{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4NKDTV2XXXS3KOCK2NLTXXXFZT","short_pith_number":"pith:4NKDTV2X","canonical_record":{"source":{"id":"1609.09011","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T17:24:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"82125e34e9cc3ba54ad755c27b30ced719ad82e2a8ae9bd313ac786b9e93d83d","abstract_canon_sha256":"a1c053fcde77d78118f817c00a28b52b8d52c53bbc37f64a78d9a7e6f8b3fd08"},"schema_version":"1.0"},"canonical_sha256":"e35439d757bde5b5384ad3573bdee5ccebfa1b74ce80fbe5bacb69d4ea88b188","source":{"kind":"arxiv","id":"1609.09011","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09011","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09011v3","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09011","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"4NKDTV2XXXS3","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NKDTV2XXXS3KOCK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NKDTV2X","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4NKDTV2XXXS3KOCK2NLTXXXFZT","target":"record","payload":{"canonical_record":{"source":{"id":"1609.09011","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T17:24:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"82125e34e9cc3ba54ad755c27b30ced719ad82e2a8ae9bd313ac786b9e93d83d","abstract_canon_sha256":"a1c053fcde77d78118f817c00a28b52b8d52c53bbc37f64a78d9a7e6f8b3fd08"},"schema_version":"1.0"},"canonical_sha256":"e35439d757bde5b5384ad3573bdee5ccebfa1b74ce80fbe5bacb69d4ea88b188","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:30.418600Z","signature_b64":"dDdMGV1dCAMZlDSWLvxTYPUC8c62+ZDNTv07M47WjZaIbTT2fCO8WFqa8ZQV77+PNqKEEainEFT0vIxblH6XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e35439d757bde5b5384ad3573bdee5ccebfa1b74ce80fbe5bacb69d4ea88b188","last_reissued_at":"2026-05-17T23:56:30.418235Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:30.418235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.09011","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":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hy77by4/hrjeTXlj5Q2G9OEBWSVR2T+JyiIjQYzM5KgThLG9te0DrIwS/XF1rmw4sXghg+9QDJqDIDtU0IFvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:05:44.639285Z"},"content_sha256":"e5ca0df9a188cb11c882bd4d2e585c334dee6c86dc14f3eeb4d694ab54e910e0","schema_version":"1.0","event_id":"sha256:e5ca0df9a188cb11c882bd4d2e585c334dee6c86dc14f3eeb4d694ab54e910e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4NKDTV2XXXS3KOCK2NLTXXXFZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed energy universality for Dyson Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Benjamin Landon, Horng-Tzer Yau, Philippe Sosoe","submitted_at":"2016-09-28T17:24:26Z","abstract_excerpt":"We consider Dyson Brownian motion for classical values of $\\beta$ with deterministic initial data $V$. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time $t \\gtrsim 1/N$ if the density of states of $V$ is bounded above and below down to scales $\\eta \\ll t$ in a window of size $L \\gg \\sqrt{t}.$ Our results imply that fixed energy universality holds for essentially any random matrix ensemble for which averaged energy universality was previously known. Our methodology builds on the homogenization theory developed in [BEYY] which reduces th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09011","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":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0F9oLGAWgKIAiJWwwdGbwcmFQZiGhu9cmrLjYbI5E0O5ynIxKMJXSJjl59Q7rVABnA+zF610i4Dk35gTcl+xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:05:44.639660Z"},"content_sha256":"5ac4142dfc9a3d6548fb11a509c567eb98e468ce0d9e7aa0b8fafa2b03ed73b5","schema_version":"1.0","event_id":"sha256:5ac4142dfc9a3d6548fb11a509c567eb98e468ce0d9e7aa0b8fafa2b03ed73b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/bundle.json","state_url":"https://pith.science/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/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":"2026-06-02T21:05:44Z","links":{"resolver":"https://pith.science/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT","bundle":"https://pith.science/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/bundle.json","state":"https://pith.science/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NKDTV2XXXS3KOCK2NLTXXXFZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4NKDTV2XXXS3KOCK2NLTXXXFZT","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":"a1c053fcde77d78118f817c00a28b52b8d52c53bbc37f64a78d9a7e6f8b3fd08","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T17:24:26Z","title_canon_sha256":"82125e34e9cc3ba54ad755c27b30ced719ad82e2a8ae9bd313ac786b9e93d83d"},"schema_version":"1.0","source":{"id":"1609.09011","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09011","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09011v3","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09011","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"4NKDTV2XXXS3","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NKDTV2XXXS3KOCK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NKDTV2X","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5ac4142dfc9a3d6548fb11a509c567eb98e468ce0d9e7aa0b8fafa2b03ed73b5","target":"graph","created_at":"2026-05-17T23:56:30Z","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 consider Dyson Brownian motion for classical values of $\\beta$ with deterministic initial data $V$. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time $t \\gtrsim 1/N$ if the density of states of $V$ is bounded above and below down to scales $\\eta \\ll t$ in a window of size $L \\gg \\sqrt{t}.$ Our results imply that fixed energy universality holds for essentially any random matrix ensemble for which averaged energy universality was previously known. Our methodology builds on the homogenization theory developed in [BEYY] which reduces th","authors_text":"Benjamin Landon, Horng-Tzer Yau, Philippe Sosoe","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T17:24:26Z","title":"Fixed energy universality for Dyson Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09011","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:e5ca0df9a188cb11c882bd4d2e585c334dee6c86dc14f3eeb4d694ab54e910e0","target":"record","created_at":"2026-05-17T23:56:30Z","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":"a1c053fcde77d78118f817c00a28b52b8d52c53bbc37f64a78d9a7e6f8b3fd08","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T17:24:26Z","title_canon_sha256":"82125e34e9cc3ba54ad755c27b30ced719ad82e2a8ae9bd313ac786b9e93d83d"},"schema_version":"1.0","source":{"id":"1609.09011","kind":"arxiv","version":3}},"canonical_sha256":"e35439d757bde5b5384ad3573bdee5ccebfa1b74ce80fbe5bacb69d4ea88b188","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e35439d757bde5b5384ad3573bdee5ccebfa1b74ce80fbe5bacb69d4ea88b188","first_computed_at":"2026-05-17T23:56:30.418235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.418235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dDdMGV1dCAMZlDSWLvxTYPUC8c62+ZDNTv07M47WjZaIbTT2fCO8WFqa8ZQV77+PNqKEEainEFT0vIxblH6XAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.418600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09011","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5ca0df9a188cb11c882bd4d2e585c334dee6c86dc14f3eeb4d694ab54e910e0","sha256:5ac4142dfc9a3d6548fb11a509c567eb98e468ce0d9e7aa0b8fafa2b03ed73b5"],"state_sha256":"6b093ca29d22d0a67a6044b2c4f86f26a2a925d212fbcb894e3319289747caef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuRmBsz1Z83YXz/Bi8O2CbCkfE00x2+P/Dp0MuIMK0MUkpWKvzW8zBFIS7MVPZjp/RPpfHQYWPZXzPwGX21tCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:05:44.641941Z","bundle_sha256":"f710a818ec73b5ece880db20ceb7d9c2056391551c0e4d05271628826c466db2"}}