{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5VFFLMRGTDIF727IV6JNIB7CDR","short_pith_number":"pith:5VFFLMRG","canonical_record":{"source":{"id":"1205.3598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T08:46:18Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"10218514f75b41bee0494e4adeb2b910cdfdccb016ea954cd001c5ffc3d6cb15","abstract_canon_sha256":"c846f87a612cbccf73644d2f3edfe24604c138516ea3d42d4a6f1e1514b6d4d4"},"schema_version":"1.0"},"canonical_sha256":"ed4a55b22698d05febe8af92d407e21c5de9dabc7fbe91b968320d753e56b641","source":{"kind":"arxiv","id":"1205.3598","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3598","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3598v2","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3598","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"5VFFLMRGTDIF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VFFLMRGTDIF727I","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VFFLMRG","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5VFFLMRGTDIF727IV6JNIB7CDR","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T08:46:18Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"10218514f75b41bee0494e4adeb2b910cdfdccb016ea954cd001c5ffc3d6cb15","abstract_canon_sha256":"c846f87a612cbccf73644d2f3edfe24604c138516ea3d42d4a6f1e1514b6d4d4"},"schema_version":"1.0"},"canonical_sha256":"ed4a55b22698d05febe8af92d407e21c5de9dabc7fbe91b968320d753e56b641","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:25.913233Z","signature_b64":"VTGcUGK0bLnHi55Thl7DJaVvywmvalPtAiT027DxWkGJo0OOmNZn7FM9hoiLz+cmuZP8vjh7gS+Gk50XdM0FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed4a55b22698d05febe8af92d407e21c5de9dabc7fbe91b968320d753e56b641","last_reissued_at":"2026-05-18T03:35:25.912399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:25.912399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3598","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":"2026-05-18T03:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yyttck3L2oSlayhlbpLCeT2aXaZfNe6mR32ZDE3Xhrftw4ZSl+W6d2sP+varKtAr3He3oIlmwOYusPkNyTgYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:14:10.569069Z"},"content_sha256":"09f5e13cb614e64cb9c6f9d2fd38a8e6a1f543e6cae66262d34a7d90a91a7795","schema_version":"1.0","event_id":"sha256:09f5e13cb614e64cb9c6f9d2fd38a8e6a1f543e6cae66262d34a7d90a91a7795"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5VFFLMRGTDIF727IV6JNIB7CDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant $\\beta$-ensembles and the Gauss-Wigner crossover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Alice Guionnet, Jean-Philippe Bouchaud, Romain Allez","submitted_at":"2012-05-16T08:46:18Z","abstract_excerpt":"We define a new diffusive matrix model converging towards the $\\beta$ -Dyson Brownian motion for all $\\beta\\in [0,2]$ that provides an explicit construction of $\\beta$-ensembles of random matrices that is invariant under the orthogonal/unitary group. For small values of $\\beta$, our process allows one to interpolate smoothly between the Gaussian distribution and the Wigner semi-circle. The interpolating limit distributions form a one parameter family that can be explicitly computed. This also allows us to compute the finite-size corrections to the semi-circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3598","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":"2026-05-18T03:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sOREQD4gEYFWCOwtDhw6mtSSkYbQtI0lNzJr90UoEXeDFX6QmgtwyynuBMz4RU4VsxiOSGw6JWX6naFXgSaZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:14:10.569422Z"},"content_sha256":"83321ac3cd35dcb87a6901ab288c4de112612e4b1c7fa80e2ce1e83b6fdefa9e","schema_version":"1.0","event_id":"sha256:83321ac3cd35dcb87a6901ab288c4de112612e4b1c7fa80e2ce1e83b6fdefa9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VFFLMRGTDIF727IV6JNIB7CDR/bundle.json","state_url":"https://pith.science/pith/5VFFLMRGTDIF727IV6JNIB7CDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VFFLMRGTDIF727IV6JNIB7CDR/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":"2026-06-02T06:14:10Z","links":{"resolver":"https://pith.science/pith/5VFFLMRGTDIF727IV6JNIB7CDR","bundle":"https://pith.science/pith/5VFFLMRGTDIF727IV6JNIB7CDR/bundle.json","state":"https://pith.science/pith/5VFFLMRGTDIF727IV6JNIB7CDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VFFLMRGTDIF727IV6JNIB7CDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5VFFLMRGTDIF727IV6JNIB7CDR","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":"c846f87a612cbccf73644d2f3edfe24604c138516ea3d42d4a6f1e1514b6d4d4","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T08:46:18Z","title_canon_sha256":"10218514f75b41bee0494e4adeb2b910cdfdccb016ea954cd001c5ffc3d6cb15"},"schema_version":"1.0","source":{"id":"1205.3598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3598","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3598v2","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3598","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"5VFFLMRGTDIF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VFFLMRGTDIF727I","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VFFLMRG","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:83321ac3cd35dcb87a6901ab288c4de112612e4b1c7fa80e2ce1e83b6fdefa9e","target":"graph","created_at":"2026-05-18T03:35:25Z","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 define a new diffusive matrix model converging towards the $\\beta$ -Dyson Brownian motion for all $\\beta\\in [0,2]$ that provides an explicit construction of $\\beta$-ensembles of random matrices that is invariant under the orthogonal/unitary group. For small values of $\\beta$, our process allows one to interpolate smoothly between the Gaussian distribution and the Wigner semi-circle. The interpolating limit distributions form a one parameter family that can be explicitly computed. This also allows us to compute the finite-size corrections to the semi-circle.","authors_text":"Alice Guionnet, Jean-Philippe Bouchaud, Romain Allez","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T08:46:18Z","title":"Invariant $\\beta$-ensembles and the Gauss-Wigner crossover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3598","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":"sha256:09f5e13cb614e64cb9c6f9d2fd38a8e6a1f543e6cae66262d34a7d90a91a7795","target":"record","created_at":"2026-05-18T03:35:25Z","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":"c846f87a612cbccf73644d2f3edfe24604c138516ea3d42d4a6f1e1514b6d4d4","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T08:46:18Z","title_canon_sha256":"10218514f75b41bee0494e4adeb2b910cdfdccb016ea954cd001c5ffc3d6cb15"},"schema_version":"1.0","source":{"id":"1205.3598","kind":"arxiv","version":2}},"canonical_sha256":"ed4a55b22698d05febe8af92d407e21c5de9dabc7fbe91b968320d753e56b641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4a55b22698d05febe8af92d407e21c5de9dabc7fbe91b968320d753e56b641","first_computed_at":"2026-05-18T03:35:25.912399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:25.912399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VTGcUGK0bLnHi55Thl7DJaVvywmvalPtAiT027DxWkGJo0OOmNZn7FM9hoiLz+cmuZP8vjh7gS+Gk50XdM0FBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:25.913233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f5e13cb614e64cb9c6f9d2fd38a8e6a1f543e6cae66262d34a7d90a91a7795","sha256:83321ac3cd35dcb87a6901ab288c4de112612e4b1c7fa80e2ce1e83b6fdefa9e"],"state_sha256":"959ed21aa8a1693ca9c287c0a31153fe5b03bf18f1762d0edf70efa5cb5b538b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zXJdel/0642UNEakJ1qGCcBob4fzI+3URaxyh7gBtNYuyq2ib5xGuTZf4Lmov5APQDoDizF8R9oPkeXw9T3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:14:10.571301Z","bundle_sha256":"070b846c6b71493599689faa19e087ee58d83c5fa68d1b87b675a7708c0d97a4"}}