{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TW6JUIYXCARC3I2YDNFTAWUOB6","short_pith_number":"pith:TW6JUIYX","canonical_record":{"source":{"id":"1310.0727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T15:03:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e2a61dc6d45971c43bdf61520a26369f3d801751f3fda3d35ce89adc6a4f030e","abstract_canon_sha256":"490a23466e3f092cf7741a0cc09fc84b8bdf7d73563fd2238f4ffde996171fb5"},"schema_version":"1.0"},"canonical_sha256":"9dbc9a231710222da3581b4b305a8e0fb4408196648c38b5ec8585f065750695","source":{"kind":"arxiv","id":"1310.0727","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0727","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0727v2","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0727","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"TW6JUIYXCARC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TW6JUIYXCARC3I2Y","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TW6JUIYX","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TW6JUIYXCARC3I2YDNFTAWUOB6","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T15:03:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e2a61dc6d45971c43bdf61520a26369f3d801751f3fda3d35ce89adc6a4f030e","abstract_canon_sha256":"490a23466e3f092cf7741a0cc09fc84b8bdf7d73563fd2238f4ffde996171fb5"},"schema_version":"1.0"},"canonical_sha256":"9dbc9a231710222da3581b4b305a8e0fb4408196648c38b5ec8585f065750695","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:13.332364Z","signature_b64":"IY4PW2fn0wfZvNzBLTGvUNshHM9zI8d7fBf6q+1QdsLngNfh3RpW2/+GOjJ18akaiOeCVbKVknTeA13zPfiJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dbc9a231710222da3581b4b305a8e0fb4408196648c38b5ec8585f065750695","last_reissued_at":"2026-05-18T02:50:13.331644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:13.331644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0727","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3fk/5p7uHjDVfatU40Za5y0X5aKGpU+UqQS0Pr2zzqBFJl+zjbk7SeMEIB5GnF8hSTmNPeCr/VyEqs/6ik+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:59.756293Z"},"content_sha256":"dd5b00e1519cccd8b764890b6b697b3195afa280f774973defaa05cc1b91cf9b","schema_version":"1.0","event_id":"sha256:dd5b00e1519cccd8b764890b6b697b3195afa280f774973defaa05cc1b91cf9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TW6JUIYXCARC3I2YDNFTAWUOB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the second order universality at the edge of Coulomb gases on the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Djalil Chafa\\\"i (CEREMADE, IUF), Sandrine P\\'ech\\'e (LPMA)","submitted_at":"2013-10-02T15:03:01Z","abstract_excerpt":"We consider in this note a class of two-dimensional determinantal Coulomb gases confined by a radial external field. As the number of particles tends to infinity, their empirical distribution tends to a probability measure supported in a centered ring of the complex plane. A quadratic confinement corresponds to the complex Ginibre Ensemble. In this case, it is also already known that the asymptotic fluctuation of the radial edge follows a Gumbel law. We establish in this note the universality of this edge behavior, beyond the quadratic case. The approach, inspired by earlier works of Kostlan a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0727","kind":"arxiv","version":2},"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":"2026-05-18T02:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oA5K75c5qz9aUTq65e+v9Aa6HDEDNyDnzH5ZPEljPHN0yWphwncu3kE6KgDU0rmh1vBT7alacV82B5aYiiL7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:59.756670Z"},"content_sha256":"dda8b43c7f59fb005faffea014f90172d7bf95fdcf5e9f1665fe799d298b15b6","schema_version":"1.0","event_id":"sha256:dda8b43c7f59fb005faffea014f90172d7bf95fdcf5e9f1665fe799d298b15b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/bundle.json","state_url":"https://pith.science/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/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":"2026-06-01T08:27:59Z","links":{"resolver":"https://pith.science/pith/TW6JUIYXCARC3I2YDNFTAWUOB6","bundle":"https://pith.science/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/bundle.json","state":"https://pith.science/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TW6JUIYXCARC3I2YDNFTAWUOB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TW6JUIYXCARC3I2YDNFTAWUOB6","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":"490a23466e3f092cf7741a0cc09fc84b8bdf7d73563fd2238f4ffde996171fb5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T15:03:01Z","title_canon_sha256":"e2a61dc6d45971c43bdf61520a26369f3d801751f3fda3d35ce89adc6a4f030e"},"schema_version":"1.0","source":{"id":"1310.0727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0727","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0727v2","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0727","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"TW6JUIYXCARC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TW6JUIYXCARC3I2Y","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TW6JUIYX","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:dda8b43c7f59fb005faffea014f90172d7bf95fdcf5e9f1665fe799d298b15b6","target":"graph","created_at":"2026-05-18T02:50:13Z","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 in this note a class of two-dimensional determinantal Coulomb gases confined by a radial external field. As the number of particles tends to infinity, their empirical distribution tends to a probability measure supported in a centered ring of the complex plane. A quadratic confinement corresponds to the complex Ginibre Ensemble. In this case, it is also already known that the asymptotic fluctuation of the radial edge follows a Gumbel law. We establish in this note the universality of this edge behavior, beyond the quadratic case. The approach, inspired by earlier works of Kostlan a","authors_text":"Djalil Chafa\\\"i (CEREMADE, IUF), Sandrine P\\'ech\\'e (LPMA)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T15:03:01Z","title":"A note on the second order universality at the edge of Coulomb gases on the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0727","kind":"arxiv","version":2},"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:dd5b00e1519cccd8b764890b6b697b3195afa280f774973defaa05cc1b91cf9b","target":"record","created_at":"2026-05-18T02:50:13Z","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":"490a23466e3f092cf7741a0cc09fc84b8bdf7d73563fd2238f4ffde996171fb5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T15:03:01Z","title_canon_sha256":"e2a61dc6d45971c43bdf61520a26369f3d801751f3fda3d35ce89adc6a4f030e"},"schema_version":"1.0","source":{"id":"1310.0727","kind":"arxiv","version":2}},"canonical_sha256":"9dbc9a231710222da3581b4b305a8e0fb4408196648c38b5ec8585f065750695","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dbc9a231710222da3581b4b305a8e0fb4408196648c38b5ec8585f065750695","first_computed_at":"2026-05-18T02:50:13.331644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:13.331644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IY4PW2fn0wfZvNzBLTGvUNshHM9zI8d7fBf6q+1QdsLngNfh3RpW2/+GOjJ18akaiOeCVbKVknTeA13zPfiJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:13.332364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd5b00e1519cccd8b764890b6b697b3195afa280f774973defaa05cc1b91cf9b","sha256:dda8b43c7f59fb005faffea014f90172d7bf95fdcf5e9f1665fe799d298b15b6"],"state_sha256":"5624772896d1fab4c04104be46aefd5bc3828a25015075c8ebacc57d766aafe3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFV9z+EYvuV6z0dbIJpyvetUEN1t650TVBpwiuQUg4Yf5EtFYUvlOLxTeTZuY5kkuNY/WE2ERw9gOlz/KRtyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:27:59.758644Z","bundle_sha256":"44220ee20d3b72a9a0e55d1a52455c105f0a37b4615bd06ceead6f1a570b49c7"}}