{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AUWHDF7SDJGT5MYVDCFTZ37XQT","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":"e3d738f34e2a32274136fdb8a28b62ff1e9705a177aa0dfe99dcad7723a535f4","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-03-03T18:37:53Z","title_canon_sha256":"c15dd6e0de856a09a86dc8acb21f0d8a5028c6c553fb0f82093baadda64181c5"},"schema_version":"1.0","source":{"id":"2603.03245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03245","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03245v2","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03245","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_12","alias_value":"AUWHDF7SDJGT","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_16","alias_value":"AUWHDF7SDJGT5MYV","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_8","alias_value":"AUWHDF7S","created_at":"2026-05-26T01:02:32Z"}],"graph_snapshots":[{"event_id":"sha256:178efa0640196066a55dbfef60374f70708fed975b34c2091bc041d847ae2eb8","target":"graph","created_at":"2026-05-26T01:02:32Z","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/2603.03245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the problem of testing whether or not a given probability measure $\\mu$ on $\\mathbb{R}^{d}$ can be decomposed as a mixture of two probability measures whose second order statistics are significantly different. We call this the problem of testing the mixture model hypothesis. To tackle it, we introduce a new set of computable orthogonal invariants of $\\mu$, namely, the eigenvalues of the 4th moment operator $T_{\\mu}$ associated with the measure. We prove that the largest eigenvalue is always an outlier eigenvalue. Further, we show how the first and second largest eigenva","authors_text":"Joe Kileel, March T. Boedihardjo, Vandy Tombs","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-03-03T18:37:53Z","title":"Testing the mixture model hypothesis via spectral gap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03245","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:defd9e0296add592bc9527d0b1aa19bb079eaed58e8714c78c778567d715246c","target":"record","created_at":"2026-05-26T01:02:32Z","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":"e3d738f34e2a32274136fdb8a28b62ff1e9705a177aa0dfe99dcad7723a535f4","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-03-03T18:37:53Z","title_canon_sha256":"c15dd6e0de856a09a86dc8acb21f0d8a5028c6c553fb0f82093baadda64181c5"},"schema_version":"1.0","source":{"id":"2603.03245","kind":"arxiv","version":2}},"canonical_sha256":"052c7197f21a4d3eb315188b3ceff784ff2da570e81514920097a978e7d606a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"052c7197f21a4d3eb315188b3ceff784ff2da570e81514920097a978e7d606a7","first_computed_at":"2026-05-26T01:02:32.637895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:02:32.637895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IOX+lh/rqgYN3Mm4EbUW2CWQ9UYEZQ3DwHy8sUeKdc2u3lIWH95LwNnpsYE8X1uSEpjvHqiR9S6g4REW8ErPCg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:02:32.638869Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.03245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defd9e0296add592bc9527d0b1aa19bb079eaed58e8714c78c778567d715246c","sha256:178efa0640196066a55dbfef60374f70708fed975b34c2091bc041d847ae2eb8"],"state_sha256":"3720a950653192a27092756016aec84c016c65135326db1cf444d6afe79d048c"}