{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VTMBVKOCEOVCF7QSDLIR5YWR3T","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":"a7ba5fc91038b61596caf25c33f32547d6e3ad91f55cfe7fddd6f5884e11d896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-12T06:54:10Z","title_canon_sha256":"ec5bc433493f1dfe4e8dc7d80b008a5e84a82a27f6748c26abba5f65e216d750"},"schema_version":"1.0","source":{"id":"1510.03157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03157","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03157v2","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03157","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"VTMBVKOCEOVC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VTMBVKOCEOVCF7QS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VTMBVKOC","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:36fa3d0ff5eb780dc572a049ed758cacfff1df6c51919051fd7e7534f4961891","target":"graph","created_at":"2026-05-18T00:55:04Z","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":"This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a couple consisting of a Markov trend and a linear decision process for which both the \"deterministic\" and the noise components rely on trend-dependent matrices. We discuss approximate, approximate null and exact null-controllability. Several examples are given to illustrate the links between these concepts and to compare our results with their continuous-time cou","authors_text":"Dan Goreac, Tidiane Diallo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-12T06:54:10Z","title":"Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03157","kind":"arxiv","version":2},"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:e85eea8455b6254e790ceddde7dac5c0cf6f413cef43410c1731782daf59db3b","target":"record","created_at":"2026-05-18T00:55:04Z","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":"a7ba5fc91038b61596caf25c33f32547d6e3ad91f55cfe7fddd6f5884e11d896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-12T06:54:10Z","title_canon_sha256":"ec5bc433493f1dfe4e8dc7d80b008a5e84a82a27f6748c26abba5f65e216d750"},"schema_version":"1.0","source":{"id":"1510.03157","kind":"arxiv","version":2}},"canonical_sha256":"acd81aa9c223aa22fe121ad11ee2d1dcd993ea3405b7fad8cbecce83b8a40f85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd81aa9c223aa22fe121ad11ee2d1dcd993ea3405b7fad8cbecce83b8a40f85","first_computed_at":"2026-05-18T00:55:04.301878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:04.301878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sf1Oz2DuaAg21jKDsDvPeFz7wNRR6wGZBZgwkJV9VQFLPQBKyvWNaIInYCkIobOop5rGhDP/t/3WDscVGhLpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:04.302367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e85eea8455b6254e790ceddde7dac5c0cf6f413cef43410c1731782daf59db3b","sha256:36fa3d0ff5eb780dc572a049ed758cacfff1df6c51919051fd7e7534f4961891"],"state_sha256":"7fcd5447010fa729a2c5f8a4df8c29da068c73aff68a0281097b4a81c84b9753"}