{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UD2I3QJPJC6SX7UWDB7HHQG6VS","short_pith_number":"pith:UD2I3QJP","schema_version":"1.0","canonical_sha256":"a0f48dc12f48bd2bfe96187e73c0deacb9e718316fd71a637bf8a64603ac06b4","source":{"kind":"arxiv","id":"2607.13761","version":1},"attestation_state":"computed","paper":{"title":"Nonstandard likelihood-ratio limits under semidefinite rank constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Didier Concordet","submitted_at":"2026-07-15T12:21:26Z","abstract_excerpt":"We study likelihood-ratio tests for the hypothesis that a positive-semidefinite matrix has rank at most a prescribed value. The null hypothesis is stratified: points of maximal allowed rank lie on a regular boundary stratum, whereas lower-rank points are singular. Consequently, the usual chi-bar-square calibration on the top stratum does not by itself describe the whole composite null, especially along sequences whose rank changes at the local $n^{-1/2}$ scale.\n  After profiling regular nuisance parameters, we derive a common reduced Gaussian experiment for every fixed null rank and for all ad"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.13761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-15T12:21:26Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"27f977203c010766be3647c9f86252459e39cf3a087b5f47e634dd3786110eea","abstract_canon_sha256":"f5f89e88b0bd9a41031f067c73bcc1472648a31afd9e0350b8d5b83d275b518d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:05.017760Z","signature_b64":"fbCb7/RqezcY/gjpyLATMwTSqwHLlwEdxbabWuanWDIB7GMjtodZNxiviuRJJKBGlrsCBY8oWqRcu6k+enZ/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0f48dc12f48bd2bfe96187e73c0deacb9e718316fd71a637bf8a64603ac06b4","last_reissued_at":"2026-07-16T01:23:05.016923Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:05.016923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonstandard likelihood-ratio limits under semidefinite rank constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Didier Concordet","submitted_at":"2026-07-15T12:21:26Z","abstract_excerpt":"We study likelihood-ratio tests for the hypothesis that a positive-semidefinite matrix has rank at most a prescribed value. The null hypothesis is stratified: points of maximal allowed rank lie on a regular boundary stratum, whereas lower-rank points are singular. Consequently, the usual chi-bar-square calibration on the top stratum does not by itself describe the whole composite null, especially along sequences whose rank changes at the local $n^{-1/2}$ scale.\n  After profiling regular nuisance parameters, we derive a common reduced Gaussian experiment for every fixed null rank and for all ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13761","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/2607.13761/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.13761","created_at":"2026-07-16T01:23:05.017359+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13761v1","created_at":"2026-07-16T01:23:05.017359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13761","created_at":"2026-07-16T01:23:05.017359+00:00"},{"alias_kind":"pith_short_12","alias_value":"UD2I3QJPJC6S","created_at":"2026-07-16T01:23:05.017359+00:00"},{"alias_kind":"pith_short_16","alias_value":"UD2I3QJPJC6SX7UW","created_at":"2026-07-16T01:23:05.017359+00:00"},{"alias_kind":"pith_short_8","alias_value":"UD2I3QJP","created_at":"2026-07-16T01:23:05.017359+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS","json":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS.json","graph_json":"https://pith.science/api/pith-number/UD2I3QJPJC6SX7UWDB7HHQG6VS/graph.json","events_json":"https://pith.science/api/pith-number/UD2I3QJPJC6SX7UWDB7HHQG6VS/events.json","paper":"https://pith.science/paper/UD2I3QJP"},"agent_actions":{"view_html":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS","download_json":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS.json","view_paper":"https://pith.science/paper/UD2I3QJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13761&json=true","fetch_graph":"https://pith.science/api/pith-number/UD2I3QJPJC6SX7UWDB7HHQG6VS/graph.json","fetch_events":"https://pith.science/api/pith-number/UD2I3QJPJC6SX7UWDB7HHQG6VS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS/action/storage_attestation","attest_author":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS/action/author_attestation","sign_citation":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS/action/citation_signature","submit_replication":"https://pith.science/pith/UD2I3QJPJC6SX7UWDB7HHQG6VS/action/replication_record"}},"created_at":"2026-07-16T01:23:05.017359+00:00","updated_at":"2026-07-16T01:23:05.017359+00:00"}