{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PRIYMN6DF5PUCDOBPTYDSC4II4","short_pith_number":"pith:PRIYMN6D","canonical_record":{"source":{"id":"2501.00401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-31T11:40:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5e2a3270c0f0aee61e60434361f7f46659255064d1515375a8e45df8791e4a7c","abstract_canon_sha256":"66ade2cdc51b96e9813632cb657580b149da4332d1e7d42a7850c1559d6a2456"},"schema_version":"1.0"},"canonical_sha256":"7c518637c32f5f410dc17cf0390b884733003c495730606dbce02e45c61f316e","source":{"kind":"arxiv","id":"2501.00401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.00401","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"arxiv_version","alias_value":"2501.00401v1","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.00401","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_12","alias_value":"PRIYMN6DF5PU","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_16","alias_value":"PRIYMN6DF5PUCDOB","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_8","alias_value":"PRIYMN6D","created_at":"2026-07-05T09:55:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PRIYMN6DF5PUCDOBPTYDSC4II4","target":"record","payload":{"canonical_record":{"source":{"id":"2501.00401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-31T11:40:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5e2a3270c0f0aee61e60434361f7f46659255064d1515375a8e45df8791e4a7c","abstract_canon_sha256":"66ade2cdc51b96e9813632cb657580b149da4332d1e7d42a7850c1559d6a2456"},"schema_version":"1.0"},"canonical_sha256":"7c518637c32f5f410dc17cf0390b884733003c495730606dbce02e45c61f316e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:44.536402Z","signature_b64":"vc7xUTd/pXt8xYBHOKPHDhgtEcW1EnrI8H8D8X0UwCFiwRSv4mRxn7P2fmtRjcameE2b1njq13VIMEwHZxXABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c518637c32f5f410dc17cf0390b884733003c495730606dbce02e45c61f316e","last_reissued_at":"2026-07-05T09:55:44.535968Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:44.535968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.00401","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":"2026-07-05T09:55:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twVNLqyU9EAWyfhAMhO8hrcVYyhidNxoRhBMul0bxVWe3nGmFyOuB5wFuVHKsYXE439Wch2EhpBQI9ZzHHQXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:23:02.077415Z"},"content_sha256":"63b93bdda1efa53f58885978a29764072b23acdf1e9cc35138e288230c14bb78","schema_version":"1.0","event_id":"sha256:63b93bdda1efa53f58885978a29764072b23acdf1e9cc35138e288230c14bb78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PRIYMN6DF5PUCDOBPTYDSC4II4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Gaudin model for the general linear Lie superalgebra and the completeness of the Bethe ansatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Ngau Lam, Wan Keng Cheong","submitted_at":"2024-12-31T11:40:54Z","abstract_excerpt":"Let $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$ be the Gaudin algebra of the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}$ with respect to a sequence $\\underline{\\boldsymbol{z}} \\in \\mathbb{C}^\\ell$ of pairwise distinct complex numbers, and let $M$ be any $\\ell$-fold tensor product of irreducible polynomial modules over $\\mathfrak{gl}_{m|n}$. We show that the singular space $M^{\\rm sing}$ of $M$ is a cyclic $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$-module and the Gaudin algebra $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})_{M^{\\rm sing}}$ of $M^{\\rm sing}$ is a Frobenius "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00401/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":"2026-07-05T09:55:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/LpAhWtLikfRP4HJT9PRZaVRRYRTuVpPMD349JFgSrMQ+5RmhgucJ8znJbU2ejgQe3FnINoAwRz4UTmmiNzzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:23:02.077893Z"},"content_sha256":"6c8fb42202fe7216202ebeccac081d9f78afe618e6e4b1d1e59d4680a1ea4463","schema_version":"1.0","event_id":"sha256:6c8fb42202fe7216202ebeccac081d9f78afe618e6e4b1d1e59d4680a1ea4463"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/bundle.json","state_url":"https://pith.science/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/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":"2026-08-13T14:23:02Z","links":{"resolver":"https://pith.science/pith/PRIYMN6DF5PUCDOBPTYDSC4II4","bundle":"https://pith.science/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/bundle.json","state":"https://pith.science/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRIYMN6DF5PUCDOBPTYDSC4II4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PRIYMN6DF5PUCDOBPTYDSC4II4","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":"66ade2cdc51b96e9813632cb657580b149da4332d1e7d42a7850c1559d6a2456","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-31T11:40:54Z","title_canon_sha256":"5e2a3270c0f0aee61e60434361f7f46659255064d1515375a8e45df8791e4a7c"},"schema_version":"1.0","source":{"id":"2501.00401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.00401","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"arxiv_version","alias_value":"2501.00401v1","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.00401","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_12","alias_value":"PRIYMN6DF5PU","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_16","alias_value":"PRIYMN6DF5PUCDOB","created_at":"2026-07-05T09:55:44Z"},{"alias_kind":"pith_short_8","alias_value":"PRIYMN6D","created_at":"2026-07-05T09:55:44Z"}],"graph_snapshots":[{"event_id":"sha256:6c8fb42202fe7216202ebeccac081d9f78afe618e6e4b1d1e59d4680a1ea4463","target":"graph","created_at":"2026-07-05T09:55:44Z","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/2501.00401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$ be the Gaudin algebra of the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}$ with respect to a sequence $\\underline{\\boldsymbol{z}} \\in \\mathbb{C}^\\ell$ of pairwise distinct complex numbers, and let $M$ be any $\\ell$-fold tensor product of irreducible polynomial modules over $\\mathfrak{gl}_{m|n}$. We show that the singular space $M^{\\rm sing}$ of $M$ is a cyclic $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$-module and the Gaudin algebra $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})_{M^{\\rm sing}}$ of $M^{\\rm sing}$ is a Frobenius ","authors_text":"Ngau Lam, Wan Keng Cheong","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-31T11:40:54Z","title":"The Gaudin model for the general linear Lie superalgebra and the completeness of the Bethe ansatz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00401","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":"sha256:63b93bdda1efa53f58885978a29764072b23acdf1e9cc35138e288230c14bb78","target":"record","created_at":"2026-07-05T09:55:44Z","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":"66ade2cdc51b96e9813632cb657580b149da4332d1e7d42a7850c1559d6a2456","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-31T11:40:54Z","title_canon_sha256":"5e2a3270c0f0aee61e60434361f7f46659255064d1515375a8e45df8791e4a7c"},"schema_version":"1.0","source":{"id":"2501.00401","kind":"arxiv","version":1}},"canonical_sha256":"7c518637c32f5f410dc17cf0390b884733003c495730606dbce02e45c61f316e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c518637c32f5f410dc17cf0390b884733003c495730606dbce02e45c61f316e","first_computed_at":"2026-07-05T09:55:44.535968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:44.535968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vc7xUTd/pXt8xYBHOKPHDhgtEcW1EnrI8H8D8X0UwCFiwRSv4mRxn7P2fmtRjcameE2b1njq13VIMEwHZxXABQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:44.536402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.00401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b93bdda1efa53f58885978a29764072b23acdf1e9cc35138e288230c14bb78","sha256:6c8fb42202fe7216202ebeccac081d9f78afe618e6e4b1d1e59d4680a1ea4463"],"state_sha256":"a8597c14fa63b3bf24d25f0e741a9239b5d74fe70bfbcf96ccfba16c6b965331"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ts/Fxi9DMyuZVcxhK9b3bHpfIGgYNqUmPlGnwAt6IKgFeffQ5HKVD/YbEmYTm2bHBeF/agGumNZ8IsZoKgE9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:23:02.081180Z","bundle_sha256":"328a53239ed038f2824d2b531147bfcfe80151c95aad31e6083b600d73860993"}}