{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:E2IZYEYFJH5EJJG362YYBMCOFZ","short_pith_number":"pith:E2IZYEYF","canonical_record":{"source":{"id":"1208.0762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T14:44:14Z","cross_cats_sorted":["math.CA","math.MP","math.PR"],"title_canon_sha256":"a082931bff29f2fa2e04d23b05df24709ff95734b4cdaa0e02c1d1179d02fd01","abstract_canon_sha256":"e9adfc9053192070fedc3f85aaf384b1225480de2c0ced6c2357c7e63eeb0e48"},"schema_version":"1.0"},"canonical_sha256":"26919c130549fa44a4dbf6b180b04e2e68da359b56adf16ab68fc5bf733a7b3f","source":{"kind":"arxiv","id":"1208.0762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0762","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0762v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0762","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"E2IZYEYFJH5E","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E2IZYEYFJH5EJJG3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E2IZYEYF","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:E2IZYEYFJH5EJJG362YYBMCOFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T14:44:14Z","cross_cats_sorted":["math.CA","math.MP","math.PR"],"title_canon_sha256":"a082931bff29f2fa2e04d23b05df24709ff95734b4cdaa0e02c1d1179d02fd01","abstract_canon_sha256":"e9adfc9053192070fedc3f85aaf384b1225480de2c0ced6c2357c7e63eeb0e48"},"schema_version":"1.0"},"canonical_sha256":"26919c130549fa44a4dbf6b180b04e2e68da359b56adf16ab68fc5bf733a7b3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:22.882576Z","signature_b64":"e2Lnv5LcvQ0rrb18qpiV/EO96t5uK/XrSXwYQieHoCr5XvkJ+ZbQuUkSJanogPT7wO+qRzkDeVUMhE9+uqzABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26919c130549fa44a4dbf6b180b04e2e68da359b56adf16ab68fc5bf733a7b3f","last_reissued_at":"2026-05-18T03:49:22.881648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:22.881648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0762","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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IyDpRZSxBcBzEB+mTtESb0O8oDxINprrCm0VYd4ez21sq5x3fMfZFyzSPclhzfWFn87ySIknPOl7PuXbwpyCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:36:57.886125Z"},"content_sha256":"2656c3754a24b92392a2cea59d52dd563b7d6b27fed5a8b580239bd63da6a8b3","schema_version":"1.0","event_id":"sha256:2656c3754a24b92392a2cea59d52dd563b7d6b27fed5a8b580239bd63da6a8b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:E2IZYEYFJH5EJJG362YYBMCOFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transitions between critical kernels: from the tacnode kernel and critical kernel in the two-matrix model to the Pearcey kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dries Geudens, Lun Zhang","submitted_at":"2012-08-03T14:44:14Z","abstract_excerpt":"In this paper we study two multicritical correlation kernels and prove that they converge to the Pearcey kernel in a certain double scaling limit. The first kernel appears in a model of non-intersecting Brownian motions at a tacnode. The second arises as a triple scaling limit of the eigenvalue correlation kernel in the Hermitian two-matrix model with quartic/quadratic potentials. The two kernels are different but can be expressed in terms of the same tacnode Riemann-Hilbert problem. The proof is based on a steepest descent analysis of this Riemann-Hilbert problem. A special feature in the ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0762","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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fo+lUL7KIo4Txp1GPviEqNSOZOb/BAKIVojhOvB42KwPBamGyBsMug69MpNfpnSSmm/fS0nTEiQJVlrKqI51CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:36:57.886552Z"},"content_sha256":"0d9013003e73a1d2ffcf6fb0cc4040c7f9b7dbfbf2c866fead04928d0f26fc1d","schema_version":"1.0","event_id":"sha256:0d9013003e73a1d2ffcf6fb0cc4040c7f9b7dbfbf2c866fead04928d0f26fc1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/bundle.json","state_url":"https://pith.science/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/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":"2026-05-31T16:36:57Z","links":{"resolver":"https://pith.science/pith/E2IZYEYFJH5EJJG362YYBMCOFZ","bundle":"https://pith.science/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/bundle.json","state":"https://pith.science/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2IZYEYFJH5EJJG362YYBMCOFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E2IZYEYFJH5EJJG362YYBMCOFZ","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":"e9adfc9053192070fedc3f85aaf384b1225480de2c0ced6c2357c7e63eeb0e48","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T14:44:14Z","title_canon_sha256":"a082931bff29f2fa2e04d23b05df24709ff95734b4cdaa0e02c1d1179d02fd01"},"schema_version":"1.0","source":{"id":"1208.0762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0762","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0762v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0762","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"E2IZYEYFJH5E","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E2IZYEYFJH5EJJG3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E2IZYEYF","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:0d9013003e73a1d2ffcf6fb0cc4040c7f9b7dbfbf2c866fead04928d0f26fc1d","target":"graph","created_at":"2026-05-18T03:49:22Z","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":"In this paper we study two multicritical correlation kernels and prove that they converge to the Pearcey kernel in a certain double scaling limit. The first kernel appears in a model of non-intersecting Brownian motions at a tacnode. The second arises as a triple scaling limit of the eigenvalue correlation kernel in the Hermitian two-matrix model with quartic/quadratic potentials. The two kernels are different but can be expressed in terms of the same tacnode Riemann-Hilbert problem. The proof is based on a steepest descent analysis of this Riemann-Hilbert problem. A special feature in the ana","authors_text":"Dries Geudens, Lun Zhang","cross_cats":["math.CA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T14:44:14Z","title":"Transitions between critical kernels: from the tacnode kernel and critical kernel in the two-matrix model to the Pearcey kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0762","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":"sha256:2656c3754a24b92392a2cea59d52dd563b7d6b27fed5a8b580239bd63da6a8b3","target":"record","created_at":"2026-05-18T03:49:22Z","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":"e9adfc9053192070fedc3f85aaf384b1225480de2c0ced6c2357c7e63eeb0e48","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T14:44:14Z","title_canon_sha256":"a082931bff29f2fa2e04d23b05df24709ff95734b4cdaa0e02c1d1179d02fd01"},"schema_version":"1.0","source":{"id":"1208.0762","kind":"arxiv","version":1}},"canonical_sha256":"26919c130549fa44a4dbf6b180b04e2e68da359b56adf16ab68fc5bf733a7b3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26919c130549fa44a4dbf6b180b04e2e68da359b56adf16ab68fc5bf733a7b3f","first_computed_at":"2026-05-18T03:49:22.881648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:22.881648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2Lnv5LcvQ0rrb18qpiV/EO96t5uK/XrSXwYQieHoCr5XvkJ+ZbQuUkSJanogPT7wO+qRzkDeVUMhE9+uqzABA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:22.882576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2656c3754a24b92392a2cea59d52dd563b7d6b27fed5a8b580239bd63da6a8b3","sha256:0d9013003e73a1d2ffcf6fb0cc4040c7f9b7dbfbf2c866fead04928d0f26fc1d"],"state_sha256":"edc48d44a9b34b6242362f308a06e226b77546e80e81e1aca2763580911a4cdf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wTD0my53KPaKBaXgLZm7o1avEVWl7t/APK8n9sA+ziTJt8/4Yns1IlcbpjuNd33/IfE4g7FD8RXLiLSZmIUsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:36:57.888982Z","bundle_sha256":"b5f1b0ae72af6aa2cdbb12d9a5f7e467e1c3efd3d29bb872f6ee501c180b242f"}}