{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OFEXQ5754S55RUWNC62DFCCPBN","short_pith_number":"pith:OFEXQ575","canonical_record":{"source":{"id":"2207.11164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-22T16:01:51Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"9e8ebc5bcdfe60539dc35d6dd9edf57cd9ba10bb7b3cbf286967ab8b8229f5ee","abstract_canon_sha256":"16a866b005a363760c594c4ca0d9df5a705e54b5a256f04ef216405c8b0f624f"},"schema_version":"1.0"},"canonical_sha256":"71497877fde4bbd8d2cd17b432884f0b463d84840ba3064b8a39986f58a100aa","source":{"kind":"arxiv","id":"2207.11164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.11164","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"2207.11164v1","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.11164","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"OFEXQ5754S55","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_16","alias_value":"OFEXQ5754S55RUWN","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_8","alias_value":"OFEXQ575","created_at":"2026-07-05T04:42:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OFEXQ5754S55RUWNC62DFCCPBN","target":"record","payload":{"canonical_record":{"source":{"id":"2207.11164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-22T16:01:51Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"9e8ebc5bcdfe60539dc35d6dd9edf57cd9ba10bb7b3cbf286967ab8b8229f5ee","abstract_canon_sha256":"16a866b005a363760c594c4ca0d9df5a705e54b5a256f04ef216405c8b0f624f"},"schema_version":"1.0"},"canonical_sha256":"71497877fde4bbd8d2cd17b432884f0b463d84840ba3064b8a39986f58a100aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:42:44.173202Z","signature_b64":"A7crONSw2FlVh2ZFEWN/rS/1uqmPaK/GYjqReqT/SiHsOBLmAaLaS8ZAaaUcg6k3THrO53CJGAuFbYZ5XioUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71497877fde4bbd8d2cd17b432884f0b463d84840ba3064b8a39986f58a100aa","last_reissued_at":"2026-07-05T04:42:44.172807Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:42:44.172807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.11164","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":"2026-07-05T04:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCq462LT/zpbgeog/FbVX83f1aVFFDS0P8LoKBzHI9ijiSSB+PAZTejeLR9g+MHDw3sneZa4uq6dXLUFuuXRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:21:09.914765Z"},"content_sha256":"6007978f11c4288a7327c118c1bdce18d966ec352b415fdd8eabcad270e23754","schema_version":"1.0","event_id":"sha256:6007978f11c4288a7327c118c1bdce18d966ec352b415fdd8eabcad270e23754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OFEXQ5754S55RUWNC62DFCCPBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Identifiability Bounds for Mixture Models with Grouped Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Ren\\'e Saitenmacher, Robert A. Vandermeulen","submitted_at":"2022-07-22T16:01:51Z","abstract_excerpt":"Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the same mixture component. In this work we generalize that result and show that, if every subset of $k$ mixture components of a mixture model are linearly independent, then that mixture model is identifiable with only $(2m-1)/(k-1)$ samples per group. We further show that this value cannot be improved. We prove an analogous result for a stronger form of identifiab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11164","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/2207.11164/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":"2026-07-05T04:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwoT7CcE1sdCWdAiYhxK3vkptHq/HJMHSsFRLPCsiDcbj3soS0qtfUHBh+kouuBduhuuB62IcAcOd8iuQKNvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:21:09.915294Z"},"content_sha256":"12067ac8ce58781835c387c02e7898db22fa9c250f71bc995179c8bce49d6197","schema_version":"1.0","event_id":"sha256:12067ac8ce58781835c387c02e7898db22fa9c250f71bc995179c8bce49d6197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFEXQ5754S55RUWNC62DFCCPBN/bundle.json","state_url":"https://pith.science/pith/OFEXQ5754S55RUWNC62DFCCPBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFEXQ5754S55RUWNC62DFCCPBN/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":"2026-08-08T15:21:09Z","links":{"resolver":"https://pith.science/pith/OFEXQ5754S55RUWNC62DFCCPBN","bundle":"https://pith.science/pith/OFEXQ5754S55RUWNC62DFCCPBN/bundle.json","state":"https://pith.science/pith/OFEXQ5754S55RUWNC62DFCCPBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFEXQ5754S55RUWNC62DFCCPBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OFEXQ5754S55RUWNC62DFCCPBN","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":"16a866b005a363760c594c4ca0d9df5a705e54b5a256f04ef216405c8b0f624f","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-22T16:01:51Z","title_canon_sha256":"9e8ebc5bcdfe60539dc35d6dd9edf57cd9ba10bb7b3cbf286967ab8b8229f5ee"},"schema_version":"1.0","source":{"id":"2207.11164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.11164","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"2207.11164v1","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.11164","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"OFEXQ5754S55","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_16","alias_value":"OFEXQ5754S55RUWN","created_at":"2026-07-05T04:42:44Z"},{"alias_kind":"pith_short_8","alias_value":"OFEXQ575","created_at":"2026-07-05T04:42:44Z"}],"graph_snapshots":[{"event_id":"sha256:12067ac8ce58781835c387c02e7898db22fa9c250f71bc995179c8bce49d6197","target":"graph","created_at":"2026-07-05T04:42:44Z","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/2207.11164/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the same mixture component. In this work we generalize that result and show that, if every subset of $k$ mixture components of a mixture model are linearly independent, then that mixture model is identifiable with only $(2m-1)/(k-1)$ samples per group. We further show that this value cannot be improved. We prove an analogous result for a stronger form of identifiab","authors_text":"Ren\\'e Saitenmacher, Robert A. Vandermeulen","cross_cats":["cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-22T16:01:51Z","title":"Generalized Identifiability Bounds for Mixture Models with Grouped Samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11164","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":"sha256:6007978f11c4288a7327c118c1bdce18d966ec352b415fdd8eabcad270e23754","target":"record","created_at":"2026-07-05T04:42:44Z","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":"16a866b005a363760c594c4ca0d9df5a705e54b5a256f04ef216405c8b0f624f","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-22T16:01:51Z","title_canon_sha256":"9e8ebc5bcdfe60539dc35d6dd9edf57cd9ba10bb7b3cbf286967ab8b8229f5ee"},"schema_version":"1.0","source":{"id":"2207.11164","kind":"arxiv","version":1}},"canonical_sha256":"71497877fde4bbd8d2cd17b432884f0b463d84840ba3064b8a39986f58a100aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71497877fde4bbd8d2cd17b432884f0b463d84840ba3064b8a39986f58a100aa","first_computed_at":"2026-07-05T04:42:44.172807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:42:44.172807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A7crONSw2FlVh2ZFEWN/rS/1uqmPaK/GYjqReqT/SiHsOBLmAaLaS8ZAaaUcg6k3THrO53CJGAuFbYZ5XioUCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:42:44.173202Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.11164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6007978f11c4288a7327c118c1bdce18d966ec352b415fdd8eabcad270e23754","sha256:12067ac8ce58781835c387c02e7898db22fa9c250f71bc995179c8bce49d6197"],"state_sha256":"52cbe5b437d8d0cf383cd84f451c54069958c68b936ed369553457e8cd38a272"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UrG03UxEjVgTTDlOHvQJeGA+GrcAoe/QSWrfBc9tqk9/H+thNk/ajF1IK4Hj+dOQ8qfESR4k4fJXY6JJqEIrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:21:09.920998Z","bundle_sha256":"4784fbf2464e9581cb1e79dfd3eeb26dbb7e1ecb9e7caef59dc3175922e52a62"}}