{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:5HARROXP7NXH45XZV4K5R464T6","short_pith_number":"pith:5HARROXP","canonical_record":{"source":{"id":"2110.14005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-10-26T20:23:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"64b1d5f74da132f3492628b15b0e725ac18ca9c5852970636e0d945fae9ac4ce","abstract_canon_sha256":"1bed284adf35e3608664923b3b2c945dd4c926b562c17a7764c3dd8a2def29e4"},"schema_version":"1.0"},"canonical_sha256":"e9c118baeffb6e7e76f9af15d8f3dc9fa47123aae7273b8ec429cc93ce1d1214","source":{"kind":"arxiv","id":"2110.14005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14005","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14005v1","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14005","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"5HARROXP7NXH","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_16","alias_value":"5HARROXP7NXH45XZ","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_8","alias_value":"5HARROXP","created_at":"2026-07-05T04:15:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:5HARROXP7NXH45XZV4K5R464T6","target":"record","payload":{"canonical_record":{"source":{"id":"2110.14005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-10-26T20:23:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"64b1d5f74da132f3492628b15b0e725ac18ca9c5852970636e0d945fae9ac4ce","abstract_canon_sha256":"1bed284adf35e3608664923b3b2c945dd4c926b562c17a7764c3dd8a2def29e4"},"schema_version":"1.0"},"canonical_sha256":"e9c118baeffb6e7e76f9af15d8f3dc9fa47123aae7273b8ec429cc93ce1d1214","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:48.119650Z","signature_b64":"90H0YFkGF4BAkJW7o3mzk6td/dqQQUujNfKHsKuK1m7gGPcOn7IPKiQcD/91DbEkYiZUCubFmRQ0A3Y2VlZKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9c118baeffb6e7e76f9af15d8f3dc9fa47123aae7273b8ec429cc93ce1d1214","last_reissued_at":"2026-07-05T04:15:48.119202Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:48.119202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.14005","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":"2026-07-05T04:15:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hWuPRzTBaOUVG+mJmEOSapAMK93MkBZmPB7g2M9RWWAxYttVmHpiC7BwgM18yaG2mJwvWDtTybRh3TB3QT2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:15:53.738985Z"},"content_sha256":"6c2d524351f92f2695d8495b0f4bbd31fb9c955d9018ed64de8585fa08f4140e","schema_version":"1.0","event_id":"sha256:6c2d524351f92f2695d8495b0f4bbd31fb9c955d9018ed64de8585fa08f4140e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:5HARROXP7NXH45XZV4K5R464T6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From superintegrability to tridiagonal representation of $\\beta$-ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, A. Popolitov","submitted_at":"2021-10-26T20:23:33Z","abstract_excerpt":"The wonderful formulas by I.Dumitriu and A.Edelman rewrite $\\beta$-ensemble, with eigenvalue integrals containing Vandermonde factors in the power $2\\beta$, through integrals over tridiagonal matrices, where $\\beta$-dependent are the powers of individual matrix elements, not their differences. These potentially useful formulas are usually deduced from rather complicated and non-transparent combinatorics and are not as widely known as they deserve. We explain that the superintegrability property, i.e. a simple expression of the Gaussian averages of arbitrary Jack polynomials through the same Ja"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14005","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/2110.14005/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":"2026-07-05T04:15:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"On1iHTd8IiaYNn8MNIxF49ENTc62x+igN4puDELCMHYgj4vKnuCz55TO7JUzXuAG9lQUkfzJWR8OwWhabnj3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:15:53.739878Z"},"content_sha256":"ce94a894de9c96eb282948609cb8fe50cdaa0a975a26c0bf920c36c606c27c4b","schema_version":"1.0","event_id":"sha256:ce94a894de9c96eb282948609cb8fe50cdaa0a975a26c0bf920c36c606c27c4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HARROXP7NXH45XZV4K5R464T6/bundle.json","state_url":"https://pith.science/pith