{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ARR4SUJ4Q3USO5LJNVOWGYFBLS","short_pith_number":"pith:ARR4SUJ4","canonical_record":{"source":{"id":"1011.0836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-03T10:05:44Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"ea683554fe1049bfb6aa9b984943a98f8662bdfeb6e0d225cc81055905c50b07","abstract_canon_sha256":"20eb451f6f40dae995027c28bc3c2019ed4fdd0284664c92f44ba68ed34f7781"},"schema_version":"1.0"},"canonical_sha256":"0463c9513c86e92775696d5d6360a15cb065151029a364136713e979eac230dd","source":{"kind":"arxiv","id":"1011.0836","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0836","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0836v2","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0836","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"ARR4SUJ4Q3US","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ARR4SUJ4Q3USO5LJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ARR4SUJ4","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ARR4SUJ4Q3USO5LJNVOWGYFBLS","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-03T10:05:44Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"ea683554fe1049bfb6aa9b984943a98f8662bdfeb6e0d225cc81055905c50b07","abstract_canon_sha256":"20eb451f6f40dae995027c28bc3c2019ed4fdd0284664c92f44ba68ed34f7781"},"schema_version":"1.0"},"canonical_sha256":"0463c9513c86e92775696d5d6360a15cb065151029a364136713e979eac230dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:43.581925Z","signature_b64":"/YN5J1SKxVZng1wvhYF7ItE036e1w37yi5UrIVHxu53KGLHzA0ewyNtHIMukyNLzeUJ3D2REB6QqBlCSl9ZMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0463c9513c86e92775696d5d6360a15cb065151029a364136713e979eac230dd","last_reissued_at":"2026-05-18T04:19:43.581452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:43.581452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0836","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":"2026-05-18T04:19:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OPAMYvER+rOOmHkK8fiMm+eCqMje/mQaWruiEGMp7m1YG/xysmwNSaEbbOMSpSZWJh3soTW5xcWdvl3R/6GWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:44:29.961671Z"},"content_sha256":"6c5df78184b2368ae922b2f4e8b7a0ce2bc0ba30ec305e327ee7198251d38dfd","schema_version":"1.0","event_id":"sha256:6c5df78184b2368ae922b2f4e8b7a0ce2bc0ba30ec305e327ee7198251d38dfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ARR4SUJ4Q3USO5LJNVOWGYFBLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Mario Kieburg","submitted_at":"2010-11-03T10:05:44Z","abstract_excerpt":"The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0836","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":"2026-05-18T04:19:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngvsLjE4xhJoNg+zuT5faSoE8rWSp5hMk29TI2ySiK3xBTOWZwzo+D6GZS3oIykr1RaZXx1Ruu9smPu3lYjJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:44:29.962376Z"},"content_sha256":"ea43e454a802fbacc4492cd7045d25a246047499f6908a05286185a98031fe1a","schema_version":"1.0","event_id":"sha256:ea43e454a802fbacc4492cd7045d25a246047499f6908a05286185a98031fe1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/bundle.json","state_url":"https://pith.science/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/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":"2026-05-23T23:44:29Z","links":{"resolver":"https://pith.science/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS","bundle":"https://pith.science/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/bundle.json","state":"https://pith.science/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARR4SUJ4Q3USO5LJNVOWGYFBLS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ARR4SUJ4Q3USO5LJNVOWGYFBLS","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":"20eb451f6f40dae995027c28bc3c2019ed4fdd0284664c92f44ba68ed34f7781","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-03T10:05:44Z","title_canon_sha256":"ea683554fe1049bfb6aa9b984943a98f8662bdfeb6e0d225cc81055905c50b07"},"schema_version":"1.0","source":{"id":"1011.0836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0836","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0836v2","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0836","created_at":"2026-05-18T04:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"ARR4SUJ4Q3US","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ARR4SUJ4Q3USO5LJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ARR4SUJ4","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ea43e454a802fbacc4492cd7045d25a246047499f6908a05286185a98031fe1a","target":"graph","created_at":"2026-05-18T04:19:43Z","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":"The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integral","authors_text":"Mario Kieburg","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-03T10:05:44Z","title":"On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0836","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":"sha256:6c5df78184b2368ae922b2f4e8b7a0ce2bc0ba30ec305e327ee7198251d38dfd","target":"record","created_at":"2026-05-18T04:19:43Z","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":"20eb451f6f40dae995027c28bc3c2019ed4fdd0284664c92f44ba68ed34f7781","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-03T10:05:44Z","title_canon_sha256":"ea683554fe1049bfb6aa9b984943a98f8662bdfeb6e0d225cc81055905c50b07"},"schema_version":"1.0","source":{"id":"1011.0836","kind":"arxiv","version":2}},"canonical_sha256":"0463c9513c86e92775696d5d6360a15cb065151029a364136713e979eac230dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0463c9513c86e92775696d5d6360a15cb065151029a364136713e979eac230dd","first_computed_at":"2026-05-18T04:19:43.581452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:43.581452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/YN5J1SKxVZng1wvhYF7ItE036e1w37yi5UrIVHxu53KGLHzA0ewyNtHIMukyNLzeUJ3D2REB6QqBlCSl9ZMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:43.581925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c5df78184b2368ae922b2f4e8b7a0ce2bc0ba30ec305e327ee7198251d38dfd","sha256:ea43e454a802fbacc4492cd7045d25a246047499f6908a05286185a98031fe1a"],"state_sha256":"3cb60fa3581a2af3d803a8a244c534aa30f1f6bf8141a7a8ef0de6939acb91ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k6e6IkXhkqybNhmEv6s4/ALYWePnoz2mw+8WUpIn/GC268848iSwVMiH2w+do1uC9PhTbOvmiDQ4vA6jYMVpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:44:29.966127Z","bundle_sha256":"7298d56fbec57532d219bc4b727dae687203866e5df6850c6bb06f68e3cb4e26"}}