{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:G4GRHELMN5OC76FI5JTQ6ZOUQJ","short_pith_number":"pith:G4GRHELM","canonical_record":{"source":{"id":"2405.00386","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-01T08:36:31Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"681ebd5aec450cec1eff3a5a2e41c2cf38c3fd3fe52c2b20abf4e5fb5a53c504","abstract_canon_sha256":"ed38ae38b54c0ca2677174d2f4bcfd792d8900f407f2e0a6d27599b54219aae5"},"schema_version":"1.0"},"canonical_sha256":"370d13916c6f5c2ff8a8ea670f65d4824ece0a5ee92648825375d41d13e21901","source":{"kind":"arxiv","id":"2405.00386","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.00386","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"2405.00386v1","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.00386","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"G4GRHELMN5OC","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_16","alias_value":"G4GRHELMN5OC76FI","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_8","alias_value":"G4GRHELM","created_at":"2026-07-05T08:14:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:G4GRHELMN5OC76FI5JTQ6ZOUQJ","target":"record","payload":{"canonical_record":{"source":{"id":"2405.00386","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-01T08:36:31Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"681ebd5aec450cec1eff3a5a2e41c2cf38c3fd3fe52c2b20abf4e5fb5a53c504","abstract_canon_sha256":"ed38ae38b54c0ca2677174d2f4bcfd792d8900f407f2e0a6d27599b54219aae5"},"schema_version":"1.0"},"canonical_sha256":"370d13916c6f5c2ff8a8ea670f65d4824ece0a5ee92648825375d41d13e21901","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:14:12.272298Z","signature_b64":"CPiYX6iJFxOZ2wnRCMj0h4sfJyeY/biCAdirP5ClU5lmlEha0f4rH06n2eCQDY4nl9qOHGgKAIa8cMvFSg6bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370d13916c6f5c2ff8a8ea670f65d4824ece0a5ee92648825375d41d13e21901","last_reissued_at":"2026-07-05T08:14:12.271838Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:14:12.271838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.00386","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":"2026-07-05T08:14:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1uebjC4kp+6tgnH5CKAQqJ0/zRK2Qk3facTuUEEjzIii7+E82h0Wt2R9xEeZ2iwY8Gyk4cX1EoBOJJBO4A9cCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:18:04.042609Z"},"content_sha256":"731b53b8dd6a88f9ad5f497009393c0df4cad83d423603ade9272f758dbab2c9","schema_version":"1.0","event_id":"sha256:731b53b8dd6a88f9ad5f497009393c0df4cad83d423603ade9272f758dbab2c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:G4GRHELMN5OC76FI5JTQ6ZOUQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large gap probabilities of complex and symplectic spherical ensembles with point charges","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Seongjae Park, Sung-Soo Byun","submitted_at":"2024-05-01T08:36:31Z","abstract_excerpt":"We consider $n$ eigenvalues of complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases, we show that the probability that there are no eigenvalues in a spherical cap around the poles has an asymptotic behaviour as $n\\to \\infty$ of the form $$ \\exp\\Big( c_1 n^2 + c_2 n\\log n + c_3 n + c_4 \\sqrt n + c_5 \\log n + c_6 + \\mathcal{O}(n^{-\\frac1{12}}) \\Big) $$ and determine the coefficients explicitly. Our results provide the second example of precis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.00386","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/2405.00386/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":"2026-07-05T08:14:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vupa/fmh8YHxUhFNNb3qTE6+i3qmPFhRQU7BuH9ucstlFrvkYZf/bIVJWnKL3HuaHJt1pQVYWyH+KOumwJ7hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:18:04.043793Z"},"content_sha256":"15ad4d240a486a8e6e664e6b007a0cf574ffba9da0956f07de8d0d46914c0e96","schema_version":"1.0","event_id":"sha256:15ad4d240a486a8e6e664e6b007a0cf574ffba9da0956f07de8d0d46914c0e96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/bundle.json","state_url":"https://pith.science/