/5HARROXP7NXH45XZV4K5R464T6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HARROXP7NXH45XZV4K5R464T6/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":"2026-08-05T23:15:53Z","links":{"resolver":"https://pith.science/pith/5HARROXP7NXH45XZV4K5R464T6","bundle":"https://pith.science/pith/5HARROXP7NXH45XZV4K5R464T6/bundle.json","state":"https://pith.science/pith/5HARROXP7NXH45XZV4K5R464T6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HARROXP7NXH45XZV4K5R464T6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5HARROXP7NXH45XZV4K5R464T6","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":"1bed284adf35e3608664923b3b2c945dd4c926b562c17a7764c3dd8a2def29e4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-10-26T20:23:33Z","title_canon_sha256":"64b1d5f74da132f3492628b15b0e725ac18ca9c5852970636e0d945fae9ac4ce"},"schema_version":"1.0","source":{"id":"2110.14005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14005","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14005v1","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14005","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"5HARROXP7NXH","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_16","alias_value":"5HARROXP7NXH45XZ","created_at":"2026-07-05T04:15:48Z"},{"alias_kind":"pith_short_8","alias_value":"5HARROXP","created_at":"2026-07-05T04:15:48Z"}],"graph_snapshots":[{"event_id":"sha256:ce94a894de9c96eb282948609cb8fe50cdaa0a975a26c0bf920c36c606c27c4b","target":"graph","created_at":"2026-07-05T04:15:48Z","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/2110.14005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The wonderful formulas by I.Dumitriu and A.Edelman rewrite $\\beta$-ensemble, with eigenvalue integrals containing Vandermonde factors in the power $2\\beta$, through integrals over tridiagonal matrices, where $\\beta$-dependent are the powers of individual matrix elements, not their differences. These potentially useful formulas are usually deduced from rather complicated and non-transparent combinatorics and are not as widely known as they deserve. We explain that the superintegrability property, i.e. a simple expression of the Gaussian averages of arbitrary Jack polynomials through the same Ja","authors_text":"A. Mironov, A. Morozov, A. Popolitov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-10-26T20:23:33Z","title":"From superintegrability to tridiagonal representation of $\\beta$-ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14005","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":"sha256:6c2d524351f92f2695d8495b0f4bbd31fb9c955d9018ed64de8585fa08f4140e","target":"record","created_at":"2026-07-05T04:15:48Z","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":"1bed284adf35e3608664923b3b2c945dd4c926b562c17a7764c3dd8a2def29e4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-10-26T20:23:33Z","title_canon_sha256":"64b1d5f74da132f3492628b15b0e725ac18ca9c5852970636e0d945fae9ac4ce"},"schema_version":"1.0","source":{"id":"2110.14005","kind":"arxiv","version":1}},"canonical_sha256":"e9c118baeffb6e7e76f9af15d8f3dc9fa47123aae7273b8ec429cc93ce1d1214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9c118baeffb6e7e76f9af15d8f3dc9fa47123aae7273b8ec429cc93ce1d1214","first_computed_at":"2026-07-05T04:15:48.119202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:48.119202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90H0YFkGF4BAkJW7o3mzk6td/dqQQUujNfKHsKuK1m7gGPcOn7IPKiQcD/91DbEkYiZUCubFmRQ0A3Y2VlZKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:48.119650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.14005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c2d524351f92f2695d8495b0f4bbd31fb9c955d9018ed64de8585fa08f4140e","sha256:ce94a894de9c96eb282948609cb8fe50cdaa0a975a26c0bf920c36c606c27c4b"],"state_sha256":"6dfb02743a3b8e307dec647d39265354eb9989b808de44480386e6d9b08515a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMAHTIJkfmSJymGm71E/hDokEIR1r4V6bsNFxWgS1t9emGD4d0kD7c0t3zCxs/EiRQJVUjfPf1It/lOTE4N4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T23:15:53.751289Z","bundle_sha256":"c14a7491d3c4aac04e1fbecbb44533cc6b55a9e52494b65e56ac1f58eb6ff19b"}}