{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2NYJHTU7CG7ZS2WNFL67CYLVK4","short_pith_number":"pith:2NYJHTU7","canonical_record":{"source":{"id":"1503.03279","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-11T11:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"713b45ed99c26d7d9ae8158e70017fd32b4531ab837faca79b1af29d1b48a659","abstract_canon_sha256":"bc3008095c6d9aed89f707fe2a052ca10336e85e64425f2d3adcb4ee55cb4233"},"schema_version":"1.0"},"canonical_sha256":"d37093ce9f11bf996acd2afdf161755710bbdfee92b621b7d26e3db88d809d07","source":{"kind":"arxiv","id":"1503.03279","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03279","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03279v3","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03279","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"2NYJHTU7CG7Z","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NYJHTU7CG7ZS2WN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NYJHTU7","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2NYJHTU7CG7ZS2WNFL67CYLVK4","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03279","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-11T11:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"713b45ed99c26d7d9ae8158e70017fd32b4531ab837faca79b1af29d1b48a659","abstract_canon_sha256":"bc3008095c6d9aed89f707fe2a052ca10336e85e64425f2d3adcb4ee55cb4233"},"schema_version":"1.0"},"canonical_sha256":"d37093ce9f11bf996acd2afdf161755710bbdfee92b621b7d26e3db88d809d07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:33.757798Z","signature_b64":"4kdpPwcpI2ViV7hfsMk2C6n2j5D0az+VWgLe/ryYU0jbYcdwAS4Gw6RpllWUkJJZy0dkfb94arJSWLyO2o+xBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d37093ce9f11bf996acd2afdf161755710bbdfee92b621b7d26e3db88d809d07","last_reissued_at":"2026-05-18T01:36:33.757294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:33.757294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03279","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":"2026-05-18T01:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Geg1hsAogxIl4YCX9FHz7qPjLC5p9xtJ10h2semRY5x8PT9yOvb3JcB9tDkOol2zUeWcdwr/5mYAsyoecPKwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:19.317990Z"},"content_sha256":"fa7827420ef0b3d6c0eef51f9e4e719acbabd9f99b8af8eedf6b860b9b9aa901","schema_version":"1.0","event_id":"sha256:fa7827420ef0b3d6c0eef51f9e4e719acbabd9f99b8af8eedf6b860b9b9aa901"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2NYJHTU7CG7ZS2WNFL67CYLVK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Universal Central Extension of Hyperelliptic Current Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ben Cox","submitted_at":"2015-03-11T11:31:41Z","abstract_excerpt":"Let $p(t)\\in\\mathbb C[t]$ be a polynomial with distinct roots and nonzero constant term. We describe, using Fa\\'a de Bruno's formula and Bell polynomials, the universal central extension in terms of generators and relations for the hyperelliptic current Lie algebras $\\mathfrak g\\otimes R$ whose coordinate ring is of the form $R=\\mathbb C[t,t^{-1},u\\,|\\, u^2=p(t)]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03279","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":"2026-05-18T01:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evS1GZZ1vhlo1jZvw9gvcFItwQWhOIt+tVYFhL2g5vc0TXSqv1lHVp3pCUgXtteobr6ttXqa1PlXSZU0+PRCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:19.318658Z"},"content_sha256":"85006efd4a7ec023ecc732353b44075af841665915eb3223c07fa117bb14e40c","schema_version":"1.0","event_id":"sha256:85006efd4a7ec023ecc732353b44075af841665915eb3223c07fa117bb14e40c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/bundle.json","state_url":"https://pith.science/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/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":"2026-05-31T01:33:19Z","links":{"resolver":"https://pith.science/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4","bundle":"https://pith.science/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/bundle.json","state":"https://pith.science/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NYJHTU7CG7ZS2WNFL67CYLVK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NYJHTU7CG7ZS2WNFL67CYLVK4","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":"bc3008095c6d9aed89f707fe2a052ca10336e85e64425f2d3adcb4ee55cb4233","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-11T11:31:41Z","title_canon_sha256":"713b45ed99c26d7d9ae8158e70017fd32b4531ab837faca79b1af29d1b48a659"},"schema_version":"1.0","source":{"id":"1503.03279","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03279","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03279v3","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03279","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"2NYJHTU7CG7Z","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NYJHTU7CG7ZS2WN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NYJHTU7","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:85006efd4a7ec023ecc732353b44075af841665915eb3223c07fa117bb14e40c","target":"graph","created_at":"2026-05-18T01:36:33Z","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 $p(t)\\in\\mathbb C[t]$ be a polynomial with distinct roots and nonzero constant term. We describe, using Fa\\'a de Bruno's formula and Bell polynomials, the universal central extension in terms of generators and relations for the hyperelliptic current Lie algebras $\\mathfrak g\\otimes R$ whose coordinate ring is of the form $R=\\mathbb C[t,t^{-1},u\\,|\\, u^2=p(t)]$.","authors_text":"Ben Cox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-11T11:31:41Z","title":"On the Universal Central Extension of Hyperelliptic Current Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03279","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:fa7827420ef0b3d6c0eef51f9e4e719acbabd9f99b8af8eedf6b860b9b9aa901","target":"record","created_at":"2026-05-18T01:36:33Z","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":"bc3008095c6d9aed89f707fe2a052ca10336e85e64425f2d3adcb4ee55cb4233","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-11T11:31:41Z","title_canon_sha256":"713b45ed99c26d7d9ae8158e70017fd32b4531ab837faca79b1af29d1b48a659"},"schema_version":"1.0","source":{"id":"1503.03279","kind":"arxiv","version":3}},"canonical_sha256":"d37093ce9f11bf996acd2afdf161755710bbdfee92b621b7d26e3db88d809d07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d37093ce9f11bf996acd2afdf161755710bbdfee92b621b7d26e3db88d809d07","first_computed_at":"2026-05-18T01:36:33.757294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:33.757294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4kdpPwcpI2ViV7hfsMk2C6n2j5D0az+VWgLe/ryYU0jbYcdwAS4Gw6RpllWUkJJZy0dkfb94arJSWLyO2o+xBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:33.757798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03279","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa7827420ef0b3d6c0eef51f9e4e719acbabd9f99b8af8eedf6b860b9b9aa901","sha256:85006efd4a7ec023ecc732353b44075af841665915eb3223c07fa117bb14e40c"],"state_sha256":"44fdcefb41f3933c9f6e79dcd7ef739ce5d08a4fdadf2fee92841ac5d45b601d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1vofmi8lbqYaiS+Sveb/tCR4/hGMaiI9B2K3PzxfdCVFgBYatGeVrlPvL5uBiVo406fb14/+G8uysQsUnXgDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:33:19.321673Z","bundle_sha256":"037aed42f7cace38c934b32ae460ce2154216ef2838b7853d2297998e93ecc18"}}