{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PYQJECIE7LPGPYP6NUVWAPBQVD","short_pith_number":"pith:PYQJECIE","canonical_record":{"source":{"id":"1011.4983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-23T01:41:25Z","cross_cats_sorted":["math.CA","math.MP","math.PR"],"title_canon_sha256":"af3ea04208e4f055ca185858a79e9b3ed43e52e3b62d8d300640aaf279f340df","abstract_canon_sha256":"db9c815e1c2de9fa1c2d9f1415b25d6bb69f6b833b63826dfe7fe7a4182b327b"},"schema_version":"1.0"},"canonical_sha256":"7e20920904fade67e1fe6d2b603c30a8f2e4d48366aa4347c9db135d7264457c","source":{"kind":"arxiv","id":"1011.4983","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4983","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4983v1","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4983","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"PYQJECIE7LPG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PYQJECIE7LPGPYP6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PYQJECIE","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PYQJECIE7LPGPYP6NUVWAPBQVD","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-23T01:41:25Z","cross_cats_sorted":["math.CA","math.MP","math.PR"],"title_canon_sha256":"af3ea04208e4f055ca185858a79e9b3ed43e52e3b62d8d300640aaf279f340df","abstract_canon_sha256":"db9c815e1c2de9fa1c2d9f1415b25d6bb69f6b833b63826dfe7fe7a4182b327b"},"schema_version":"1.0"},"canonical_sha256":"7e20920904fade67e1fe6d2b603c30a8f2e4d48366aa4347c9db135d7264457c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:42.176447Z","signature_b64":"9HQ5fvEu8msWgkFrFGTYaJNjlNB13aj5dGm3Lf6FRayLOCVktS4HXjRcqoj1hwlSnoBOvoEKRLvgnrJmBwNZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e20920904fade67e1fe6d2b603c30a8f2e4d48366aa4347c9db135d7264457c","last_reissued_at":"2026-05-18T02:04:42.175558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:42.175558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4983","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":"2026-05-18T02:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OC2QH78xozJeouisqpk2oN90X/zZactzJ6H+omHycBkAR9h/z2xd77jofcvdGAJMbd6Fmyw/aU8hLQOjWNhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:22:38.830097Z"},"content_sha256":"dd9485209ff94c2789adbd12f90275a19f22cda2ad1b32ef25031795fd7e529b","schema_version":"1.0","event_id":"sha256:dd9485209ff94c2789adbd12f90275a19f22cda2ad1b32ef25031795fd7e529b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PYQJECIE7LPGPYP6NUVWAPBQVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Marco Bertola, Robert Buckingham, Seung-Yeop Lee, Virgil U. Pierce","submitted_at":"2010-11-23T01:41:25Z","abstract_excerpt":"Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the $n\\times n$ external source matrix has two distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity $n-r$. For a Gaussian potential, it was shown by P\\'ech\\'e \\cite{Peche:2006} that when $r$ is fixed or grows sufficiently slowly with $n$ (a small-rank source), $r$ eigen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4983","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":"2026-05-18T02:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euU/UKOA3r5Z51y7OwpswEhw2pI4yQzJUFDRgWrjnqFFr8mGz7B/05tbU7LyUfRUtdoVn8InZxWS6rKm1SkZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:22:38.830511Z"},"content_sha256":"e525cfc5b3fe3362c4f1cb21a0daaa4e648f47164a687824b57e4acb9931e941","schema_version":"1.0","event_id":"sha256:e525cfc5b3fe3362c4f1cb21a0daaa4e648f47164a687824b57e4acb9931e941"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/bundle.json","state_url":"https://pith.science/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/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":"2026-06-20T07:22:38Z","links":{"resolver":"https://pith.science/pith/PYQJECIE7LPGPYP6NUVWAPBQVD","bundle":"https://pith.science/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/bundle.json","state":"https://pith.science/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYQJECIE7LPGPYP6NUVWAPBQVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PYQJECIE7LPGPYP6NUVWAPBQVD","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":"db9c815e1c2de9fa1c2d9f1415b25d6bb69f6b833b63826dfe7fe7a4182b327b","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-23T01:41:25Z","title_canon_sha256":"af3ea04208e4f055ca185858a79e9b3ed43e52e3b62d8d300640aaf279f340df"},"schema_version":"1.0","source":{"id":"1011.4983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4983","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4983v1","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4983","created_at":"2026-05-18T02:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"PYQJECIE7LPG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PYQJECIE7LPGPYP6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PYQJECIE","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:e525cfc5b3fe3362c4f1cb21a0daaa4e648f47164a687824b57e4acb9931e941","target":"graph","created_at":"2026-05-18T02:04:42Z","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":"Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the $n\\times n$ external source matrix has two distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity $n-r$. For a Gaussian potential, it was shown by P\\'ech\\'e \\cite{Peche:2006} that when $r$ is fixed or grows sufficiently slowly with $n$ (a small-rank source), $r$ eigen","authors_text":"Marco Bertola, Robert Buckingham, Seung-Yeop Lee, Virgil U. Pierce","cross_cats":["math.CA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-23T01:41:25Z","title":"Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4983","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:dd9485209ff94c2789adbd12f90275a19f22cda2ad1b32ef25031795fd7e529b","target":"record","created_at":"2026-05-18T02:04:42Z","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":"db9c815e1c2de9fa1c2d9f1415b25d6bb69f6b833b63826dfe7fe7a4182b327b","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-23T01:41:25Z","title_canon_sha256":"af3ea04208e4f055ca185858a79e9b3ed43e52e3b62d8d300640aaf279f340df"},"schema_version":"1.0","source":{"id":"1011.4983","kind":"arxiv","version":1}},"canonical_sha256":"7e20920904fade67e1fe6d2b603c30a8f2e4d48366aa4347c9db135d7264457c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e20920904fade67e1fe6d2b603c30a8f2e4d48366aa4347c9db135d7264457c","first_computed_at":"2026-05-18T02:04:42.175558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:42.175558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9HQ5fvEu8msWgkFrFGTYaJNjlNB13aj5dGm3Lf6FRayLOCVktS4HXjRcqoj1hwlSnoBOvoEKRLvgnrJmBwNZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:42.176447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd9485209ff94c2789adbd12f90275a19f22cda2ad1b32ef25031795fd7e529b","sha256:e525cfc5b3fe3362c4f1cb21a0daaa4e648f47164a687824b57e4acb9931e941"],"state_sha256":"01b8486308ca96a0d729d065e0bca9fc834640af09b66fa15acafc6b5bec16f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6GQpyDBvYuHKqo7TRHN4W53XFl9atCIZYbUdKXbAVRw0tcZ6Uo5MU31jtg5SOV5Yka06RHldZmRkfQX4NzLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:22:38.832482Z","bundle_sha256":"c966647fd098a7585fe946cd8963977c33cea6a328b82080eb55384aa7346fa3"}}