{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MZ6KVH7DRDW4SXB6MYSAITS5AE","short_pith_number":"pith:MZ6KVH7D","canonical_record":{"source":{"id":"2009.11176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-23T14:39:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8dc0a822e037298b9ba77f32b7c76bd9304c76e5c095beeb00fdb5d1417fb22c","abstract_canon_sha256":"ef4af792a1d61aa38c90e8932ba4ace2f77825e5a5692e82a896685e0b44e4fe"},"schema_version":"1.0"},"canonical_sha256":"667caa9fe388edc95c3e6624044e5d01026ef3b0427dc269209cb210b323ce1a","source":{"kind":"arxiv","id":"2009.11176","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11176","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11176v1","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11176","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"MZ6KVH7DRDW4","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_16","alias_value":"MZ6KVH7DRDW4SXB6","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_8","alias_value":"MZ6KVH7D","created_at":"2026-07-05T01:37:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MZ6KVH7DRDW4SXB6MYSAITS5AE","target":"record","payload":{"canonical_record":{"source":{"id":"2009.11176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-23T14:39:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8dc0a822e037298b9ba77f32b7c76bd9304c76e5c095beeb00fdb5d1417fb22c","abstract_canon_sha256":"ef4af792a1d61aa38c90e8932ba4ace2f77825e5a5692e82a896685e0b44e4fe"},"schema_version":"1.0"},"canonical_sha256":"667caa9fe388edc95c3e6624044e5d01026ef3b0427dc269209cb210b323ce1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:37:36.920602Z","signature_b64":"55peD4iw2dfmGru+cSXWyGICZrX+8pDLcIcusEfPRpyu1vxEoxJPqtwU6vw22bJZ5qAdyfsju0GYkGSRg+S3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"667caa9fe388edc95c3e6624044e5d01026ef3b0427dc269209cb210b323ce1a","last_reissued_at":"2026-07-05T01:37:36.920204Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:37:36.920204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.11176","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":"2026-07-05T01:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QDo9jhLsI6uVQZMh8p4vop+bpIy2Jr+DQnJ0goDOLKxfWPkiFRDqewlUvawGVIvGphcmXL5vY9ZUkTsyGmrOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T05:57:54.504430Z"},"content_sha256":"55430bed88c2c00e12d7d349ee9178143b29f4e73daf8990d0e7990f99bdd30b","schema_version":"1.0","event_id":"sha256:55430bed88c2c00e12d7d349ee9178143b29f4e73daf8990d0e7990f99bdd30b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MZ6KVH7DRDW4SXB6MYSAITS5AE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge scaling limit of Dyson Brownian motion at equilibrium for general $\\beta \\geq 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Benjamin Landon","submitted_at":"2020-09-23T14:39:13Z","abstract_excerpt":"For general $\\beta \\geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \\to \\infty$. For each fixed time, this ensemble is distributed as the Airy$_\\beta$ random point field. We prove that the increments of the limiting process are locally Brownian. When $\\beta >1$ we prove that after subtracting a Brownian motion, the sample paths are almost surely locally $r$-H{\\\"o}lder for any $r<1-(1+\\beta)^{-1}$. Furthermore for all $\\beta \\geq 1$ we show that the limiting process solves an SDE i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11176","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.11176/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Vj3ZpxKzWE10UizbrAi48vnGRstSJVLRiTxkOGxt2og400cbc29lePEwi4tuxGOlOjc8PMfZcG5WPK4QjzFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T05:57:54.504816Z"},"content_sha256":"6d825e101504e465ac9ef3e29fc0bc925a2afac76d1da03535091c7a2760afca","schema_version":"1.0","event_id":"sha256:6d825e101504e465ac9ef3e29fc0bc925a2afac76d1da03535091c7a2760afca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/bundle.json","state_url":"https://pith.science/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/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":"2026-07-20T05:57:54Z","links":{"resolver":"https://pith.science/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE","bundle":"https://pith.science/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/bundle.json","state":"https://pith.science/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ6KVH7DRDW4SXB6MYSAITS5AE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MZ6KVH7DRDW4SXB6MYSAITS5AE","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":"ef4af792a1d61aa38c90e8932ba4ace2f77825e5a5692e82a896685e0b44e4fe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-23T14:39:13Z","title_canon_sha256":"8dc0a822e037298b9ba77f32b7c76bd9304c76e5c095beeb00fdb5d1417fb22c"},"schema_version":"1.0","source":{"id":"2009.11176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11176","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11176v1","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11176","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"MZ6KVH7DRDW4","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_16","alias_value":"MZ6KVH7DRDW4SXB6","created_at":"2026-07-05T01:37:36Z"},{"alias_kind":"pith_short_8","alias_value":"MZ6KVH7D","created_at":"2026-07-05T01:37:36Z"}],"graph_snapshots":[{"event_id":"sha256:6d825e101504e465ac9ef3e29fc0bc925a2afac76d1da03535091c7a2760afca","target":"graph","created_at":"2026-07-05T01:37:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.11176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For general $\\beta \\geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \\to \\infty$. For each fixed time, this ensemble is distributed as the Airy$_\\beta$ random point field. We prove that the increments of the limiting process are locally Brownian. When $\\beta >1$ we prove that after subtracting a Brownian motion, the sample paths are almost surely locally $r$-H{\\\"o}lder for any $r<1-(1+\\beta)^{-1}$. Furthermore for all $\\beta \\geq 1$ we show that the limiting process solves an SDE i","authors_text":"Benjamin Landon","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-23T14:39:13Z","title":"Edge scaling limit of Dyson Brownian motion at equilibrium for general $\\beta \\geq 1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11176","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":"sha256:55430bed88c2c00e12d7d349ee9178143b29f4e73daf8990d0e7990f99bdd30b","target":"record","created_at":"2026-07-05T01:37:36Z","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":"ef4af792a1d61aa38c90e8932ba4ace2f77825e5a5692e82a896685e0b44e4fe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-23T14:39:13Z","title_canon_sha256":"8dc0a822e037298b9ba77f32b7c76bd9304c76e5c095beeb00fdb5d1417fb22c"},"schema_version":"1.0","source":{"id":"2009.11176","kind":"arxiv","version":1}},"canonical_sha256":"667caa9fe388edc95c3e6624044e5d01026ef3b0427dc269209cb210b323ce1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"667caa9fe388edc95c3e6624044e5d01026ef3b0427dc269209cb210b323ce1a","first_computed_at":"2026-07-05T01:37:36.920204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:37:36.920204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"55peD4iw2dfmGru+cSXWyGICZrX+8pDLcIcusEfPRpyu1vxEoxJPqtwU6vw22bJZ5qAdyfsju0GYkGSRg+S3Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:37:36.920602Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55430bed88c2c00e12d7d349ee9178143b29f4e73daf8990d0e7990f99bdd30b","sha256:6d825e101504e465ac9ef3e29fc0bc925a2afac76d1da03535091c7a2760afca"],"state_sha256":"88fa0c33155648e9c21b1e8c28f5ca61450342501f80a4c12623d0aa3e34d867"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WdMbpO/saW+hIzUWbcBuF/bNyb8FrZE5jQJUH3CkxJBCIpuUCjtjgFyogn5f3j7QYC9yR/TGReIroHN2vH/+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T05:57:54.507358Z","bundle_sha256":"67d72921d806d9592e729c881c08791cdecea7544a47d3d6861471d36c81201c"}}