{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3IFBNCWVAQE7O7QEAB5NM34ID4","short_pith_number":"pith:3IFBNCWV","canonical_record":{"source":{"id":"1701.04618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-17T11:04:05Z","cross_cats_sorted":[],"title_canon_sha256":"32972b77dc410edd4db0831cb612535e2b765b6c719b4f249dd2f7574c24df24","abstract_canon_sha256":"a40aff2d3ce2e8e02b0549b13b2429b6fd89a8b5715aab08775173720672df74"},"schema_version":"1.0"},"canonical_sha256":"da0a168ad50409f77e04007ad66f881f2bef797754c41a4987348472fad6e1ac","source":{"kind":"arxiv","id":"1701.04618","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04618","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04618v1","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04618","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"3IFBNCWVAQE7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3IFBNCWVAQE7O7QE","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3IFBNCWV","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3IFBNCWVAQE7O7QEAB5NM34ID4","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-17T11:04:05Z","cross_cats_sorted":[],"title_canon_sha256":"32972b77dc410edd4db0831cb612535e2b765b6c719b4f249dd2f7574c24df24","abstract_canon_sha256":"a40aff2d3ce2e8e02b0549b13b2429b6fd89a8b5715aab08775173720672df74"},"schema_version":"1.0"},"canonical_sha256":"da0a168ad50409f77e04007ad66f881f2bef797754c41a4987348472fad6e1ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:43.105816Z","signature_b64":"HegaGyHwtOQCwXz8kHVLQU0/xu58YDDYCkdSSZnvhHNQBojZumUUokhtlZIyVZ2KI01Qmu3ha0jh3YpZ+f3fAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da0a168ad50409f77e04007ad66f881f2bef797754c41a4987348472fad6e1ac","last_reissued_at":"2026-05-18T00:52:43.105259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:43.105259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04618","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":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmypj9UPfLtHE9OMa1/h9QJd6pvx/UOd9Id6uQnTi1jTDtCIx2YFGKcoDUDhAc/EKWOALzi84nSM1CCzqamgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:43:46.887944Z"},"content_sha256":"8b0a89b8e67aa65c96bd7daa6837a8e9dda812db0c7d7af14423a299f148d832","schema_version":"1.0","event_id":"sha256:8b0a89b8e67aa65c96bd7daa6837a8e9dda812db0c7d7af14423a299f148d832"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3IFBNCWVAQE7O7QEAB5NM34ID4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous-time autoregressive moving-average processes in Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andre Suess, Fred Espen Benth","submitted_at":"2017-01-17T11:04:05Z","abstract_excerpt":"We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant properties of these processes and establish the equivalents of CARMA processes on the real line. Finally, CARMA processes in Hilbert space are linked to the stochastic wave equation and functional autoregressive processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04618","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":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzO3MAOlAtv10vlr7L/ZI9QP6Z07wrgbAdBL+pqmHkgp0C7iUr3nVoxvyi9+GxYUlzBkdOOlJR1PBe0zfinVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:43:46.888465Z"},"content_sha256":"baae32e4be0e7761940fe315ef3ae223ac8a499f45f4b4086dfed40280ac38ab","schema_version":"1.0","event_id":"sha256:baae32e4be0e7761940fe315ef3ae223ac8a499f45f4b4086dfed40280ac38ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/bundle.json","state_url":"https://pith.science/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/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":"2026-05-30T11:43:46Z","links":{"resolver":"https://pith.science/pith/3IFBNCWVAQE7O7QEAB5NM34ID4","bundle":"https://pith.science/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/bundle.json","state":"https://pith.science/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IFBNCWVAQE7O7QEAB5NM34ID4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3IFBNCWVAQE7O7QEAB5NM34ID4","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":"a40aff2d3ce2e8e02b0549b13b2429b6fd89a8b5715aab08775173720672df74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-17T11:04:05Z","title_canon_sha256":"32972b77dc410edd4db0831cb612535e2b765b6c719b4f249dd2f7574c24df24"},"schema_version":"1.0","source":{"id":"1701.04618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04618","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04618v1","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04618","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"3IFBNCWVAQE7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3IFBNCWVAQE7O7QE","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3IFBNCWV","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:baae32e4be0e7761940fe315ef3ae223ac8a499f45f4b4086dfed40280ac38ab","target":"graph","created_at":"2026-05-18T00:52:43Z","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":"We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant properties of these processes and establish the equivalents of CARMA processes on the real line. Finally, CARMA processes in Hilbert space are linked to the stochastic wave equation and functional autoregressive processes.","authors_text":"Andre Suess, Fred Espen Benth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-17T11:04:05Z","title":"Continuous-time autoregressive moving-average processes in Hilbert space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04618","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":"sha256:8b0a89b8e67aa65c96bd7daa6837a8e9dda812db0c7d7af14423a299f148d832","target":"record","created_at":"2026-05-18T00:52:43Z","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":"a40aff2d3ce2e8e02b0549b13b2429b6fd89a8b5715aab08775173720672df74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-17T11:04:05Z","title_canon_sha256":"32972b77dc410edd4db0831cb612535e2b765b6c719b4f249dd2f7574c24df24"},"schema_version":"1.0","source":{"id":"1701.04618","kind":"arxiv","version":1}},"canonical_sha256":"da0a168ad50409f77e04007ad66f881f2bef797754c41a4987348472fad6e1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da0a168ad50409f77e04007ad66f881f2bef797754c41a4987348472fad6e1ac","first_computed_at":"2026-05-18T00:52:43.105259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:43.105259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HegaGyHwtOQCwXz8kHVLQU0/xu58YDDYCkdSSZnvhHNQBojZumUUokhtlZIyVZ2KI01Qmu3ha0jh3YpZ+f3fAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:43.105816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b0a89b8e67aa65c96bd7daa6837a8e9dda812db0c7d7af14423a299f148d832","sha256:baae32e4be0e7761940fe315ef3ae223ac8a499f45f4b4086dfed40280ac38ab"],"state_sha256":"74ce32a6c456f9af3dd8b98ed5f58ae0c4e0dc8151812cd2263f8aaf9ac88b49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCjYcRYXVnc0O/hYNrhGr7NW9Vb69qjXqD6jY2fdP2Ee5zg69nFsxBL8vmfgNbJfPpRfKS8cU/U1P60MnHKgDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:43:46.892360Z","bundle_sha256":"d82bf369a88cf757655ac568a260f952be800fb10a245cf1d63d92b018d49bde"}}