{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GHKNAB44A4KRV5Q7MK6SDSA7X5","short_pith_number":"pith:GHKNAB44","canonical_record":{"source":{"id":"2306.12263","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-21T13:29:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"54d53e1de5ed6403e77ac9274669890bba0bbc13503e91814886cf0d3d785197","abstract_canon_sha256":"e405c0b82149b7245697049c21caf2a15383223cd312cf6047bb51e12a8d2730"},"schema_version":"1.0"},"canonical_sha256":"31d4d0079c07151af61f62bd21c81fbf5546da5bf290ce54b45fcdc96e21c944","source":{"kind":"arxiv","id":"2306.12263","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12263","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12263v4","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12263","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"GHKNAB44A4KR","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_16","alias_value":"GHKNAB44A4KRV5Q7","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_8","alias_value":"GHKNAB44","created_at":"2026-07-05T09:40:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GHKNAB44A4KRV5Q7MK6SDSA7X5","target":"record","payload":{"canonical_record":{"source":{"id":"2306.12263","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-21T13:29:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"54d53e1de5ed6403e77ac9274669890bba0bbc13503e91814886cf0d3d785197","abstract_canon_sha256":"e405c0b82149b7245697049c21caf2a15383223cd312cf6047bb51e12a8d2730"},"schema_version":"1.0"},"canonical_sha256":"31d4d0079c07151af61f62bd21c81fbf5546da5bf290ce54b45fcdc96e21c944","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:14.371463Z","signature_b64":"h/58gpLsiveYlFqtviOaj4UajTaruGdE3K8lvR07jv6EPDhDvAnngFG4cV9+UvsrpqvloCa9SAlBosmp77F/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31d4d0079c07151af61f62bd21c81fbf5546da5bf290ce54b45fcdc96e21c944","last_reissued_at":"2026-07-05T09:40:14.370981Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:14.370981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.12263","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXpPBNEg7rbHdPgEhlTBFBwDFZuSI96HD58DhDHmgvHeQMeQAoUouwy6aISuwTZ7EDafDgobc0qFM9hwK8SdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:14:59.486657Z"},"content_sha256":"1ded5ecec48d9c3a0689aea6f196225c4e4d7f7e52be7066386d971d33d62672","schema_version":"1.0","event_id":"sha256:1ded5ecec48d9c3a0689aea6f196225c4e4d7f7e52be7066386d971d33d62672"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GHKNAB44A4KRV5Q7MK6SDSA7X5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Statistics in Normal Matrix Models with Merging Singularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Meng Yang, Seung-Yeop Lee, Torben Kr\\\"uger","submitted_at":"2023-06-21T13:29:47Z","abstract_excerpt":"We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel at the singularity, which is related to the parametrix of the Painlev\\'e~II equation. The two main tools are Riemann-Hilbert problems and the generalized Christoffel-Darboux identity. The correlation kernel exhibits a novel anisotropic scaling behavior, where the corresponding spacing scale of particles is $n^{-1/3}$ in the direction of merging and $n^{-1/2}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12263","kind":"arxiv","version":4},"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/2306.12263/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":"2026-07-05T09:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBBXD7a9wm/uDeJkruNOuV/T03IOHz+TbzO2IOxHFjJ6PusuaCZHRMimpIFsDwgcodUA2Qed8dtdGqdQ5O9rDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:14:59.487194Z"},"content_sha256":"b6fb032f87d4c144178f203944029ba2cd6d9bcf486c06ef1d2430a2d07a4a09","schema_version":"1.0","event_id":"sha256:b6fb032f87d4c144178f203944029ba2cd6d9bcf486c06ef1d2430a2d07a4a09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/bundle.json","state_url":"https://pith.science/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/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":"2026-08-11T16:14:59Z","links":{"resolver":"https://pith.science/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5","bundle":"https://pith.science/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/bundle.json","state":"https://pith.science/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHKNAB44A4KRV5Q7MK6SDSA7X5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GHKNAB44A4KRV5Q7MK6SDSA7X5","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":"e405c0b82149b7245697049c21caf2a15383223cd312cf6047bb51e12a8d2730","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-21T13:29:47Z","title_canon_sha256":"54d53e1de5ed6403e77ac9274669890bba0bbc13503e91814886cf0d3d785197"},"schema_version":"1.0","source":{"id":"2306.12263","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12263","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12263v4","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12263","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"GHKNAB44A4KR","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_16","alias_value":"GHKNAB44A4KRV5Q7","created_at":"2026-07-05T09:40:14Z"},{"alias_kind":"pith_short_8","alias_value":"GHKNAB44","created_at":"2026-07-05T09:40:14Z"}],"graph_snapshots":[{"event_id":"sha256:b6fb032f87d4c144178f203944029ba2cd6d9bcf486c06ef1d2430a2d07a4a09","target":"graph","created_at":"2026-07-05T09:40:14Z","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/2306.12263/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel at the singularity, which is related to the parametrix of the Painlev\\'e~II equation. The two main tools are Riemann-Hilbert problems and the generalized Christoffel-Darboux identity. The correlation kernel exhibits a novel anisotropic scaling behavior, where the corresponding spacing scale of particles is $n^{-1/3}$ in the direction of merging and $n^{-1/2}$","authors_text":"Meng Yang, Seung-Yeop Lee, Torben Kr\\\"uger","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-21T13:29:47Z","title":"Local Statistics in Normal Matrix Models with Merging Singularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12263","kind":"arxiv","version":4},"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":"sha256:1ded5ecec48d9c3a0689aea6f196225c4e4d7f7e52be7066386d971d33d62672","target":"record","created_at":"2026-07-05T09:40:14Z","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":"e405c0b82149b7245697049c21caf2a15383223cd312cf6047bb51e12a8d2730","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-06-21T13:29:47Z","title_canon_sha256":"54d53e1de5ed6403e77ac9274669890bba0bbc13503e91814886cf0d3d785197"},"schema_version":"1.0","source":{"id":"2306.12263","kind":"arxiv","version":4}},"canonical_sha256":"31d4d0079c07151af61f62bd21c81fbf5546da5bf290ce54b45fcdc96e21c944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31d4d0079c07151af61f62bd21c81fbf5546da5bf290ce54b45fcdc96e21c944","first_computed_at":"2026-07-05T09:40:14.370981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:14.370981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h/58gpLsiveYlFqtviOaj4UajTaruGdE3K8lvR07jv6EPDhDvAnngFG4cV9+UvsrpqvloCa9SAlBosmp77F/DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:14.371463Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.12263","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ded5ecec48d9c3a0689aea6f196225c4e4d7f7e52be7066386d971d33d62672","sha256:b6fb032f87d4c144178f203944029ba2cd6d9bcf486c06ef1d2430a2d07a4a09"],"state_sha256":"59c70aff8e748ddcab92dffb1dda991058d56d210c312bcc315289aa3689a8c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OhRBlkSeQpEIIj6qM8h9CXJSGn8BuDpMDnh4NA3a13p6SR0c395htS5not8CZJasJpmg+xFMSCc5pZm7VgoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:14:59.491875Z","bundle_sha256":"6e3b4ab22e4e7c06f40bcf9577e2b72dcec8dd8989ad69c9c906072ee0aeea6a"}}