{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BLYYYG5NCOXK5OSTHGK2JL44RA","short_pith_number":"pith:BLYYYG5N","canonical_record":{"source":{"id":"2506.09165","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-10T18:27:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"74945dc47582120211679cb445fabb551142b95d45b5bcc3649b2524c3e65fc2","abstract_canon_sha256":"a5559812a7f9106dd71da254c4a3925d4d805cbeed891b4bdd5d4bfd5f97c38c"},"schema_version":"1.0"},"canonical_sha256":"0af18c1bad13aeaeba533995a4af9c882bba9f7e96643631c0b0726fb44de65a","source":{"kind":"arxiv","id":"2506.09165","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09165","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09165v2","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09165","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"BLYYYG5NCOXK","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_16","alias_value":"BLYYYG5NCOXK5OST","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_8","alias_value":"BLYYYG5N","created_at":"2026-07-05T11:48:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BLYYYG5NCOXK5OSTHGK2JL44RA","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09165","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-10T18:27:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"74945dc47582120211679cb445fabb551142b95d45b5bcc3649b2524c3e65fc2","abstract_canon_sha256":"a5559812a7f9106dd71da254c4a3925d4d805cbeed891b4bdd5d4bfd5f97c38c"},"schema_version":"1.0"},"canonical_sha256":"0af18c1bad13aeaeba533995a4af9c882bba9f7e96643631c0b0726fb44de65a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:49.832041Z","signature_b64":"59Y4fFKKdIAxfAvJcoLmToCu0STudR1PmMw0d7fgetXkoDG03/TEBrMy2rsRET0Aq1OEFrdiRybGfgTlbHGxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0af18c1bad13aeaeba533995a4af9c882bba9f7e96643631c0b0726fb44de65a","last_reissued_at":"2026-07-05T11:48:49.831529Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:49.831529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09165","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":"2026-07-05T11:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGcuJ9KoWSYc1u3EN/Tvn1FJ+ZLv+K5ILkt3gz3kAiEA3AHeSWw2SA88ZqmP0pPbU+omEn5Ro/eewZFXW4oyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:38:32.329570Z"},"content_sha256":"c463c38b2734e72366a7d985efb20a5ab7b7423bf32b11b91d9a59cf95baa2cd","schema_version":"1.0","event_id":"sha256:c463c38b2734e72366a7d985efb20a5ab7b7423bf32b11b91d9a59cf95baa2cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BLYYYG5NCOXK5OSTHGK2JL44RA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Pengkun Yang, Yichen Lyu","submitted_at":"2025-06-10T18:27:07Z","abstract_excerpt":"This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework applicable to diverse statistical settings. Our results rigorously demonstrate how increased dimensionality, coupled with diversity in variables, inherently facilitates identifiability. For the estimation problem, we establish near-optimal minimax rate bounds for the high-dimensional nonparametric density estimation under latent structures with smooth marginals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09165","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.09165/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":"2026-07-05T11:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unqEzeLqpQWpwj0/2mvFOiOOApXpfzRVE8rX+8I8UVzSL/0qDkrSVjhL1qY3x4Ik4XZDvJys47pSxHFXyrf/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:38:32.330075Z"},"content_sha256":"0a853cb8e02721a8627d3159f637f842cfd51385eb363ea51d0df6ea48ef05c7","schema_version":"1.0","event_id":"sha256:0a853cb8e02721a8627d3159f637f842cfd51385eb363ea51d0df6ea48ef05c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/bundle.json","state_url":"https://pith.science/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/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":"2026-08-09T01:38:32Z","links":{"resolver":"https://pith.science/pith/BLYYYG5NCOXK5OSTHGK2JL44RA","bundle":"https://pith.science/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/bundle.json","state":"https://pith.science/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLYYYG5NCOXK5OSTHGK2JL44RA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BLYYYG5NCOXK5OSTHGK2JL44RA","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":"a5559812a7f9106dd71da254c4a3925d4d805cbeed891b4bdd5d4bfd5f97c38c","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-10T18:27:07Z","title_canon_sha256":"74945dc47582120211679cb445fabb551142b95d45b5bcc3649b2524c3e65fc2"},"schema_version":"1.0","source":{"id":"2506.09165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09165","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09165v2","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09165","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"BLYYYG5NCOXK","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_16","alias_value":"BLYYYG5NCOXK5OST","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_8","alias_value":"BLYYYG5N","created_at":"2026-07-05T11:48:49Z"}],"graph_snapshots":[{"event_id":"sha256:0a853cb8e02721a8627d3159f637f842cfd51385eb363ea51d0df6ea48ef05c7","target":"graph","created_at":"2026-07-05T11:48:49Z","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/2506.09165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework applicable to diverse statistical settings. Our results rigorously demonstrate how increased dimensionality, coupled with diversity in variables, inherently facilitates identifiability. For the estimation problem, we establish near-optimal minimax rate bounds for the high-dimensional nonparametric density estimation under latent structures with smooth marginals.","authors_text":"Pengkun Yang, Yichen Lyu","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-10T18:27:07Z","title":"Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09165","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:c463c38b2734e72366a7d985efb20a5ab7b7423bf32b11b91d9a59cf95baa2cd","target":"record","created_at":"2026-07-05T11:48:49Z","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":"a5559812a7f9106dd71da254c4a3925d4d805cbeed891b4bdd5d4bfd5f97c38c","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-10T18:27:07Z","title_canon_sha256":"74945dc47582120211679cb445fabb551142b95d45b5bcc3649b2524c3e65fc2"},"schema_version":"1.0","source":{"id":"2506.09165","kind":"arxiv","version":2}},"canonical_sha256":"0af18c1bad13aeaeba533995a4af9c882bba9f7e96643631c0b0726fb44de65a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0af18c1bad13aeaeba533995a4af9c882bba9f7e96643631c0b0726fb44de65a","first_computed_at":"2026-07-05T11:48:49.831529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:48:49.831529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59Y4fFKKdIAxfAvJcoLmToCu0STudR1PmMw0d7fgetXkoDG03/TEBrMy2rsRET0Aq1OEFrdiRybGfgTlbHGxAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:48:49.832041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c463c38b2734e72366a7d985efb20a5ab7b7423bf32b11b91d9a59cf95baa2cd","sha256:0a853cb8e02721a8627d3159f637f842cfd51385eb363ea51d0df6ea48ef05c7"],"state_sha256":"e01bde06f5b2f3416c84c4b59fff3fa5e519f33a5044e25efed15f425d93e1d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VRHUGXOxt8ZeuC1lEKiVCFbXY3DLJ9ejr4ZaYF8TW92zi9mNWT/Nfp7kaHYis/1PGTFCeJrvEXGtYJIUJPy7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:38:32.334568Z","bundle_sha256":"0a7e1838524b8f83abbd631aca94723211fbd096820010b29a99bee543613be0"}}