{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EUUBYQ3JPFF3BXQBVW772762J7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5bfcf93cc204ca9bcc4eec31a2bc865bb35ec8b0a9cc8c2fa0eed484770ace26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-09-27T20:07:54Z","title_canon_sha256":"33bb3626377e470c84bf1f495850c4d858ae775684cbe24d9fb8f35d70589ed3"},"schema_version":"1.0","source":{"id":"0909.4965","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4965","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4965v3","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4965","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"EUUBYQ3JPFF3","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EUUBYQ3JPFF3BXQB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EUUBYQ3J","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:1cff601052e16ad9e6ca037c8e42016ef56b2db03190b619847382dbac407f2a","target":"graph","created_at":"2026-05-18T01:33:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X$ be a general cyclic cover of $\\mathbb{CP}^{1}$ ramified at $m$ points, $\\lambda_1...\\lambda_m.$ we define a class of non positive divisors on $X$ of degree $g-1$ supported in the pre images of the branch points on $X$, such that the the standard theta function doesn't vanish on their image in $J(X).$ These divisors generalize the divisors introduced in [BR] and [Na]. Generalizing the results of [BR],[Na] and [EG] we show that up to a certain determinant of the non standard periods of $X$, the value of the theta functions at these divisors is a polynomial in the branch point of the curv","authors_text":"Yaacov Kopeliovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-09-27T20:07:54Z","title":"General cyclic covers and their Thomae formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4965","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6466e4048e1a430a094a8009c0b9e199a8208d111f6d848a803f3d1781714e49","target":"record","created_at":"2026-05-18T01:33:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5bfcf93cc204ca9bcc4eec31a2bc865bb35ec8b0a9cc8c2fa0eed484770ace26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-09-27T20:07:54Z","title_canon_sha256":"33bb3626377e470c84bf1f495850c4d858ae775684cbe24d9fb8f35d70589ed3"},"schema_version":"1.0","source":{"id":"0909.4965","kind":"arxiv","version":3}},"canonical_sha256":"25281c4369794bb0de01adbffd7fda4ff097cbc928cd7398fccaded13a69698b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25281c4369794bb0de01adbffd7fda4ff097cbc928cd7398fccaded13a69698b","first_computed_at":"2026-05-18T01:33:57.372117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.372117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A70VCoHPr+51KWmVNyui/x12D5/dt8bJcVg+jDZLtPiJn1WC4ctrmL8B9N40GBMcXDB0drTC0svnjgroMrBjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.372555Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4965","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6466e4048e1a430a094a8009c0b9e199a8208d111f6d848a803f3d1781714e49","sha256:1cff601052e16ad9e6ca037c8e42016ef56b2db03190b619847382dbac407f2a"],"state_sha256":"c9a4bffba636be08f9249a2210d8626cb63d6570bf25f707200238095d8d28ac"}