{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XGW3KNGNH7H6KBS6B5TRFEYLMQ","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":"9a9dd129caf561509d785d9e75ed228f0cc8d2e3a18b7c6694353a020784c440","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-28T11:01:55Z","title_canon_sha256":"4eca33cae6742305ac06417825284ddd4c0910128193472e54491bec5762889d"},"schema_version":"1.0","source":{"id":"1906.12130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.12130","created_at":"2026-05-17T23:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"1906.12130v1","created_at":"2026-05-17T23:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.12130","created_at":"2026-05-17T23:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"XGW3KNGNH7H6","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XGW3KNGNH7H6KBS6","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XGW3KNGN","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:ad0cd2eb360eecf7c207796bc069513ce00dd32b594a933c6d25bf4981d36677","target":"graph","created_at":"2026-05-17T23:41:59Z","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 the limiting process that arises at the hard edge of Muttalib--Borodin ensembles. This point process depends on $\\theta > 0$ and has a kernel built out of Wright's generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form \\begin{equation*} \\mathbb{P}(\\mbox{gap on } [0,s]) = C \\exp \\left( -a s^{2\\rho} + b s^{\\rho} + c \\ln s \\right) (1 + o(1)) \\qquad \\mbox{as }s \\to + \\infty, \\end{equation*} where the constants $\\rho$, $a$, and $b$ ha","authors_text":"Christophe Charlier, Jonatan Lenells, Julian Mauersberger","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-28T11:01:55Z","title":"Higher order large gap asymptotics at the hard edge for Muttalib--Borodin ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12130","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":"sha256:18f0f40b363fa3de36ed85b06adb0990177cd7a7aca61c59776a2b62f740549c","target":"record","created_at":"2026-05-17T23:41:59Z","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":"9a9dd129caf561509d785d9e75ed228f0cc8d2e3a18b7c6694353a020784c440","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-28T11:01:55Z","title_canon_sha256":"4eca33cae6742305ac06417825284ddd4c0910128193472e54491bec5762889d"},"schema_version":"1.0","source":{"id":"1906.12130","kind":"arxiv","version":1}},"canonical_sha256":"b9adb534cd3fcfe5065e0f6712930b640d17c20b7195c747b98883872fbfff6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9adb534cd3fcfe5065e0f6712930b640d17c20b7195c747b98883872fbfff6c","first_computed_at":"2026-05-17T23:41:59.199281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:59.199281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z86qgdbC0LTcx4dhI4LUXnUCg9n842fOGzInu042+IYe7F0QIIvjyFswOgvpCxOIsQzk/CZqKQPBpjjdsWjeAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:59.199648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.12130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f0f40b363fa3de36ed85b06adb0990177cd7a7aca61c59776a2b62f740549c","sha256:ad0cd2eb360eecf7c207796bc069513ce00dd32b594a933c6d25bf4981d36677"],"state_sha256":"c6b651c1eb6813ce3c6b0d31a7fd6355b76ebfa488405cb35811c69f348fe637"}