{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2DABR24P3NGBZB4YWMD7TMWJO4","short_pith_number":"pith:2DABR24P","canonical_record":{"source":{"id":"1809.08172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-21T15:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"1d2744227cfd3efe21ad6f38ad609757817f91d84d52622ccc85302a0a4630b5","abstract_canon_sha256":"a3709e5e60984b715948ee07d587cbfdd72090ecde6e3fbb8dd3f2209c9031e0"},"schema_version":"1.0"},"canonical_sha256":"d0c018eb8fdb4c1c8798b307f9b2c9771d796e8cdf0434cfa34db3d584d7a47d","source":{"kind":"arxiv","id":"1809.08172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08172","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08172v1","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08172","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"2DABR24P3NGB","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2DABR24P3NGBZB4Y","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2DABR24P","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2DABR24P3NGBZB4YWMD7TMWJO4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-21T15:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"1d2744227cfd3efe21ad6f38ad609757817f91d84d52622ccc85302a0a4630b5","abstract_canon_sha256":"a3709e5e60984b715948ee07d587cbfdd72090ecde6e3fbb8dd3f2209c9031e0"},"schema_version":"1.0"},"canonical_sha256":"d0c018eb8fdb4c1c8798b307f9b2c9771d796e8cdf0434cfa34db3d584d7a47d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:10.207217Z","signature_b64":"BZu6fI1KlsNkdnfYgHUcQ+C0ebTMpWxhcyY0H8NqI5F4D5lg3FfDdytBCN7WxPSuy7yx45qPgk1ih7O2Nr6BDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0c018eb8fdb4c1c8798b307f9b2c9771d796e8cdf0434cfa34db3d584d7a47d","last_reissued_at":"2026-05-18T00:05:10.206606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:10.206606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08172","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":"2026-05-18T00:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rb2S1qlTxKa4mafKzRchdZDzlzFLbHYQwvHd/8U7zvCTH1B8xGvZFAvCHzSDfrdLEqKfxDEZT2FFwdeP50b0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:03:37.878858Z"},"content_sha256":"cfacdf743d2ccb51c7f33539deaff809693edf67ec2a9024793b58f1d538f6e7","schema_version":"1.0","event_id":"sha256:cfacdf743d2ccb51c7f33539deaff809693edf67ec2a9024793b58f1d538f6e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2DABR24P3NGBZB4YWMD7TMWJO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Boundary Centralizer Algebras for $\\mathfrak{gl}(n|m)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jieru Zhu","submitted_at":"2018-09-21T15:21:52Z","abstract_excerpt":"We define an action of the degenerate two boundary braid algebra $\\mathcal{G}_d$ on the $\\mathbb{C}$-vector space $M\\otimes N\\otimes V^{\\otimes d}$, where $M$ and $N$ are arbitrary modules for the general linear Lie superalgebra $\\mathfrak{gl}(n|m)$, and $V$ is the natural representation. When $M$ and $N$ are parametrized by rectangular hook Young diagrams, this action factors through a quotient $\\mathcal{H}^{\\operatorname{ext}}_d$. The irreducible summands of $M\\otimes N\\otimes V^{\\otimes d}$ for the centralizer of $\\mathfrak{gl}(n|m)$, remain irreducible once regarded as modules for this quo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08172","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":""},"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":"2026-05-18T00:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Gmwsa0TCVvmLiTWkzzzClwwuL6TTGCoY6Am1W0lJVkc2VmoJwfx63wFD0nqP6rUFwchbOdHB09GI5bzLYYVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:03:37.879209Z"},"content_sha256":"c484dd95f4deaf96c714d1190eb60ef147fcca0ffa67fc72b9efa5b9cd2cf3ff","schema_version":"1.0","event_id":"sha256:c484dd95f4deaf96c714d1190eb60ef147fcca0ffa67fc72b9efa5b9cd2cf3ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DABR24P3NGBZB4YWMD7TMWJO4/bundle.json","state_