{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3ECV6543HAVUL7W2JPYUGFSHPV","short_pith_number":"pith:3ECV6543","canonical_record":{"source":{"id":"1412.3634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-11T12:49:34Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"9118a3db7bd95d9f449f846d8b2c57b1d0c0dbe2cf4e24fc2391fb853ee84d77","abstract_canon_sha256":"d5a71865a1346fc45add5d8bcaebf6f24903b900adf6f67c736bd4ec834d20ca"},"schema_version":"1.0"},"canonical_sha256":"d9055f779b382b45feda4bf14316477d506e8aefb1260a099641ca3a93cc7b59","source":{"kind":"arxiv","id":"1412.3634","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3634","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3634v1","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3634","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"3ECV6543HAVU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3ECV6543HAVUL7W2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3ECV6543","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3ECV6543HAVUL7W2JPYUGFSHPV","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-11T12:49:34Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"9118a3db7bd95d9f449f846d8b2c57b1d0c0dbe2cf4e24fc2391fb853ee84d77","abstract_canon_sha256":"d5a71865a1346fc45add5d8bcaebf6f24903b900adf6f67c736bd4ec834d20ca"},"schema_version":"1.0"},"canonical_sha256":"d9055f779b382b45feda4bf14316477d506e8aefb1260a099641ca3a93cc7b59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:16.718094Z","signature_b64":"LRJKwF0hEUbluO6/+4Vj7OV25J90xHqI5+5KCsauGCvZtQPbRTbDf3fH7xPuMcwAwtYVbqhU5HNPU/Wr2RhkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9055f779b382b45feda4bf14316477d506e8aefb1260a099641ca3a93cc7b59","last_reissued_at":"2026-05-18T01:23:16.717303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:16.717303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3634","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":"2026-05-18T01:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1BkSfi3D8tRMffoV1P++6EvZtAV373+AeL3AXYUL33ttTarh29lFiSfzW0pDcOiZ+enaRLYNkDMW7agQBFcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:47:00.007939Z"},"content_sha256":"b399aae23afc2ab8766f7386e1b856653233ef9551161faf2b49602ca57b2c60","schema_version":"1.0","event_id":"sha256:b399aae23afc2ab8766f7386e1b856653233ef9551161faf2b49602ca57b2c60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3ECV6543HAVUL7W2JPYUGFSHPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum learning of classical stochastic processes: The Completely-Positive Realization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Alex Monr\\`as, Andreas Winter","submitted_at":"2014-12-11T12:49:34Z","abstract_excerpt":"Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a textbook example, known as the positive realization problem (PRP). The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and positive systems theory.\n  We consider the scenario where the latent variables are quantum states, and the system dynamics is constrained only by physical transformations on the quantum s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3634","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":"2026-05-18T01:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZwZ5ZMbJGMiqIq7ZMuWVEiGF3EWCO3LfhCKbJzk7DFhXWIcGG+sfybzJ22HbtpKQTp2Wx35i3PvB/u4Nb/RCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:47:00.008292Z"},"content_sha256":"e8df2e0bd6e7c9a8251cd1eb2110ea6c277739c044caf1b6bcd7c4fb8c80a2cd","schema_version":"1.0","event_id":"sha256:e8df2e0bd6e7c9a8251cd1eb2110ea6c277739c044caf1b6bcd7c4fb8c80a2cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ECV6543HAVUL7W2JPYUGFSHPV/bundle.json","state_url":"https://pith.science/pith/3ECV6543HAVUL7W2JPYUGFSHPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ECV6543HAVUL7W2JPYUGFSHPV/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":"2026-06-04T14:47:00Z","links":{"resolver":"https://pith.science/pith/3ECV6543HAVUL7W2JPYUGFSHPV","bundle":"https://pith.science/pith/3ECV6543HAVUL7W2JPYUGFSHPV/bundle.json","state":"https://pith.science/pith/3ECV6543HAVUL7W2JPYUGFSHPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ECV6543HAVUL7W2JPYUGFSHPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3ECV6543HAVUL7W2JPYUGFSHPV","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":"d5a71865a1346fc45add5d8bcaebf6f24903b900adf6f67c736bd4ec834d20ca","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-11T12:49:34Z","title_canon_sha256":"9118a3db7bd95d9f449f846d8b2c57b1d0c0dbe2cf4e24fc2391fb853ee84d77"},"schema_version":"1.0","source":{"id":"1412.3634","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3634","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3634v1","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3634","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"3ECV6543HAVU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3ECV6543HAVUL7W2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3ECV6543","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:e8df2e0bd6e7c9a8251cd1eb2110ea6c277739c044caf1b6bcd7c4fb8c80a2cd","target":"graph","created_at":"2026-05-18T01:23:16Z","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":"Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a textbook example, known as the positive realization problem (PRP). The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and positive systems theory.\n  We consider the scenario where the latent variables are quantum states, and the system dynamics is constrained only by physical transformations on the quantum s","authors_text":"Alex Monr\\`as, Andreas Winter","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-11T12:49:34Z","title":"Quantum learning of classical stochastic processes: The Completely-Positive Realization Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3634","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:b399aae23afc2ab8766f7386e1b856653233ef9551161faf2b49602ca57b2c60","target":"record","created_at":"2026-05-18T01:23:16Z","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":"d5a71865a1346fc45add5d8bcaebf6f24903b900adf6f67c736bd4ec834d20ca","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-11T12:49:34Z","title_canon_sha256":"9118a3db7bd95d9f449f846d8b2c57b1d0c0dbe2cf4e24fc2391fb853ee84d77"},"schema_version":"1.0","source":{"id":"1412.3634","kind":"arxiv","version":1}},"canonical_sha256":"d9055f779b382b45feda4bf14316477d506e8aefb1260a099641ca3a93cc7b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9055f779b382b45feda4bf14316477d506e8aefb1260a099641ca3a93cc7b59","first_computed_at":"2026-05-18T01:23:16.717303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:16.717303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRJKwF0hEUbluO6/+4Vj7OV25J90xHqI5+5KCsauGCvZtQPbRTbDf3fH7xPuMcwAwtYVbqhU5HNPU/Wr2RhkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:16.718094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3634","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b399aae23afc2ab8766f7386e1b856653233ef9551161faf2b49602ca57b2c60","sha256:e8df2e0bd6e7c9a8251cd1eb2110ea6c277739c044caf1b6bcd7c4fb8c80a2cd"],"state_sha256":"687389fcdb07174cfb8acad51107cae3c22d7ace8ccede2b2028ffe517f64521"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEuOte5kQEEke4co+dhy+KqvLZFp2SEjoLGEb+CrGdwCNvOlR/rb2rIb4EsVpXaR68U5txqsPh8nBWTyiyxBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:47:00.010204Z","bundle_sha256":"c20374ef96cf8988cbaca721f348d7452c0661e5a6a4648ec984dafa4e44d953"}}