{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:K2JBXKH2DADSTHD6MXNTYS3TSN","short_pith_number":"pith:K2JBXKH2","canonical_record":{"source":{"id":"math-ph/0602017","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-02-07T15:39:27Z","cross_cats_sorted":["math.AC","math.MP"],"title_canon_sha256":"0367caf5b1f61e0b495c60eb49d2201010b77f79eb054cbf3049dced4d477823","abstract_canon_sha256":"0ab6ed21bfcf0faca348162819ca1a642f8272769d446dc2832c8ccae8099e24"},"schema_version":"1.0"},"canonical_sha256":"56921ba8fa1807299c7e65db3c4b739345449d6f84f02b6ffd1265df7716e834","source":{"kind":"arxiv","id":"math-ph/0602017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0602017","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0602017v1","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0602017","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"K2JBXKH2DADS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"K2JBXKH2DADSTHD6","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"K2JBXKH2","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:K2JBXKH2DADSTHD6MXNTYS3TSN","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0602017","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-02-07T15:39:27Z","cross_cats_sorted":["math.AC","math.MP"],"title_canon_sha256":"0367caf5b1f61e0b495c60eb49d2201010b77f79eb054cbf3049dced4d477823","abstract_canon_sha256":"0ab6ed21bfcf0faca348162819ca1a642f8272769d446dc2832c8ccae8099e24"},"schema_version":"1.0"},"canonical_sha256":"56921ba8fa1807299c7e65db3c4b739345449d6f84f02b6ffd1265df7716e834","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.981232Z","signature_b64":"0o06NIP1NYE1OfsKAGXe/kdnL5BEDUO1jeoDtOeX1guXHN0GXQK9ESyUGw50NZ3xnhfpoOfF1z+Lt3Kl0vUhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56921ba8fa1807299c7e65db3c4b739345449d6f84f02b6ffd1265df7716e834","last_reissued_at":"2026-05-18T01:30:15.980613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.980613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0602017","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGB03M4ss7lZ8oaLCOXU6AgPbMF46t7i3qI4XCPkd2OXyyP6JpFuWs0WpIZzRfb7JoZXqWZDLZYofmu+8DV2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:10:26.855239Z"},"content_sha256":"6cd43d0d0175cb49f64886ec380c8beda74a808b5ac33163dc43f0c2d5af41dc","schema_version":"1.0","event_id":"sha256:6cd43d0d0175cb49f64886ec380c8beda74a808b5ac33163dc43f0c2d5af41dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:K2JBXKH2DADSTHD6MXNTYS3TSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thomae type formulae for singular Z_N curves","license":"","headline":"","cross_cats":["math.AC","math.MP"],"primary_cat":"math-ph","authors_text":"Tamara Grava, Victor Enolskii","submitted_at":"2006-02-07T15:39:27Z","abstract_excerpt":"We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0602017","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Htpsj//3RVgwtAeQjvv0dgriWSHN8V6IJ/7xSnIWWPgql4lc2wDTFRzyZkVqv0fdmq7fWpob8vfQNsdzM2q0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:10:26.855959Z"},"content_sha256":"c5371a09261b762dd2bafa68dfb4306a92b4e999499d13067a4a2f1853cec96f","schema_version":"1.0","event_id":"sha256:c5371a09261b762dd2bafa68dfb4306a92b4e999499d13067a4a2f1853cec96f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/bundle.json","state_url":"https://pith.science/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/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":"2026-06-06T17:10:26Z","links":{"resolver":"https://pith.science/pith/K2JBXKH2DADSTHD6MXNTYS3TSN","bundle":"https://pith.science/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/bundle.json","state":"https://pith.science/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2JBXKH2DADSTHD6MXNTYS3TSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:K2JBXKH2DADSTHD6MXNTYS3TSN","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":"0ab6ed21bfcf0faca348162819ca1a642f8272769d446dc2832c8ccae8099e24","cross_cats_sorted":["math.AC","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-02-07T15:39:27Z","title_canon_sha256":"0367caf5b1f61e0b495c60eb49d2201010b77f79eb054cbf3049dced4d477823"},"schema_version":"1.0","source":{"id":"math-ph/0602017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0602017","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0602017v1","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0602017","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"K2JBXKH2DADS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"K2JBXKH2DADSTHD6","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"K2JBXKH2","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:c5371a09261b762dd2bafa68dfb4306a92b4e999499d13067a4a2f1853cec96f","target":"graph","created_at":"2026-05-18T01:30:15Z","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 give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.","authors_text":"Tamara Grava, Victor Enolskii","cross_cats":["math.AC","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-02-07T15:39:27Z","title":"Thomae type formulae for singular Z_N curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0602017","kind":"arxiv","version":1},"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":"sha256:6cd43d0d0175cb49f64886ec380c8beda74a808b5ac33163dc43f0c2d5af41dc","target":"record","created_at":"2026-05-18T01:30:15Z","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":"0ab6ed21bfcf0faca348162819ca1a642f8272769d446dc2832c8ccae8099e24","cross_cats_sorted":["math.AC","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-02-07T15:39:27Z","title_canon_sha256":"0367caf5b1f61e0b495c60eb49d2201010b77f79eb054cbf3049dced4d477823"},"schema_version":"1.0","source":{"id":"math-ph/0602017","kind":"arxiv","version":1}},"canonical_sha256":"56921ba8fa1807299c7e65db3c4b739345449d6f84f02b6ffd1265df7716e834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56921ba8fa1807299c7e65db3c4b739345449d6f84f02b6ffd1265df7716e834","first_computed_at":"2026-05-18T01:30:15.980613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.980613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0o06NIP1NYE1OfsKAGXe/kdnL5BEDUO1jeoDtOeX1guXHN0GXQK9ESyUGw50NZ3xnhfpoOfF1z+Lt3Kl0vUhCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.981232Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0602017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cd43d0d0175cb49f64886ec380c8beda74a808b5ac33163dc43f0c2d5af41dc","sha256:c5371a09261b762dd2bafa68dfb4306a92b4e999499d13067a4a2f1853cec96f"],"state_sha256":"1272030714178ac1535d0511a3ca2901a5a8c3cff056b3cdb79467e31189e35c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"op2kSFZseuZY2Nk+W7bMhrmw/HmtktAobpMBgqvR0qRcs0Uh/TMVsBPCE3L9+PiA/LHlRkCYcNqmeSekJKipCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:10:26.859835Z","bundle_sha256":"b4ce392449f27c0e99b449c32f615d9514c07d7a19085813483045bd3a8d76da"}}