{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AZU5NHQEBV477MD3QLUBUKH735","short_pith_number":"pith:AZU5NHQE","canonical_record":{"source":{"id":"1502.02158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-02-07T16:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"09aaa601e0a688bddb89aa8aca1d28addfc455b8260c819683ee1bbee7cdd46a","abstract_canon_sha256":"f9865c9237051e5e910cf5f6fd3be3667e1be4f024af75284a498fe74f911231"},"schema_version":"1.0"},"canonical_sha256":"0669d69e040d79ffb07b82e81a28ffdf599aefecebaa0d6263b992fc1a4fbf49","source":{"kind":"arxiv","id":"1502.02158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02158","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02158v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02158","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"AZU5NHQEBV47","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"AZU5NHQEBV477MD3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"AZU5NHQE","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AZU5NHQEBV477MD3QLUBUKH735","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-02-07T16:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"09aaa601e0a688bddb89aa8aca1d28addfc455b8260c819683ee1bbee7cdd46a","abstract_canon_sha256":"f9865c9237051e5e910cf5f6fd3be3667e1be4f024af75284a498fe74f911231"},"schema_version":"1.0"},"canonical_sha256":"0669d69e040d79ffb07b82e81a28ffdf599aefecebaa0d6263b992fc1a4fbf49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:43.462985Z","signature_b64":"iKOmuNP1YRhk4ID/ERTlxopB8SUqta0i06qvSyFsdEG8AH4NYsCVDhGEPScyPFpjWUxNRviJP6wRtcrAxJ7eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0669d69e040d79ffb07b82e81a28ffdf599aefecebaa0d6263b992fc1a4fbf49","last_reissued_at":"2026-05-18T02:27:43.462415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:43.462415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02158","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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKXLKGzhmCAdY1taiJBR17ihNAdwxXeiwGoAGT3nTRLUlHH2RUcqWQLc4hcOW96kLSElgCuEyLLV3DXHTs2uAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:56:05.845469Z"},"content_sha256":"c2fe6948a6c89d151b70526ccf27ca4fc0662cfd76515ce9325ecc35bf75e42a","schema_version":"1.0","event_id":"sha256:c2fe6948a6c89d151b70526ccf27ca4fc0662cfd76515ce9325ecc35bf75e42a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AZU5NHQEBV477MD3QLUBUKH735","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Parametric-Output HMMs with Two Aliased States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Boaz Nadler, Roi Weiss","submitted_at":"2015-02-07T16:21:28Z","abstract_excerpt":"In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distribut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02158","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":""},"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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWM6u59JQC6z7wlA8srzTT0RLXsVpwLfBs0XXF1BseaM5Bc/IHqEMbKv9EX+ATjIj8+/c1XJT0mgM3RwCQnTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:56:05.845816Z"},"content_sha256":"fd33509339c2528edef503cd88971d22c4526dd5e4968e89607f212584a65d3d","schema_version":"1.0","event_id":"sha256:fd33509339c2528edef503cd88971d22c4526dd5e4968e89607f212584a65d3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZU5NHQEBV477MD3QLUBUKH735/bundle.json","state_url":"https://pith.science/pith/AZU5NHQEBV477MD3QLUBUKH735/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZU5NHQEBV477MD3QLUBUKH735/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":"2026-06-24T08:56:05Z","links":{"resolver":"https://pith.science/pith/AZU5NHQEBV477MD3QLUBUKH735","bundle":"https://pith.science/pith/AZU5NHQEBV477MD3QLUBUKH735/bundle.json","state":"https://pith.science/pith/AZU5NHQEBV477MD3QLUBUKH735/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZU5NHQEBV477MD3QLUBUKH735/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AZU5NHQEBV477MD3QLUBUKH735","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":"f9865c9237051e5e910cf5f6fd3be3667e1be4f024af75284a498fe74f911231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-02-07T16:21:28Z","title_canon_sha256":"09aaa601e0a688bddb89aa8aca1d28addfc455b8260c819683ee1bbee7cdd46a"},"schema_version":"1.0","source":{"id":"1502.02158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02158","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02158v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02158","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"AZU5NHQEBV47","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"AZU5NHQEBV477MD3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"AZU5NHQE","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:fd33509339c2528edef503cd88971d22c4526dd5e4968e89607f212584a65d3d","target":"graph","created_at":"2026-05-18T02:27:43Z","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":"In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distribut","authors_text":"Boaz Nadler, Roi Weiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-02-07T16:21:28Z","title":"Learning Parametric-Output HMMs with Two Aliased States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02158","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:c2fe6948a6c89d151b70526ccf27ca4fc0662cfd76515ce9325ecc35bf75e42a","target":"record","created_at":"2026-05-18T02:27:43Z","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":"f9865c9237051e5e910cf5f6fd3be3667e1be4f024af75284a498fe74f911231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-02-07T16:21:28Z","title_canon_sha256":"09aaa601e0a688bddb89aa8aca1d28addfc455b8260c819683ee1bbee7cdd46a"},"schema_version":"1.0","source":{"id":"1502.02158","kind":"arxiv","version":1}},"canonical_sha256":"0669d69e040d79ffb07b82e81a28ffdf599aefecebaa0d6263b992fc1a4fbf49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0669d69e040d79ffb07b82e81a28ffdf599aefecebaa0d6263b992fc1a4fbf49","first_computed_at":"2026-05-18T02:27:43.462415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:43.462415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iKOmuNP1YRhk4ID/ERTlxopB8SUqta0i06qvSyFsdEG8AH4NYsCVDhGEPScyPFpjWUxNRviJP6wRtcrAxJ7eBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:43.462985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2fe6948a6c89d151b70526ccf27ca4fc0662cfd76515ce9325ecc35bf75e42a","sha256:fd33509339c2528edef503cd88971d22c4526dd5e4968e89607f212584a65d3d"],"state_sha256":"de473f85f152a98f9d3d1227db4b5ee7e5c9766caf5ef791a6f5b0b9d51325f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MyNiMNGAJCaaPf5twQhnMDjblLn5ajwQ2EElgPBIhxt61xKFusode/R6VupqN7++ToolnpoZqgAcQEkWvlAAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:56:05.847583Z","bundle_sha256":"2754dc8a72baba1a7edcfbae26af70e8ed2fe131f78975f6f864dfd205c5ff08"}}