{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XY3U2NGVMHF2HZVVEDJES44CCR","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":"2768b5d5721b049df36c90f8822d7bebbedcb773f45b8ec455b6cc856055e783","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-19T22:51:23Z","title_canon_sha256":"112dcf4264919f3351609094bcaf9b191a89b426c2c03fedf4f3af37b85dc8ab"},"schema_version":"1.0","source":{"id":"1501.04663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04663","created_at":"2026-05-18T02:29:03Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04663v1","created_at":"2026-05-18T02:29:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04663","created_at":"2026-05-18T02:29:03Z"},{"alias_kind":"pith_short_12","alias_value":"XY3U2NGVMHF2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XY3U2NGVMHF2HZVV","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XY3U2NGV","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:bb34abc70b8b8ec921c52adac3c391b05787c868a70a769ffe7a52b85ab9a83d","target":"graph","created_at":"2026-05-18T02:29:03Z","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":"At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring modalities that operate on different temporal scales. Fundamental to the description of network dynamics is the direction of interaction between nodes, accompanied by a measure of the strength of such interactions. Granger causality (GC) and its associated frequency domain strength measures (GEMs) (due to Geweke) provide a framework for the formulation and analysi","authors_text":"Victor Solo","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-19T22:51:23Z","title":"State Space Methods for Granger-Geweke Causality Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04663","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":"sha256:8445c2aae71c55e8b000add411fac884fe191e9bb13a716b934f611e5111a768","target":"record","created_at":"2026-05-18T02:29:03Z","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":"2768b5d5721b049df36c90f8822d7bebbedcb773f45b8ec455b6cc856055e783","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-19T22:51:23Z","title_canon_sha256":"112dcf4264919f3351609094bcaf9b191a89b426c2c03fedf4f3af37b85dc8ab"},"schema_version":"1.0","source":{"id":"1501.04663","kind":"arxiv","version":1}},"canonical_sha256":"be374d34d561cba3e6b520d24973821465c90c30f40e48486b218bceb1afde74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be374d34d561cba3e6b520d24973821465c90c30f40e48486b218bceb1afde74","first_computed_at":"2026-05-18T02:29:03.142351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:03.142351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+w9SgzBhP0VGEQHNQtSBOfN3bcCbfWVKWpazep3akD5UHfe5G3r7PFMZiCivRiRGFZQ3KT+9YH32rRAObWHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:03.142780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8445c2aae71c55e8b000add411fac884fe191e9bb13a716b934f611e5111a768","sha256:bb34abc70b8b8ec921c52adac3c391b05787c868a70a769ffe7a52b85ab9a83d"],"state_sha256":"e010fb29ad3b46ad8d12d9d68e1d421e95d32a59590f1ed228b1fa18192dd7f4"}