ6VMO","created_at":"2026-05-18T12:27:46.883200+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/IFJZ6VMOL7BDIDWZHN2KKZW33Y","json":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y.json","graph_json":"https://pith.science/api/pith-number/IFJZ6VMOL7BDIDWZHN2KKZW33Y/graph.json","events_json":"https://pith.science/api/pith-number/IFJZ6VMOL7BDIDWZHN2KKZW33Y/events.json","paper":"https://pith.science/paper/IFJZ6VMO"},"agent_actions":{"view_html":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y","download_json":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y.json","view_paper":"https://pith.science/paper/IFJZ6VMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3201&json=true","fetch_graph":"https://pith.science/api/pith-number/IFJZ6VMOL7BDIDWZHN2KKZW33Y/graph.json","fetch_events":"https://pith.science/api/pith-number/IFJZ6VMOL7BDIDWZHN2KKZW33Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y/action/storage_attestation","attest_author":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y/action/author_attestation","sign_citation":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y/action/citation_signature","submit_replication":"https://pith.science/pith/IFJZ6VMOL7BDIDWZHN2KKZW33Y/action/replication_record"}},"created_at":"2026-05-18T02:44:06.971886+00:00","updated_at":"2026-05-18T02:44:06.971886+00:00"}