{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2MB3TQV7Z2PPGI2FNVYYA5ITGA","short_pith_number":"pith:2MB3TQV7","canonical_record":{"source":{"id":"1601.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-04T14:15:10Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"d8b6a98dad91e44c8db5463249780455290e3b1950baf1776821976826f16d6c","abstract_canon_sha256":"f485bdc002c4a056938381ce656dc10188e9fa387c6ca5b1193655bbcc19d370"},"schema_version":"1.0"},"canonical_sha256":"d303b9c2bfce9ef323456d7180751330225b87b986e871b87720eeb3a61aeee7","source":{"kind":"arxiv","id":"1601.00511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00511","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00511v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00511","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"2MB3TQV7Z2PP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2MB3TQV7Z2PPGI2F","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2MB3TQV7","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2MB3TQV7Z2PPGI2FNVYYA5ITGA","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-04T14:15:10Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"d8b6a98dad91e44c8db5463249780455290e3b1950baf1776821976826f16d6c","abstract_canon_sha256":"f485bdc002c4a056938381ce656dc10188e9fa387c6ca5b1193655bbcc19d370"},"schema_version":"1.0"},"canonical_sha256":"d303b9c2bfce9ef323456d7180751330225b87b986e871b87720eeb3a61aeee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.986788Z","signature_b64":"zWRsPmROn7I1CBtTpL1K5Ytpiu36o1lTle3y+j1MZpSrLdfBcxst7QrZkufqWwp96a98kXwkEJ8vUPbYoahGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d303b9c2bfce9ef323456d7180751330225b87b986e871b87720eeb3a61aeee7","last_reissued_at":"2026-05-18T00:38:13.986035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.986035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00511","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MImwWNvOzQJaAES2YvnCeGJxKfKErXH3BSixr25NXFHr7wqljVHViOc5ZYgG+w8e7lAFq0lSVZxBHrD9LincDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:42:42.615493Z"},"content_sha256":"342f827e6f60c7f69d37c9251d8b3a66bfd5b5629d6d02d1c59ae3ee3279cf08","schema_version":"1.0","event_id":"sha256:342f827e6f60c7f69d37c9251d8b3a66bfd5b5629d6d02d1c59ae3ee3279cf08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2MB3TQV7Z2PPGI2FNVYYA5ITGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian perturbations of hard edge random matrix ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Antoine Doeraene, Tom Claeys","submitted_at":"2016-01-04T14:15:10Z","abstract_excerpt":"We study the eigenvalue correlations of random Hermitian $n\\times n$ matrices of the form $S=M+\\epsilon H$, where $H$ is a GUE matrix, $\\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose eigenvalue density is a polynomial ensemble. We show that there is a soft-to-hard edge transition in the microscopic behaviour of the eigenvalues of $S$ close to $0$ if $\\epsilon$ tends to $0$ together with $n\\to +\\infty$ at a critical speed, depending on the random matrix $M$. In a double scaling limit, we obtain a new family of limiting eigenvalue correlation kerne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00511","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTVZHegRhJabWYV/o1ff5lt1c2bosMpaWZOUhpAfG4g5SR78E7XKEzGlVwsa1BjN26H8FP4FEFxNElD66eWvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:42:42.616203Z"},"content_sha256":"9fa3391c99a691a066b70cf74ec35f8400e7ccc44aea3b09920e1168e524aba0","schema_version":"1.0","event_id":"sha256:9fa3391c99a691a066b70cf74ec35f8400e7ccc44aea3b09920e1168e524aba0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/bundle.json","state_url":"https://pith.science/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/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":"2026-05-30T08:42:42Z","links":{"resolver":"https://pith.science/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA","bundle":"https://pith.science/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/bundle.json","state":"https://pith.science/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MB3TQV7Z2PPGI2FNVYYA5ITGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2MB3TQV7Z2PPGI2FNVYYA5ITGA","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":"f485bdc002c4a056938381ce656dc10188e9fa387c6ca5b1193655bbcc19d370","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-04T14:15:10Z","title_canon_sha256":"d8b6a98dad91e44c8db5463249780455290e3b1950baf1776821976826f16d6c"},"schema_version":"1.0","source":{"id":"1601.00511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00511","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00511v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00511","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"2MB3TQV7Z2PP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2MB3TQV7Z2PPGI2F","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2MB3TQV7","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:9fa3391c99a691a066b70cf74ec35f8400e7ccc44aea3b09920e1168e524aba0","target":"graph","created_at":"2026-05-18T00:38:13Z","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 study the eigenvalue correlations of random Hermitian $n\\times n$ matrices of the form $S=M+\\epsilon H$, where $H$ is a GUE matrix, $\\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose eigenvalue density is a polynomial ensemble. We show that there is a soft-to-hard edge transition in the microscopic behaviour of the eigenvalues of $S$ close to $0$ if $\\epsilon$ tends to $0$ together with $n\\to +\\infty$ at a critical speed, depending on the random matrix $M$. In a double scaling limit, we obtain a new family of limiting eigenvalue correlation kerne","authors_text":"Antoine Doeraene, Tom Claeys","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-04T14:15:10Z","title":"Gaussian perturbations of hard edge random matrix ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00511","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":"sha256:342f827e6f60c7f69d37c9251d8b3a66bfd5b5629d6d02d1c59ae3ee3279cf08","target":"record","created_at":"2026-05-18T00:38:13Z","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":"f485bdc002c4a056938381ce656dc10188e9fa387c6ca5b1193655bbcc19d370","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-04T14:15:10Z","title_canon_sha256":"d8b6a98dad91e44c8db5463249780455290e3b1950baf1776821976826f16d6c"},"schema_version":"1.0","source":{"id":"1601.00511","kind":"arxiv","version":1}},"canonical_sha256":"d303b9c2bfce9ef323456d7180751330225b87b986e871b87720eeb3a61aeee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d303b9c2bfce9ef323456d7180751330225b87b986e871b87720eeb3a61aeee7","first_computed_at":"2026-05-18T00:38:13.986035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.986035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zWRsPmROn7I1CBtTpL1K5Ytpiu36o1lTle3y+j1MZpSrLdfBcxst7QrZkufqWwp96a98kXwkEJ8vUPbYoahGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.986788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342f827e6f60c7f69d37c9251d8b3a66bfd5b5629d6d02d1c59ae3ee3279cf08","sha256:9fa3391c99a691a066b70cf74ec35f8400e7ccc44aea3b09920e1168e524aba0"],"state_sha256":"d349e92c5d9b1647749e191f972d8ed460ab58306c21421338aec748ef8dc43d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLPp0ylC34rnkY1ICPKsNAKhAiorAGwi5MY9x5pEdTrV4Z1cpzzZWRZPd2Cfnww/C25yKSA9xeX5xRuktSxUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:42:42.620044Z","bundle_sha256":"ae35d59cc2e154b3a41490ee0272827a63f6a10b5cc0cb5545dc596cb43e99de"}}