{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EGR7NPGDGOL5A3I2XAGIIHANL3","short_pith_number":"pith:EGR7NPGD","canonical_record":{"source":{"id":"1512.08524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-12-28T21:01:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d1da16d1333300ec87fc23a7cc592284c51c1d0472172d3b521af073ad424f1f","abstract_canon_sha256":"9a73658028ba4651cbe19a6d91e68f742a976aed0bf8f072c80dfc3eac0cb633"},"schema_version":"1.0"},"canonical_sha256":"21a3f6bcc33397d06d1ab80c841c0d5ece376def39546475d1ca23ba9f196b67","source":{"kind":"arxiv","id":"1512.08524","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08524","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08524v2","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08524","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"EGR7NPGDGOL5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EGR7NPGDGOL5A3I2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EGR7NPGD","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EGR7NPGDGOL5A3I2XAGIIHANL3","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-12-28T21:01:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d1da16d1333300ec87fc23a7cc592284c51c1d0472172d3b521af073ad424f1f","abstract_canon_sha256":"9a73658028ba4651cbe19a6d91e68f742a976aed0bf8f072c80dfc3eac0cb633"},"schema_version":"1.0"},"canonical_sha256":"21a3f6bcc33397d06d1ab80c841c0d5ece376def39546475d1ca23ba9f196b67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:25.771090Z","signature_b64":"VEdqHGs9aOhHFVf0ocLGlkzpgO/NqnG5SGUOWgQwGUfqweLF6pJ2AenTbKzkOv5ZQvB8lNwPUAHvTzK7IJGlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21a3f6bcc33397d06d1ab80c841c0d5ece376def39546475d1ca23ba9f196b67","last_reissued_at":"2026-05-18T01:00:25.770577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:25.770577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08524","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjx04KgTZnrJyIPVuXG+xv3HtrzctimPwqAdJ5o+t1OySBU4v4Va465+vXs9tFkHDdjHTONnVBSMNQ1+GXwMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:56:28.390881Z"},"content_sha256":"85f7ee7d34dacee5cf04a459ac2004a3c979a38d7a6855d53e128fc6b640ecdd","schema_version":"1.0","event_id":"sha256:85f7ee7d34dacee5cf04a459ac2004a3c979a38d7a6855d53e128fc6b640ecdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EGR7NPGDGOL5A3I2XAGIIHANL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Gaudin model associated to Lie algebras of classical types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"A. Varchenko, E. Mukhin, Kang Lu","submitted_at":"2015-12-28T21:01:44Z","abstract_excerpt":"We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe Ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We also show that except for the type D, the joint spectrum of Gaudin Hamiltonians in such tensor products is simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08524","kind":"arxiv","version":2},"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":"2026-05-18T01:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xNFY/ooh70SjnxRRXfA+SsnnRxOToU5IYMqTSi6VO9DQwGn6nGA2qV3LBfjh6gLXgk73y67X70K0OClW7E5nCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:56:28.391231Z"},"content_sha256":"db98a7a4032806fa1392e4319d2cf8c85d88edad55d8f8408c9e440862292e8a","schema_version":"1.0","event_id":"sha256:db98a7a4032806fa1392e4319d2cf8c85d88edad55d8f8408c9e440862292e8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/bundle.json","state_url":"https://pith.science/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/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":"2026-06-10T21:56:28Z","links":{"resolver":"https://pith.science/pith/EGR7NPGDGOL5A3I2XAGIIHANL3","bundle":"https://pith.science/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/bundle.json","state":"https://pith.science/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGR7NPGDGOL5A3I2XAGIIHANL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EGR7NPGDGOL5A3I2XAGIIHANL3","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":"9a73658028ba4651cbe19a6d91e68f742a976aed0bf8f072c80dfc3eac0cb633","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-12-28T21:01:44Z","title_canon_sha256":"d1da16d1333300ec87fc23a7cc592284c51c1d0472172d3b521af073ad424f1f"},"schema_version":"1.0","source":{"id":"1512.08524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08524","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08524v2","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08524","created_at":"2026-05-18T01:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"EGR7NPGDGOL5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EGR7NPGDGOL5A3I2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EGR7NPGD","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:db98a7a4032806fa1392e4319d2cf8c85d88edad55d8f8408c9e440862292e8a","target":"graph","created_at":"2026-05-18T01:00:25Z","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 derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe Ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We also show that except for the type D, the joint spectrum of Gaudin Hamiltonians in such tensor products is simple.","authors_text":"A. Varchenko, E. Mukhin, Kang Lu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-12-28T21:01:44Z","title":"On the Gaudin model associated to Lie algebras of classical types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08524","kind":"arxiv","version":2},"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":"sha256:85f7ee7d34dacee5cf04a459ac2004a3c979a38d7a6855d53e128fc6b640ecdd","target":"record","created_at":"2026-05-18T01:00:25Z","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":"9a73658028ba4651cbe19a6d91e68f742a976aed0bf8f072c80dfc3eac0cb633","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-12-28T21:01:44Z","title_canon_sha256":"d1da16d1333300ec87fc23a7cc592284c51c1d0472172d3b521af073ad424f1f"},"schema_version":"1.0","source":{"id":"1512.08524","kind":"arxiv","version":2}},"canonical_sha256":"21a3f6bcc33397d06d1ab80c841c0d5ece376def39546475d1ca23ba9f196b67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a3f6bcc33397d06d1ab80c841c0d5ece376def39546475d1ca23ba9f196b67","first_computed_at":"2026-05-18T01:00:25.770577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:25.770577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VEdqHGs9aOhHFVf0ocLGlkzpgO/NqnG5SGUOWgQwGUfqweLF6pJ2AenTbKzkOv5ZQvB8lNwPUAHvTzK7IJGlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:25.771090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85f7ee7d34dacee5cf04a459ac2004a3c979a38d7a6855d53e128fc6b640ecdd","sha256:db98a7a4032806fa1392e4319d2cf8c85d88edad55d8f8408c9e440862292e8a"],"state_sha256":"57a7e4d89daeafac932371d02e4042636c8be3a81be562e63045763bf94f2e46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVmjwZjX2OzKOxPZA+pLKrvabjIfeRmZ4LpZCWxrRzK5gKKg2isfPm7l73gHp42Fi8Ff1Su4MKDNAKtCL/DZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:56:28.393188Z","bundle_sha256":"2fe6808263cfac867e9e25231dd7c3dbb817387ec0c18b62c55abe7e17bf6675"}}