{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:6ZI42SIXFINZX6DFPJNRBDBEPN","short_pith_number":"pith:6ZI42SIX","canonical_record":{"source":{"id":"2112.10955","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-12-21T03:09:43Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.DS"],"title_canon_sha256":"0931e9ad5e4a8491c450334b92ee059d3aaca9bc0fb511f128b6ae499e5b8868","abstract_canon_sha256":"3d746b02089974503a4c21d31fa341dd9dc7cc628382973abca5499bb3c370ab"},"schema_version":"1.0"},"canonical_sha256":"f651cd49172a1b9bf8657a5b108c247b7c76d2bf26a2a9c166576611af26ee10","source":{"kind":"arxiv","id":"2112.10955","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10955","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10955v6","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10955","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"6ZI42SIXFINZ","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_16","alias_value":"6ZI42SIXFINZX6DF","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_8","alias_value":"6ZI42SIX","created_at":"2026-07-05T07:29:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:6ZI42SIXFINZX6DFPJNRBDBEPN","target":"record","payload":{"canonical_record":{"source":{"id":"2112.10955","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-12-21T03:09:43Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.DS"],"title_canon_sha256":"0931e9ad5e4a8491c450334b92ee059d3aaca9bc0fb511f128b6ae499e5b8868","abstract_canon_sha256":"3d746b02089974503a4c21d31fa341dd9dc7cc628382973abca5499bb3c370ab"},"schema_version":"1.0"},"canonical_sha256":"f651cd49172a1b9bf8657a5b108c247b7c76d2bf26a2a9c166576611af26ee10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:29:24.676200Z","signature_b64":"iXV3qFOU3qQPE/iynZsSiugEuHz8pYnQAPkL817g5DGuin8IIpQBRBS4U85zQxW/5ePMT1W+D2SRUhuE6ZLXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f651cd49172a1b9bf8657a5b108c247b7c76d2bf26a2a9c166576611af26ee10","last_reissued_at":"2026-07-05T07:29:24.675712Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:29:24.675712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.10955","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgziZSPoRDbN/0mrs1JytefitdCpFCrRZAuKC4L6s8lpYyDCa1tx6cPquvFP0pdkQeKLAF4J69st0tKzbfqQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:43:04.315046Z"},"content_sha256":"ef083986f3435d3169a62d06f1df5f00aef0e6fd4874ad02fdcd863a914e2bff","schema_version":"1.0","event_id":"sha256:ef083986f3435d3169a62d06f1df5f00aef0e6fd4874ad02fdcd863a914e2bff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:6ZI42SIXFINZX6DFPJNRBDBEPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joint Learning of Linear Time-Invariant Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","eess.SY","math.DS"],"primary_cat":"stat.ML","authors_text":"Aditya Modi, Ambuj Tewari, George Michailidis, Mohamad Kazem Shirani Faradonbeh","submitted_at":"2021-12-21T03:09:43Z","abstract_excerpt":"Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear systems to estimate their transition matrices more accurately. To address this problem, the current paper investigates methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10955","kind":"arxiv","version":6},"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/2112.10955/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":"2026-07-05T07:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lqsWljhw81FoCbtasGcmnmTlYq/pqfRNlWB6wR6o4m+OcekVg1bYhuZHXdm8eVBhPp2HvO3mojTAwLtDlgddDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:43:04.316151Z"},"content_sha256":"23d74377831b42fe4e678393ac7b514b5ce77c924b13042da38ff02f5a09172d","schema_version":"1.0","event_id":"sha256:23d74377831b42fe4e678393ac7b514b5ce77c924b13042da38ff02f5a09172d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/bundle.json","state_url":"https://pith.science/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/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":"2026-08-08T00:43:04Z","links":{"resolver":"https://pith.science/pith/6ZI42SIXFINZX6DFPJNRBDBEPN","bundle":"https://pith.science/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/bundle.json","state":"https://pith.science/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZI42SIXFINZX6DFPJNRBDBEPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6ZI42SIXFINZX6DFPJNRBDBEPN","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":"3d746b02089974503a4c21d31fa341dd9dc7cc628382973abca5499bb3c370ab","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-12-21T03:09:43Z","title_canon_sha256":"0931e9ad5e4a8491c450334b92ee059d3aaca9bc0fb511f128b6ae499e5b8868"},"schema_version":"1.0","source":{"id":"2112.10955","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10955","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10955v6","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10955","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"6ZI42SIXFINZ","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_16","alias_value":"6ZI42SIXFINZX6DF","created_at":"2026-07-05T07:29:24Z"},{"alias_kind":"pith_short_8","alias_value":"6ZI42SIX","created_at":"2026-07-05T07:29:24Z"}],"graph_snapshots":[{"event_id":"sha256:23d74377831b42fe4e678393ac7b514b5ce77c924b13042da38ff02f5a09172d","target":"graph","created_at":"2026-07-05T07:29:24Z","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/2112.10955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear systems to estimate their transition matrices more accurately. To address this problem, the current paper investigates methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that ","authors_text":"Aditya Modi, Ambuj Tewari, George Michailidis, Mohamad Kazem Shirani Faradonbeh","cross_cats":["cs.LG","cs.SY","eess.SY","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-12-21T03:09:43Z","title":"Joint Learning of Linear Time-Invariant Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10955","kind":"arxiv","version":6},"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:ef083986f3435d3169a62d06f1df5f00aef0e6fd4874ad02fdcd863a914e2bff","target":"record","created_at":"2026-07-05T07:29:24Z","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":"3d746b02089974503a4c21d31fa341dd9dc7cc628382973abca5499bb3c370ab","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-12-21T03:09:43Z","title_canon_sha256":"0931e9ad5e4a8491c450334b92ee059d3aaca9bc0fb511f128b6ae499e5b8868"},"schema_version":"1.0","source":{"id":"2112.10955","kind":"arxiv","version":6}},"canonical_sha256":"f651cd49172a1b9bf8657a5b108c247b7c76d2bf26a2a9c166576611af26ee10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f651cd49172a1b9bf8657a5b108c247b7c76d2bf26a2a9c166576611af26ee10","first_computed_at":"2026-07-05T07:29:24.675712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:29:24.675712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iXV3qFOU3qQPE/iynZsSiugEuHz8pYnQAPkL817g5DGuin8IIpQBRBS4U85zQxW/5ePMT1W+D2SRUhuE6ZLXAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:29:24.676200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.10955","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef083986f3435d3169a62d06f1df5f00aef0e6fd4874ad02fdcd863a914e2bff","sha256:23d74377831b42fe4e678393ac7b514b5ce77c924b13042da38ff02f5a09172d"],"state_sha256":"81b4f4433f444bd09ca7d48db90a126ea0b0de1b35b442423e4202fbd998b303"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2IKr3fLB0832FHOKJb+0tyZbQCspD+EaxISohSM0EEeiDI6U0s6y83AD5zjreVpIVUDVn8ravmQBVDj8arSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T00:43:04.359145Z","bundle_sha256":"ba29d8af054333b856f7e4a18a1667ea0d66a35c62d5175aafcd043787830fed"}}