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/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":"2026-08-10T18:18:04Z","links":{"resolver":"https://pith.science/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ","bundle":"https://pith.science/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/bundle.json","state":"https://pith.science/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4GRHELMN5OC76FI5JTQ6ZOUQJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G4GRHELMN5OC76FI5JTQ6ZOUQJ","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":"ed38ae38b54c0ca2677174d2f4bcfd792d8900f407f2e0a6d27599b54219aae5","cross_cats_sorted":["math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-01T08:36:31Z","title_canon_sha256":"681ebd5aec450cec1eff3a5a2e41c2cf38c3fd3fe52c2b20abf4e5fb5a53c504"},"schema_version":"1.0","source":{"id":"2405.00386","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.00386","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"2405.00386v1","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.00386","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"G4GRHELMN5OC","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_16","alias_value":"G4GRHELMN5OC76FI","created_at":"2026-07-05T08:14:12Z"},{"alias_kind":"pith_short_8","alias_value":"G4GRHELM","created_at":"2026-07-05T08:14:12Z"}],"graph_snapshots":[{"event_id":"sha256:15ad4d240a486a8e6e664e6b007a0cf574ffba9da0956f07de8d0d46914c0e96","target":"graph","created_at":"2026-07-05T08:14:12Z","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/2405.00386/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider $n$ eigenvalues of complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases, we show that the probability that there are no eigenvalues in a spherical cap around the poles has an asymptotic behaviour as $n\\to \\infty$ of the form $$ \\exp\\Big( c_1 n^2 + c_2 n\\log n + c_3 n + c_4 \\sqrt n + c_5 \\log n + c_6 + \\mathcal{O}(n^{-\\frac1{12}}) \\Big) $$ and determine the coefficients explicitly. Our results provide the second example of precis","authors_text":"Seongjae Park, Sung-Soo Byun","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-01T08:36:31Z","title":"Large gap probabilities of complex and symplectic spherical ensembles with point charges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.00386","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":"sha256:731b53b8dd6a88f9ad5f497009393c0df4cad83d423603ade9272f758dbab2c9","target":"record","created_at":"2026-07-05T08:14:12Z","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":"ed38ae38b54c0ca2677174d2f4bcfd792d8900f407f2e0a6d27599b54219aae5","cross_cats_sorted":["math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-01T08:36:31Z","title_canon_sha256":"681ebd5aec450cec1eff3a5a2e41c2cf38c3fd3fe52c2b20abf4e5fb5a53c504"},"schema_version":"1.0","source":{"id":"2405.00386","kind":"arxiv","version":1}},"canonical_sha256":"370d13916c6f5c2ff8a8ea670f65d4824ece0a5ee92648825375d41d13e21901","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370d13916c6f5c2ff8a8ea670f65d4824ece0a5ee92648825375d41d13e21901","first_computed_at":"2026-07-05T08:14:12.271838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:14:12.271838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CPiYX6iJFxOZ2wnRCMj0h4sfJyeY/biCAdirP5ClU5lmlEha0f4rH06n2eCQDY4nl9qOHGgKAIa8cMvFSg6bCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:14:12.272298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.00386","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:731b53b8dd6a88f9ad5f497009393c0df4cad83d423603ade9272f758dbab2c9","sha256:15ad4d240a486a8e6e664e6b007a0cf574ffba9da0956f07de8d0d46914c0e96"],"state_sha256":"20c91cdb034c7c26b22f818886e86c138b96fd50a3855dfadc12de28a5c22581"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3BHQhxt4bbnMBVal9D2owbZgkeLNyvOm1qFam6oFNwTYt3Cm3HS6KpW6mXVmKXZ4elJ27XrXqmfeaaiVDFRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T18:18:04.058302Z","bundle_sha256":"bc4dd8027382a7078fa0c423f32130e2649a86eda980ae01526ef01470045148"}}