{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P43TLWDT4VW3JJMPCYPVDP27D6","short_pith_number":"pith:P43TLWDT","canonical_record":{"source":{"id":"1807.07340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"5790a366fb87acc37282f9c8ebddedf45204d33b355cfc82646f7dc8d99eaef6","abstract_canon_sha256":"7713fa0ea926fdb02cc62ac52bfd336fa459fc7406c29b973d269ab76770f06b"},"schema_version":"1.0"},"canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","source":{"kind":"arxiv","id":"1807.07340","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07340","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07340v4","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07340","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"pith_short_12","alias_value":"P43TLWDT4VW3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P43TLWDT4VW3JJMP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P43TLWDT","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P43TLWDT4VW3JJMPCYPVDP27D6","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"5790a366fb87acc37282f9c8ebddedf45204d33b355cfc82646f7dc8d99eaef6","abstract_canon_sha256":"7713fa0ea926fdb02cc62ac52bfd336fa459fc7406c29b973d269ab76770f06b"},"schema_version":"1.0"},"canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:50.928504Z","signature_b64":"1z6u8MiPr9Cas8ja19uzH39W0qgMBowv7MUGWUu2s5dho33PRcKEOsAePdtJdZ7m1vhj9JOVqWhMsTFo+OouDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","last_reissued_at":"2026-05-17T23:48:50.927827Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:50.927827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07340","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zqHQKTI3HFg3F+OTs3YR9tZMQznxLNPLH5FgRN7F2uiPZhXgTKfe7Hl6TdNC8rSvdjHHWSivs3ntAOcw2IbuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:02:32.098724Z"},"content_sha256":"89685c3c055edacde0286b2ac228d3dbef4084caf2b8271329bdb271d891f9fd","schema_version":"1.0","event_id":"sha256:89685c3c055edacde0286b2ac228d3dbef4084caf2b8271329bdb271d891f9fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P43TLWDT4VW3JJMPCYPVDP27D6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Capelli eigenvalue problem for Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hadi Salmasian, Siddhartha Sahi, Vera Serganova","submitted_at":"2018-07-19T10:51:50Z","abstract_excerpt":"For a finite dimensional unital complex simple Jordan superalgebra $J$, the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\\mathfrak g_\\flat\\cong \\mathfrak g_\\flat(-1)\\oplus\\mathfrak g_\\flat(0)\\oplus\\mathfrak g_\\flat(1)$, such that $\\mathfrak g_\\flat(-1)\\cong J$. Set $V:=\\mathfrak g_\\flat(-1)^*$ and $\\mathfrak g:=\\mathfrak g_\\flat(0)$.\n  In most cases, the space $\\mathcal P(V)$ of superpolynomials on $V$ is a completely reducible and multiplicity-free representation of $\\mathfrak g$, with a decomposition $\\mathcal P(V):=\\bigoplus_{\\lambda\\in\\Omega}V_\\lambda$, where $\\left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07340","kind":"arxiv","version":4},"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":"2026-05-17T23:48:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPL3IJVxNq0pNe4eKlWnyXzCWKvIhdjDyvUZA9c5CrHD8RfZGdspImYJguZzRj9BuaWqtONh9+JaKXMWU/aZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:02:32.099070Z"},"content_sha256":"b4cc56951f9dc249bf94c3bc4fd2e90c7f4aa214634de7442c86461268bf78c1","schema_version":"1.0","event_id":"sha256:b4cc56951f9dc249bf94c3bc4fd2e90c7f4aa214634de7442c86461268bf78c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/bundle.json","state_url":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P43TLWDT4VW3JJMPCYPVDP27D6/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":"2026-06-01T17:02:32Z","links":{"resolver":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6","bundle":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/bundle.json","state":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P43TLWDT4VW3JJMPCYPVDP27D6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P43TLWDT4VW3JJMPCYPVDP27D6","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":"7713fa0ea926fdb02cc62ac52bfd336fa459fc7406c29b973d269ab76770f06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","title_canon_sha256":"5790a366fb87acc37282f9c8ebddedf45204d33b355cfc82646f7dc8d99eaef6"},"schema_version":"1.0","source":{"id":"1807.07340","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07340","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07340v4","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07340","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"pith_short_12","alias_value":"P43TLWDT4VW3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P43TLWDT4VW3JJMP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P43TLWDT","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:b4cc56951f9dc249bf94c3bc4fd2e90c7f4aa214634de7442c86461268bf78c1","target":"graph","created_at":"2026-05-17T23:48:50Z","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":"For a finite dimensional unital complex simple Jordan superalgebra $J$, the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\\mathfrak g_\\flat\\cong \\mathfrak g_\\flat(-1)\\oplus\\mathfrak g_\\flat(0)\\oplus\\mathfrak g_\\flat(1)$, such that $\\mathfrak g_\\flat(-1)\\cong J$. Set $V:=\\mathfrak g_\\flat(-1)^*$ and $\\mathfrak g:=\\mathfrak g_\\flat(0)$.\n  In most cases, the space $\\mathcal P(V)$ of superpolynomials on $V$ is a completely reducible and multiplicity-free representation of $\\mathfrak g$, with a decomposition $\\mathcal P(V):=\\bigoplus_{\\lambda\\in\\Omega}V_\\lambda$, where $\\left","authors_text":"Hadi Salmasian, Siddhartha Sahi, Vera Serganova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","title":"The Capelli eigenvalue problem for Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07340","kind":"arxiv","version":4},"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":"sha256:89685c3c055edacde0286b2ac228d3dbef4084caf2b8271329bdb271d891f9fd","target":"record","created_at":"2026-05-17T23:48:50Z","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":"7713fa0ea926fdb02cc62ac52bfd336fa459fc7406c29b973d269ab76770f06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","title_canon_sha256":"5790a366fb87acc37282f9c8ebddedf45204d33b355cfc82646f7dc8d99eaef6"},"schema_version":"1.0","source":{"id":"1807.07340","kind":"arxiv","version":4}},"canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","first_computed_at":"2026-05-17T23:48:50.927827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:50.927827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1z6u8MiPr9Cas8ja19uzH39W0qgMBowv7MUGWUu2s5dho33PRcKEOsAePdtJdZ7m1vhj9JOVqWhMsTFo+OouDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:50.928504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07340","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89685c3c055edacde0286b2ac228d3dbef4084caf2b8271329bdb271d891f9fd","sha256:b4cc56951f9dc249bf94c3bc4fd2e90c7f4aa214634de7442c86461268bf78c1"],"state_sha256":"132ded61948d9d016d3094d7c17a2301f45c6f2e3fd92481d75fd55e9f11e925"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBtyCg/fPYUPUAPXNdrK3TJsk4ekPKHTchkhmwN7AD5aBoPMm87Ih5pEQFbu3iwWHIdGJe0QCrckwUBx5SCQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:02:32.101064Z","bundle_sha256":"3426df2a9dd52af8c089b1cf0a7238548ffe3a5dc20fb1bd3d7fd43cd0c4a359"}}