url":"https://pith.science/pith/2DABR24P3NGBZB4YWMD7TMWJO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DABR24P3NGBZB4YWMD7TMWJO4/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":"2026-06-02T18:03:37Z","links":{"resolver":"https://pith.science/pith/2DABR24P3NGBZB4YWMD7TMWJO4","bundle":"https://pith.science/pith/2DABR24P3NGBZB4YWMD7TMWJO4/bundle.json","state":"https://pith.science/pith/2DABR24P3NGBZB4YWMD7TMWJO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DABR24P3NGBZB4YWMD7TMWJO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2DABR24P3NGBZB4YWMD7TMWJO4","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":"a3709e5e60984b715948ee07d587cbfdd72090ecde6e3fbb8dd3f2209c9031e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-21T15:21:52Z","title_canon_sha256":"1d2744227cfd3efe21ad6f38ad609757817f91d84d52622ccc85302a0a4630b5"},"schema_version":"1.0","source":{"id":"1809.08172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08172","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08172v1","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08172","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"2DABR24P3NGB","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2DABR24P3NGBZB4Y","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2DABR24P","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:c484dd95f4deaf96c714d1190eb60ef147fcca0ffa67fc72b9efa5b9cd2cf3ff","target":"graph","created_at":"2026-05-18T00:05:10Z","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 define an action of the degenerate two boundary braid algebra $\\mathcal{G}_d$ on the $\\mathbb{C}$-vector space $M\\otimes N\\otimes V^{\\otimes d}$, where $M$ and $N$ are arbitrary modules for the general linear Lie superalgebra $\\mathfrak{gl}(n|m)$, and $V$ is the natural representation. When $M$ and $N$ are parametrized by rectangular hook Young diagrams, this action factors through a quotient $\\mathcal{H}^{\\operatorname{ext}}_d$. The irreducible summands of $M\\otimes N\\otimes V^{\\otimes d}$ for the centralizer of $\\mathfrak{gl}(n|m)$, remain irreducible once regarded as modules for this quo","authors_text":"Jieru Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-21T15:21:52Z","title":"Two Boundary Centralizer Algebras for $\\mathfrak{gl}(n|m)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08172","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:cfacdf743d2ccb51c7f33539deaff809693edf67ec2a9024793b58f1d538f6e7","target":"record","created_at":"2026-05-18T00:05:10Z","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":"a3709e5e60984b715948ee07d587cbfdd72090ecde6e3fbb8dd3f2209c9031e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-21T15:21:52Z","title_canon_sha256":"1d2744227cfd3efe21ad6f38ad609757817f91d84d52622ccc85302a0a4630b5"},"schema_version":"1.0","source":{"id":"1809.08172","kind":"arxiv","version":1}},"canonical_sha256":"d0c018eb8fdb4c1c8798b307f9b2c9771d796e8cdf0434cfa34db3d584d7a47d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0c018eb8fdb4c1c8798b307f9b2c9771d796e8cdf0434cfa34db3d584d7a47d","first_computed_at":"2026-05-18T00:05:10.206606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:10.206606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BZu6fI1KlsNkdnfYgHUcQ+C0ebTMpWxhcyY0H8NqI5F4D5lg3FfDdytBCN7WxPSuy7yx45qPgk1ih7O2Nr6BDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:10.207217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfacdf743d2ccb51c7f33539deaff809693edf67ec2a9024793b58f1d538f6e7","sha256:c484dd95f4deaf96c714d1190eb60ef147fcca0ffa67fc72b9efa5b9cd2cf3ff"],"state_sha256":"b306bd5f52e93d37d27b02059fa9cfd9393adf8d4fab978e1b64e66cb7a2ef19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5a0eb/FGear2QcRkW8Q/OCuefE9yQL7sNNkHlE3CuK6m7Av6T5KV8MeEQvjdQTARKtwFkOF0AzufFgl0ejkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:03:37.881229Z","bundle_sha256":"d85491a6252d385d26703654407813588e1c80b5ded7f825caeb54e09fd31299"}}