{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V7B4DB42644KXVWM3TC6M2J54V","short_pith_number":"pith:V7B4DB42","canonical_record":{"source":{"id":"1308.6374","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-29T06:31:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8c4726cd53510a8a327a4cc13b2acca6e6e3c7937a216068a0470df37acdfd53","abstract_canon_sha256":"0ebbdc2a5827e14c1d4e5d6595245a23a123eb4c1a3049fd73581ce2f9eadf83"},"schema_version":"1.0"},"canonical_sha256":"afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188","source":{"kind":"arxiv","id":"1308.6374","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6374","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6374v4","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6374","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"V7B4DB42644K","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7B4DB42644KXVWM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7B4DB42","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V7B4DB42644KXVWM3TC6M2J54V","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6374","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-29T06:31:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8c4726cd53510a8a327a4cc13b2acca6e6e3c7937a216068a0470df37acdfd53","abstract_canon_sha256":"0ebbdc2a5827e14c1d4e5d6595245a23a123eb4c1a3049fd73581ce2f9eadf83"},"schema_version":"1.0"},"canonical_sha256":"afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:26.726863Z","signature_b64":"rX/3W0NXbiLpJ8aZDeER6ryxdr5v8+glyVfY8BBmYCM+F1BGVwvF/4H6fYN7wIq6V8vUEf8mvKNvSh3v2WFvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188","last_reissued_at":"2026-05-18T02:25:26.726018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:26.726018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6374","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDssib8RRrr9GzwGxjvbE89YI+e5sziYjR6pzo3xOmjBUxMcPGimZbMsVeCEL8Xejujy2IKLhCDrR0nQu6I6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:35:50.902046Z"},"content_sha256":"f4d5127a610d968eadd4c461323e22868e6f5c5a1819daa909b33bc4f0e48860","schema_version":"1.0","event_id":"sha256:f4d5127a610d968eadd4c461323e22868e6f5c5a1819daa909b33bc4f0e48860"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V7B4DB42644KXVWM3TC6M2J54V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Albert Schwarz, Jia-Ming Liou, Renjun Xu","submitted_at":"2013-08-29T06:31:43Z","abstract_excerpt":"We analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $\\leq 6$. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for lower genera."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6374","kind":"arxiv","version":4},"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":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqtJruWIyyQz1hA4pUkuf+XQS3bx7nx9EzDGORcUhj4qWfEbUJyjuAoXbHjHh9kePrqJZZi+QtHUOsDG70NrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:35:50.902805Z"},"content_sha256":"d796d1dabf43e42018ace3597feae581c5878a6f4722f676225caa296129333a","schema_version":"1.0","event_id":"sha256:d796d1dabf43e42018ace3597feae581c5878a6f4722f676225caa296129333a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7B4DB42644KXVWM3TC6M2J54V/bundle.json","state_url":"https://pith.science/pith/V7B4DB42644KXVWM3TC6M2J54V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7B4DB42644KXVWM3TC6M2J54V/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":"2026-06-05T01:35:50Z","links":{"resolver":"https://pith.science/pith/V7B4DB42644KXVWM3TC6M2J54V","bundle":"https://pith.science/pith/V7B4DB42644KXVWM3TC6M2J54V/bundle.json","state":"https://pith.science/pith/V7B4DB42644KXVWM3TC6M2J54V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7B4DB42644KXVWM3TC6M2J54V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V7B4DB42644KXVWM3TC6M2J54V","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":"0ebbdc2a5827e14c1d4e5d6595245a23a123eb4c1a3049fd73581ce2f9eadf83","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-29T06:31:43Z","title_canon_sha256":"8c4726cd53510a8a327a4cc13b2acca6e6e3c7937a216068a0470df37acdfd53"},"schema_version":"1.0","source":{"id":"1308.6374","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6374","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6374v4","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6374","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"V7B4DB42644K","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7B4DB42644KXVWM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7B4DB42","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:d796d1dabf43e42018ace3597feae581c5878a6f4722f676225caa296129333a","target":"graph","created_at":"2026-05-18T02:25:26Z","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 analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $\\leq 6$. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for lower genera.","authors_text":"Albert Schwarz, Jia-Ming Liou, Renjun Xu","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-29T06:31:43Z","title":"Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6374","kind":"arxiv","version":4},"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:f4d5127a610d968eadd4c461323e22868e6f5c5a1819daa909b33bc4f0e48860","target":"record","created_at":"2026-05-18T02:25:26Z","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":"0ebbdc2a5827e14c1d4e5d6595245a23a123eb4c1a3049fd73581ce2f9eadf83","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-29T06:31:43Z","title_canon_sha256":"8c4726cd53510a8a327a4cc13b2acca6e6e3c7937a216068a0470df37acdfd53"},"schema_version":"1.0","source":{"id":"1308.6374","kind":"arxiv","version":4}},"canonical_sha256":"afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188","first_computed_at":"2026-05-18T02:25:26.726018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:26.726018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rX/3W0NXbiLpJ8aZDeER6ryxdr5v8+glyVfY8BBmYCM+F1BGVwvF/4H6fYN7wIq6V8vUEf8mvKNvSh3v2WFvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:26.726863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6374","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d5127a610d968eadd4c461323e22868e6f5c5a1819daa909b33bc4f0e48860","sha256:d796d1dabf43e42018ace3597feae581c5878a6f4722f676225caa296129333a"],"state_sha256":"462c4aeed6b6c3c0f9902bd35b0e5bb02de0e5501563e6a17051930c402679f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiRikx3hbTuqKEDLlCASM5GcYcJV4QVj3pRg0vG8dB5x5e389tXSuSYPzm+U7s1V2UUgOo/16RpoMeuPLurXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:35:50.907035Z","bundle_sha256":"ef2c274669eb1deb315aee3eda5bf7ba28205c5f066c9e75fa78246a4dca954a"}}