{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:YUFCQN3KCGHXRKVWEVPV3EITS6","short_pith_number":"pith:YUFCQN3K","canonical_record":{"source":{"id":"alg-geom/9608016","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-08-20T12:59:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"074b6bef66e4e136b6f2c3cadf7db2f973ba4618f45b205cbe156ee9373a9c7f","abstract_canon_sha256":"612e8b4c8f0e662cbf99423e198c50a845ab2b53b5e4f082b30ee6c4ee20a6f4"},"schema_version":"1.0"},"canonical_sha256":"c50a28376a118f78aab6255f5d9113979b17d43fec51ed7c2c5863aa18cd9a56","source":{"kind":"arxiv","id":"alg-geom/9608016","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9608016","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9608016v3","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9608016","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"YUFCQN3KCGHX","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YUFCQN3KCGHXRKVW","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YUFCQN3K","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:YUFCQN3KCGHXRKVWEVPV3EITS6","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9608016","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-08-20T12:59:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"074b6bef66e4e136b6f2c3cadf7db2f973ba4618f45b205cbe156ee9373a9c7f","abstract_canon_sha256":"612e8b4c8f0e662cbf99423e198c50a845ab2b53b5e4f082b30ee6c4ee20a6f4"},"schema_version":"1.0"},"canonical_sha256":"c50a28376a118f78aab6255f5d9113979b17d43fec51ed7c2c5863aa18cd9a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:48.489978Z","signature_b64":"HQBHSVJWKtu3WPmuO3otxpLdwgJfy8jVJ2JByl7yO2PRIYBMa1x/TuEWb/79J4W77CBshPg2/E8l49ALl3/iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c50a28376a118f78aab6255f5d9113979b17d43fec51ed7c2c5863aa18cd9a56","last_reissued_at":"2026-05-18T01:07:48.489414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:48.489414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9608016","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Af6NnOurfGjPspaF/B9zBcLkNqyvC4qCHyNTpa4Km658NGh/BdhxZxfHz6ppLuBleqgQWqrr3h69fDTqRA1+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:48:11.345106Z"},"content_sha256":"fa4d4b04c7112643a9c47c2736efd24f605b695cd88c6b3d5adfeed3eb815eb2","schema_version":"1.0","event_id":"sha256:fa4d4b04c7112643a9c47c2736efd24f605b695cd88c6b3d5adfeed3eb815eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:YUFCQN3KCGHXRKVWEVPV3EITS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Thomae formula for $Z_N$ curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Atsushi Nakayashiki","submitted_at":"1996-08-20T12:59:01Z","abstract_excerpt":"We shall give an elementary and rigorous proof of the Thomae formula for ${\\bf Z}_N$ curves which was discovered by Bershadsky and Radul.  Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szeg\\\"{o} kernels and proves the vanishing of zero values of derivatives of theta functions with ${\\bf Z}_N$ invariant $1/2N$ characteristics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9608016","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaInxwxBkUO2TDhWmJQ9yaQkdJRGU+CNZve4OOMTwtAbCmLVwrPgSVCNge9ccJ+ziNPjDG0gk4hj0Td7pJ2ZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:48:11.345766Z"},"content_sha256":"3a35797b24cfa6dd63297456c3b4f499b0db93eff615bb5e6a7cc38a085ed2dd","schema_version":"1.0","event_id":"sha256:3a35797b24cfa6dd63297456c3b4f499b0db93eff615bb5e6a7cc38a085ed2dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/bundle.json","state_url":"https://pith.science/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T15:48:11Z","links":{"resolver":"https://pith.science/pith/YUFCQN3KCGHXRKVWEVPV3EITS6","bundle":"https://pith.science/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/bundle.json","state":"https://pith.science/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUFCQN3KCGHXRKVWEVPV3EITS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:YUFCQN3KCGHXRKVWEVPV3EITS6","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":"612e8b4c8f0e662cbf99423e198c50a845ab2b53b5e4f082b30ee6c4ee20a6f4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-08-20T12:59:01Z","title_canon_sha256":"074b6bef66e4e136b6f2c3cadf7db2f973ba4618f45b205cbe156ee9373a9c7f"},"schema_version":"1.0","source":{"id":"alg-geom/9608016","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9608016","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9608016v3","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9608016","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"YUFCQN3KCGHX","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YUFCQN3KCGHXRKVW","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YUFCQN3K","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:3a35797b24cfa6dd63297456c3b4f499b0db93eff615bb5e6a7cc38a085ed2dd","target":"graph","created_at":"2026-05-18T01:07:48Z","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":"We shall give an elementary and rigorous proof of the Thomae formula for ${\\bf Z}_N$ curves which was discovered by Bershadsky and Radul.  Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szeg\\\"{o} kernels and proves the vanishing of zero values of derivatives of theta functions with ${\\bf Z}_N$ invariant $1/2N$ characteristics.","authors_text":"Atsushi Nakayashiki","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1996-08-20T12:59:01Z","title":"On the Thomae formula for $Z_N$ curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9608016","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:fa4d4b04c7112643a9c47c2736efd24f605b695cd88c6b3d5adfeed3eb815eb2","target":"record","created_at":"2026-05-18T01:07:48Z","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":"612e8b4c8f0e662cbf99423e198c50a845ab2b53b5e4f082b30ee6c4ee20a6f4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-08-20T12:59:01Z","title_canon_sha256":"074b6bef66e4e136b6f2c3cadf7db2f973ba4618f45b205cbe156ee9373a9c7f"},"schema_version":"1.0","source":{"id":"alg-geom/9608016","kind":"arxiv","version":3}},"canonical_sha256":"c50a28376a118f78aab6255f5d9113979b17d43fec51ed7c2c5863aa18cd9a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c50a28376a118f78aab6255f5d9113979b17d43fec51ed7c2c5863aa18cd9a56","first_computed_at":"2026-05-18T01:07:48.489414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:48.489414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQBHSVJWKtu3WPmuO3otxpLdwgJfy8jVJ2JByl7yO2PRIYBMa1x/TuEWb/79J4W77CBshPg2/E8l49ALl3/iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:48.489978Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9608016","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa4d4b04c7112643a9c47c2736efd24f605b695cd88c6b3d5adfeed3eb815eb2","sha256:3a35797b24cfa6dd63297456c3b4f499b0db93eff615bb5e6a7cc38a085ed2dd"],"state_sha256":"187783441c435ad645eedcbc0e6368d0f9610e0b8b0b3015e147c53b16ed40b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jqZexSYWkVSra5quwEBUcw22NOiCAG6P07n8UfjUeuSDIUO6CFl04V+n9M3+Qt0ml7HnugU/3lGJz8GroyqrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:48:11.348572Z","bundle_sha256":"7296e5ac857046cf618590805e0981eee61d9b33b3e8404ad226cca2a9226a1d"}}