{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GOKDLH4LMRB43QG7GM444PCIEY","short_pith_number":"pith:GOKDLH4L","canonical_record":{"source":{"id":"1309.0580","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-03T03:45:38Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"032a928c353779d2c212b827b33a963e1f67d8b1b9b07914ce96127a4e1809e7","abstract_canon_sha256":"a08ff91e8c81124b36d6a98d598cf4d4c160d283763add5ef633852800060e58"},"schema_version":"1.0"},"canonical_sha256":"3394359f8b6443cdc0df3339ce3c48260247b2f29b904533e10a3a03fd8c8402","source":{"kind":"arxiv","id":"1309.0580","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0580","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0580v6","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0580","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"GOKDLH4LMRB4","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_16","alias_value":"GOKDLH4LMRB43QG7","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_8","alias_value":"GOKDLH4L","created_at":"2026-07-05T01:43:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GOKDLH4LMRB43QG7GM444PCIEY","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0580","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-03T03:45:38Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"032a928c353779d2c212b827b33a963e1f67d8b1b9b07914ce96127a4e1809e7","abstract_canon_sha256":"a08ff91e8c81124b36d6a98d598cf4d4c160d283763add5ef633852800060e58"},"schema_version":"1.0"},"canonical_sha256":"3394359f8b6443cdc0df3339ce3c48260247b2f29b904533e10a3a03fd8c8402","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:43:36.174411Z","signature_b64":"jsTqwjX20RQxAH7g3ubRBEiJVy4Pvy7XLd7qat3BGymLWbcQPLEC3Grx9jtTDbBFzzCenKnmlRaJA5UXoDSlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3394359f8b6443cdc0df3339ce3c48260247b2f29b904533e10a3a03fd8c8402","last_reissued_at":"2026-07-05T01:43:36.174009Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:43:36.174009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0580","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJp2knuwta2OlQeJ6hynW+fn8eRAbf6kJdsSUCf5DfnY3N06SGqNb4zIPzIiaxpFoc7/vW3afMsneMD8OptxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:36:00.727033Z"},"content_sha256":"f51015dd91fb6855b55cc5e80f0ae72976c81d3135b2ec299d0f8e87007b5691","schema_version":"1.0","event_id":"sha256:f51015dd91fb6855b55cc5e80f0ae72976c81d3135b2ec299d0f8e87007b5691"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GOKDLH4LMRB43QG7GM444PCIEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on the Universal Elliptic KZB Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Richard Hain","submitted_at":"2013-09-03T03:45:38Z","abstract_excerpt":"The universal elliptic KZB equation is the integrable connection on the pro-vector bundle over M_{1,2} whose fiber over the point corresponding to the elliptic curve E and a non-zero point x of E is the unipotent completion of \\pi_1(E-{0},x). This was written down independently by Calaque, Enriquez and Etingof (arXiv:math/0702670), and by Levin and Racinet (arXiv:math/0703237). It generalizes the KZ-equation in genus 0. These notes are in four parts. The first two parts provide a detailed exposition of this connection (following Levin-Racinet); the third is a leisurely exploration of the conne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0580","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1309.0580/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpW6PzUdLi15mjZY4OMTOey8rhRLss9Ve3NhiJLG8MxwPZgA+S7TAf4qlXBdgi70SKEhrLVWr1cEvegFJP9mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:36:00.727611Z"},"content_sha256":"935863c39cfb716d4f6aceec0263ca2ab2297cccc9d244f62150a0fc247bf906","schema_version":"1.0","event_id":"sha256:935863c39cfb716d4f6aceec0263ca2ab2297cccc9d244f62150a0fc247bf906"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOKDLH4LMRB43QG7GM444PCIEY/bundle.json","state_url":"https://pith.science/pith/GOKDLH4LMRB43QG7GM444PCIEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOKDLH4LMRB43QG7GM444PCIEY/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":"2026-08-16T01:36:00Z","links":{"resolver":"https://pith.science/pith/GOKDLH4LMRB43QG7GM444PCIEY","bundle":"https://pith.science/pith/GOKDLH4LMRB43QG7GM444PCIEY/bundle.json","state":"https://pith.science/pith/GOKDLH4LMRB43QG7GM444PCIEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOKDLH4LMRB43QG7GM444PCIEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GOKDLH4LMRB43QG7GM444PCIEY","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":"a08ff91e8c81124b36d6a98d598cf4d4c160d283763add5ef633852800060e58","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-03T03:45:38Z","title_canon_sha256":"032a928c353779d2c212b827b33a963e1f67d8b1b9b07914ce96127a4e1809e7"},"schema_version":"1.0","source":{"id":"1309.0580","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0580","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0580v6","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0580","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"GOKDLH4LMRB4","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_16","alias_value":"GOKDLH4LMRB43QG7","created_at":"2026-07-05T01:43:36Z"},{"alias_kind":"pith_short_8","alias_value":"GOKDLH4L","created_at":"2026-07-05T01:43:36Z"}],"graph_snapshots":[{"event_id":"sha256:935863c39cfb716d4f6aceec0263ca2ab2297cccc9d244f62150a0fc247bf906","target":"graph","created_at":"2026-07-05T01:43:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1309.0580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The universal elliptic KZB equation is the integrable connection on the pro-vector bundle over M_{1,2} whose fiber over the point corresponding to the elliptic curve E and a non-zero point x of E is the unipotent completion of \\pi_1(E-{0},x). This was written down independently by Calaque, Enriquez and Etingof (arXiv:math/0702670), and by Levin and Racinet (arXiv:math/0703237). It generalizes the KZ-equation in genus 0. These notes are in four parts. The first two parts provide a detailed exposition of this connection (following Levin-Racinet); the third is a leisurely exploration of the conne","authors_text":"Richard Hain","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-03T03:45:38Z","title":"Notes on the Universal Elliptic KZB Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0580","kind":"arxiv","version":6},"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:f51015dd91fb6855b55cc5e80f0ae72976c81d3135b2ec299d0f8e87007b5691","target":"record","created_at":"2026-07-05T01:43:36Z","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":"a08ff91e8c81124b36d6a98d598cf4d4c160d283763add5ef633852800060e58","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-03T03:45:38Z","title_canon_sha256":"032a928c353779d2c212b827b33a963e1f67d8b1b9b07914ce96127a4e1809e7"},"schema_version":"1.0","source":{"id":"1309.0580","kind":"arxiv","version":6}},"canonical_sha256":"3394359f8b6443cdc0df3339ce3c48260247b2f29b904533e10a3a03fd8c8402","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3394359f8b6443cdc0df3339ce3c48260247b2f29b904533e10a3a03fd8c8402","first_computed_at":"2026-07-05T01:43:36.174009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:43:36.174009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jsTqwjX20RQxAH7g3ubRBEiJVy4Pvy7XLd7qat3BGymLWbcQPLEC3Grx9jtTDbBFzzCenKnmlRaJA5UXoDSlCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:43:36.174411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0580","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f51015dd91fb6855b55cc5e80f0ae72976c81d3135b2ec299d0f8e87007b5691","sha256:935863c39cfb716d4f6aceec0263ca2ab2297cccc9d244f62150a0fc247bf906"],"state_sha256":"38e6eb1adb08f5fc40a72eb97b53245995cc8de1ecfb32a722dcf3af5560c11e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvOO2BHFeU0UY+SxfVl86JxPcBY/XKgejdScX7NAUsp9wLil6/AbV/o6qc1cSYrjvPruBhmOKnAGY0MBh77GDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:36:00.731600Z","bundle_sha256":"3a40cb84b9f6453902b4a01d7e83e8da6722b59fb2ac9c564e0f89cdea000dec"}}