{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QZO65PP657RJQMBTOXYW4RRKJS","short_pith_number":"pith:QZO65PP6","canonical_record":{"source":{"id":"1609.07518","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-09-23T21:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"2605103a41e933436dfa93176f733e243cb786182b09e9626d98ed90322b3df8","abstract_canon_sha256":"6884664364a86cc24b66a9c9dfddd26ea826dc91cd27b0d255b023168eae27c2"},"schema_version":"1.0"},"canonical_sha256":"865deebdfeefe298303375f16e462a4c9c1f7078ad88bfc38708a6c26367f0a5","source":{"kind":"arxiv","id":"1609.07518","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07518","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07518v3","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07518","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"QZO65PP657RJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QZO65PP657RJQMBT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QZO65PP6","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QZO65PP657RJQMBTOXYW4RRKJS","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07518","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-09-23T21:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"2605103a41e933436dfa93176f733e243cb786182b09e9626d98ed90322b3df8","abstract_canon_sha256":"6884664364a86cc24b66a9c9dfddd26ea826dc91cd27b0d255b023168eae27c2"},"schema_version":"1.0"},"canonical_sha256":"865deebdfeefe298303375f16e462a4c9c1f7078ad88bfc38708a6c26367f0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:57.263717Z","signature_b64":"bckI8OVKq7gXD3R60FK1Zfi6Cs1WCRJAMQUjP1I94OZDY3gYt3UIQ+LZLvXUe6VviddNidhoJDUzrGMpWHLGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865deebdfeefe298303375f16e462a4c9c1f7078ad88bfc38708a6c26367f0a5","last_reissued_at":"2026-05-18T00:03:57.263114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:57.263114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07518","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9yQrlAa3NZwz8/YKAVRnVdqD5uPywwWaFg/p+SF9kuqayNo/h9rRvVAi/ul5wHw9kwVDmab3LmyisObvkeQ+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:59.284359Z"},"content_sha256":"1263248ac3a03b10f3a21ea9227157e800cab1dc5dd5cafff9ecb65c9952947f","schema_version":"1.0","event_id":"sha256:1263248ac3a03b10f3a21ea9227157e800cab1dc5dd5cafff9ecb65c9952947f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QZO65PP657RJQMBTOXYW4RRKJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Baptiste Sinquin, Michel Verhaegen","submitted_at":"2016-09-23T21:15:17Z","abstract_excerpt":"In this paper we propose a Kronecker-based modeling for identifying the spatial-temporal dynamics of large sensor arrays. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its coefficient-matrices are decomposed into a sum of Kronecker products. For a two-dimensional array of size $N \\times N$, and when the number of terms in the sum is small compared to $N$, exploiting the Kronecker structure leads to high data compression. We propose an Alternating Least Squares algorithm to identify the coefficient matrices with $\\mathcal{O}(N^3N_t)$, where $N_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07518","kind":"arxiv","version":3},"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":"2026-05-18T00:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCgeAw0L4gLTXl1N2lErFxORoUHqKqAqXFaYqv3EZX9EbSuDl2vHnKiB58sarXFCoWOX/qVLM5wzc0Up/JTaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:59.284704Z"},"content_sha256":"ca832e6e9589d2c1b33e78767ec276410bdcf407574517b5df4c07fabf54d4d0","schema_version":"1.0","event_id":"sha256:ca832e6e9589d2c1b33e78767ec276410bdcf407574517b5df4c07fabf54d4d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZO65PP657RJQMBTOXYW4RRKJS/bundle.json","state_url":"https://pith.science/pith/QZO65PP657RJQMBTOXYW4RRKJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZO65PP657RJQMBTOXYW4RRKJS/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":"2026-06-01T18:39:59Z","links":{"resolver":"https://pith.science/pith/QZO65PP657RJQMBTOXYW4RRKJS","bundle":"https://pith.science/pith/QZO65PP657RJQMBTOXYW4RRKJS/bundle.json","state":"https://pith.science/pith/QZO65PP657RJQMBTOXYW4RRKJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZO65PP657RJQMBTOXYW4RRKJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QZO65PP657RJQMBTOXYW4RRKJS","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":"6884664364a86cc24b66a9c9dfddd26ea826dc91cd27b0d255b023168eae27c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-09-23T21:15:17Z","title_canon_sha256":"2605103a41e933436dfa93176f733e243cb786182b09e9626d98ed90322b3df8"},"schema_version":"1.0","source":{"id":"1609.07518","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07518","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07518v3","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07518","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"QZO65PP657RJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QZO65PP657RJQMBT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QZO65PP6","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ca832e6e9589d2c1b33e78767ec276410bdcf407574517b5df4c07fabf54d4d0","target":"graph","created_at":"2026-05-18T00:03:57Z","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 this paper we propose a Kronecker-based modeling for identifying the spatial-temporal dynamics of large sensor arrays. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its coefficient-matrices are decomposed into a sum of Kronecker products. For a two-dimensional array of size $N \\times N$, and when the number of terms in the sum is small compared to $N$, exploiting the Kronecker structure leads to high data compression. We propose an Alternating Least Squares algorithm to identify the coefficient matrices with $\\mathcal{O}(N^3N_t)$, where $N_","authors_text":"Baptiste Sinquin, Michel Verhaegen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-09-23T21:15:17Z","title":"QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07518","kind":"arxiv","version":3},"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":"sha256:1263248ac3a03b10f3a21ea9227157e800cab1dc5dd5cafff9ecb65c9952947f","target":"record","created_at":"2026-05-18T00:03:57Z","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":"6884664364a86cc24b66a9c9dfddd26ea826dc91cd27b0d255b023168eae27c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-09-23T21:15:17Z","title_canon_sha256":"2605103a41e933436dfa93176f733e243cb786182b09e9626d98ed90322b3df8"},"schema_version":"1.0","source":{"id":"1609.07518","kind":"arxiv","version":3}},"canonical_sha256":"865deebdfeefe298303375f16e462a4c9c1f7078ad88bfc38708a6c26367f0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865deebdfeefe298303375f16e462a4c9c1f7078ad88bfc38708a6c26367f0a5","first_computed_at":"2026-05-18T00:03:57.263114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:57.263114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bckI8OVKq7gXD3R60FK1Zfi6Cs1WCRJAMQUjP1I94OZDY3gYt3UIQ+LZLvXUe6VviddNidhoJDUzrGMpWHLGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:57.263717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07518","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1263248ac3a03b10f3a21ea9227157e800cab1dc5dd5cafff9ecb65c9952947f","sha256:ca832e6e9589d2c1b33e78767ec276410bdcf407574517b5df4c07fabf54d4d0"],"state_sha256":"85ced0fdb32413ff08b770ed45f6bbbbb9eeea9b4b6f065f1a5a92090f18c45d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bt4i7HZmef3/VyykQODP3DvtciWl8RXzsYBYeJ4FO9NUTNBTsfAxVIvrY+iSPqxxt7TbZEVYzl0HbmwXJEiuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:39:59.286688Z","bundle_sha256":"b4d797f3a0b0be696951b89ab778bc0accd3b93d79704bcaee395be7b25184f2"}}