{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I4CJMQPG3QFFASLRRNWBHJEOVN","short_pith_number":"pith:I4CJMQPG","canonical_record":{"source":{"id":"1407.5606","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-21T19:31:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"13781452c03edde8d97381b9a324019a2bb51ee45740df6c97516907a596aed4","abstract_canon_sha256":"4c9f0c73e301ca85cb862791d8064d0440d35723ec3a4a7170ce660070151c0d"},"schema_version":"1.0"},"canonical_sha256":"47049641e6dc0a5049718b6c13a48eab7257790b7bbfd83304812d0932de5e53","source":{"kind":"arxiv","id":"1407.5606","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5606","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5606v3","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5606","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"I4CJMQPG3QFF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I4CJMQPG3QFFASLR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I4CJMQPG","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I4CJMQPG3QFFASLRRNWBHJEOVN","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5606","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-21T19:31:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"13781452c03edde8d97381b9a324019a2bb51ee45740df6c97516907a596aed4","abstract_canon_sha256":"4c9f0c73e301ca85cb862791d8064d0440d35723ec3a4a7170ce660070151c0d"},"schema_version":"1.0"},"canonical_sha256":"47049641e6dc0a5049718b6c13a48eab7257790b7bbfd83304812d0932de5e53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:40.877366Z","signature_b64":"WEMNt/V2e7T7UFRrCXsfPJ+flsKyskgczY9Ouua91pT04WOZe3XGw2zsVo9+Hh0ighaYncZ6WMlPfhNfDVh9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47049641e6dc0a5049718b6c13a48eab7257790b7bbfd83304812d0932de5e53","last_reissued_at":"2026-05-18T02:18:40.876576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:40.876576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5606","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8deiSjKG1sbLn7A9odst2htfS4x+H87D5rOaff6SZ0Rw55bMq9PYvOXKBu1njnfnPJ7LOvPqBduLJ/YeGStDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:55:52.924677Z"},"content_sha256":"52bf60c403c4ef6f7064ec76926791ecc18cbf1d95e61de8666b217a8e3978e7","schema_version":"1.0","event_id":"sha256:52bf60c403c4ef6f7064ec76926791ecc18cbf1d95e61de8666b217a8e3978e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I4CJMQPG3QFFASLRRNWBHJEOVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed energy universality for generalized Wigner matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hong-Tzer Yau, Jun Yin, Laszlo Erdos, Paul Bourgade","submitted_at":"2014-07-21T19:31:51Z","abstract_excerpt":"We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5606","kind":"arxiv","version":3},"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":"2026-05-18T02:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SvPQUrGmiPibzGmMyj/xim81fTUb2jPTkjdKGduYZ5FTemIPC9whjFqk/lSu6fF4p/KRJ9ye3a10m5/nO6zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:55:52.925272Z"},"content_sha256":"51f57d4ac3b168c35ca9b9138eb985a22b0f87f76772726793fae47dda5a318e","schema_version":"1.0","event_id":"sha256:51f57d4ac3b168c35ca9b9138eb985a22b0f87f76772726793fae47dda5a318e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/bundle.json","state_url":"https://pith.science/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/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":"2026-05-26T13:55:52Z","links":{"resolver":"https://pith.science/pith/I4CJMQPG3QFFASLRRNWBHJEOVN","bundle":"https://pith.science/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/bundle.json","state":"https://pith.science/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4CJMQPG3QFFASLRRNWBHJEOVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I4CJMQPG3QFFASLRRNWBHJEOVN","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":"4c9f0c73e301ca85cb862791d8064d0440d35723ec3a4a7170ce660070151c0d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-21T19:31:51Z","title_canon_sha256":"13781452c03edde8d97381b9a324019a2bb51ee45740df6c97516907a596aed4"},"schema_version":"1.0","source":{"id":"1407.5606","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5606","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5606v3","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5606","created_at":"2026-05-18T02:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"I4CJMQPG3QFF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I4CJMQPG3QFFASLR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I4CJMQPG","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:51f57d4ac3b168c35ca9b9138eb985a22b0f87f76772726793fae47dda5a318e","target":"graph","created_at":"2026-05-18T02:18:40Z","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 prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.","authors_text":"Hong-Tzer Yau, Jun Yin, Laszlo Erdos, Paul Bourgade","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-21T19:31:51Z","title":"Fixed energy universality for generalized Wigner matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5606","kind":"arxiv","version":3},"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":"sha256:52bf60c403c4ef6f7064ec76926791ecc18cbf1d95e61de8666b217a8e3978e7","target":"record","created_at":"2026-05-18T02:18:40Z","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":"4c9f0c73e301ca85cb862791d8064d0440d35723ec3a4a7170ce660070151c0d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-21T19:31:51Z","title_canon_sha256":"13781452c03edde8d97381b9a324019a2bb51ee45740df6c97516907a596aed4"},"schema_version":"1.0","source":{"id":"1407.5606","kind":"arxiv","version":3}},"canonical_sha256":"47049641e6dc0a5049718b6c13a48eab7257790b7bbfd83304812d0932de5e53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47049641e6dc0a5049718b6c13a48eab7257790b7bbfd83304812d0932de5e53","first_computed_at":"2026-05-18T02:18:40.876576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:40.876576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WEMNt/V2e7T7UFRrCXsfPJ+flsKyskgczY9Ouua91pT04WOZe3XGw2zsVo9+Hh0ighaYncZ6WMlPfhNfDVh9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:40.877366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5606","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52bf60c403c4ef6f7064ec76926791ecc18cbf1d95e61de8666b217a8e3978e7","sha256:51f57d4ac3b168c35ca9b9138eb985a22b0f87f76772726793fae47dda5a318e"],"state_sha256":"150fd9cf4cf9c0e60d400bc82945f88fafc743a84661a3bfd4f0e8178db5958c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFTgv8/Afg5pGj3G/LdDjaW3tRNLruF5CWoYqgazK0eFSovyz64R8/FZn+GgGWLFQtVi14jTSXop8xE0MzaeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:55:52.928525Z","bundle_sha256":"30c1d8e3f2fa62166aa8a9a83d7d35f69bfa384a362d1a33f3cfa475c4146c1e"}}