{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:775MLQAUXRCVMSOLKS3W7RJFEL","short_pith_number":"pith:775MLQAU","canonical_record":{"source":{"id":"1603.03221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-10T11:08:26Z","cross_cats_sorted":[],"title_canon_sha256":"3c4e4f287ab0e86620947bd0f826a9b7f7221b6470faf8e0666fed1ec6c01efe","abstract_canon_sha256":"87eac7cf6a1d9288a2ea35cdb781d304f714fdd4f156f07975a8ef095e0ad81c"},"schema_version":"1.0"},"canonical_sha256":"fffac5c014bc455649cb54b76fc52522ccfab252ac00c136d46d203f40e7cc9d","source":{"kind":"arxiv","id":"1603.03221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03221","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03221v1","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03221","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"775MLQAUXRCV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"775MLQAUXRCVMSOL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"775MLQAU","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:775MLQAUXRCVMSOLKS3W7RJFEL","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-10T11:08:26Z","cross_cats_sorted":[],"title_canon_sha256":"3c4e4f287ab0e86620947bd0f826a9b7f7221b6470faf8e0666fed1ec6c01efe","abstract_canon_sha256":"87eac7cf6a1d9288a2ea35cdb781d304f714fdd4f156f07975a8ef095e0ad81c"},"schema_version":"1.0"},"canonical_sha256":"fffac5c014bc455649cb54b76fc52522ccfab252ac00c136d46d203f40e7cc9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.742507Z","signature_b64":"e8f7MkCG4/pXAe628AobqSUBZZO6MJBKLsvdRFTcw96ucz2VU6mDeh6a8EnpfEa0ZI3770HmgXjB8kb8MxjMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fffac5c014bc455649cb54b76fc52522ccfab252ac00c136d46d203f40e7cc9d","last_reissued_at":"2026-05-18T01:19:16.742043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.742043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03221","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":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZ7CR34tz5W2UfIjFxZ1FafVsWe/REwO9ewRaZtTuvbzk8YiUA9ReFlurrTfHXwrsU1DBhhDkNm2hpGk4t/VAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:21:22.196571Z"},"content_sha256":"3588ca638500e3d606a54a85f133f6bc38f8804cff5b1994d69aa6ed14d6f819","schema_version":"1.0","event_id":"sha256:3588ca638500e3d606a54a85f133f6bc38f8804cff5b1994d69aa6ed14d6f819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:775MLQAUXRCVMSOLKS3W7RJFEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modelling, Detrending and Decorrelation of Network Time Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"G. P. Nason, M. A. Nunes, M. I. Knight","submitted_at":"2016-03-10T11:08:26Z","abstract_excerpt":"A network time series is a multivariate time series augmented by a graph that describes how variables (or nodes) are connected. We introduce the network autoregressive (integrated) moving average (NARIMA) processes: a set of flexible models for network time series. For fixed networks the NARIMA models are essentially equivalent to vector autoregressive moving average-type models. However, NARIMA models are especially useful when the structure of the graph, associated with the multivariate time series, changes over time. Such network topology changes are invisible to standard VARMA-like models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03221","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":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INDT0VXbgVFYJxL2scbr2tXYBxjEJNNoVAnFFTYmYO2+UNrh65S6y5MSdr6t5mCT6LkcYEnxKXnEaRa9DIbbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:21:22.197251Z"},"content_sha256":"74b99f338c92114725b9fa7ba53267f29d05a5693d8a11b602c268d5dd8e3327","schema_version":"1.0","event_id":"sha256:74b99f338c92114725b9fa7ba53267f29d05a5693d8a11b602c268d5dd8e3327"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/775MLQAUXRCVMSOLKS3W7RJFEL/bundle.json","state_url":"https://pith.science/pith/775MLQAUXRCVMSOLKS3W7RJFEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/775MLQAUXRCVMSOLKS3W7RJFEL/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":"2026-05-26T08:21:22Z","links":{"resolver":"https://pith.science/pith/775MLQAUXRCVMSOLKS3W7RJFEL","bundle":"https://pith.science/pith/775MLQAUXRCVMSOLKS3W7RJFEL/bundle.json","state":"https://pith.science/pith/775MLQAUXRCVMSOLKS3W7RJFEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/775MLQAUXRCVMSOLKS3W7RJFEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:775MLQAUXRCVMSOLKS3W7RJFEL","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":"87eac7cf6a1d9288a2ea35cdb781d304f714fdd4f156f07975a8ef095e0ad81c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-10T11:08:26Z","title_canon_sha256":"3c4e4f287ab0e86620947bd0f826a9b7f7221b6470faf8e0666fed1ec6c01efe"},"schema_version":"1.0","source":{"id":"1603.03221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03221","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03221v1","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03221","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"775MLQAUXRCV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"775MLQAUXRCVMSOL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"775MLQAU","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:74b99f338c92114725b9fa7ba53267f29d05a5693d8a11b602c268d5dd8e3327","target":"graph","created_at":"2026-05-18T01:19:16Z","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":"A network time series is a multivariate time series augmented by a graph that describes how variables (or nodes) are connected. We introduce the network autoregressive (integrated) moving average (NARIMA) processes: a set of flexible models for network time series. For fixed networks the NARIMA models are essentially equivalent to vector autoregressive moving average-type models. However, NARIMA models are especially useful when the structure of the graph, associated with the multivariate time series, changes over time. Such network topology changes are invisible to standard VARMA-like models.","authors_text":"G. P. Nason, M. A. Nunes, M. I. Knight","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-10T11:08:26Z","title":"Modelling, Detrending and Decorrelation of Network Time Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03221","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":"sha256:3588ca638500e3d606a54a85f133f6bc38f8804cff5b1994d69aa6ed14d6f819","target":"record","created_at":"2026-05-18T01:19:16Z","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":"87eac7cf6a1d9288a2ea35cdb781d304f714fdd4f156f07975a8ef095e0ad81c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-10T11:08:26Z","title_canon_sha256":"3c4e4f287ab0e86620947bd0f826a9b7f7221b6470faf8e0666fed1ec6c01efe"},"schema_version":"1.0","source":{"id":"1603.03221","kind":"arxiv","version":1}},"canonical_sha256":"fffac5c014bc455649cb54b76fc52522ccfab252ac00c136d46d203f40e7cc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fffac5c014bc455649cb54b76fc52522ccfab252ac00c136d46d203f40e7cc9d","first_computed_at":"2026-05-18T01:19:16.742043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:16.742043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8f7MkCG4/pXAe628AobqSUBZZO6MJBKLsvdRFTcw96ucz2VU6mDeh6a8EnpfEa0ZI3770HmgXjB8kb8MxjMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:16.742507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3588ca638500e3d606a54a85f133f6bc38f8804cff5b1994d69aa6ed14d6f819","sha256:74b99f338c92114725b9fa7ba53267f29d05a5693d8a11b602c268d5dd8e3327"],"state_sha256":"695939ce017ee837725cca62264af59a31081527ba3759b474805117e423c717"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDQoke+lzzv/GB+SzR97j96QOmz9pSNtYEybBkTIPHuvibVdegs0ADMF6oF3/dOU8cGVQSWmSe2Rin7MPZdiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:21:22.200665Z","bundle_sha256":"9ac3c7a156d798d84327b9fb97f42a62a24478d05cc82b240a5f3b7c9ed96077"}}