{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AK2ABZFEOPXC3SU36PK46FZ35C","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":"af490478895af211cc6433a6bd43fb8b1815383d82915a0b59ce2889225c1264","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-25T18:50:04Z","title_canon_sha256":"ceb2358e2985d7ec0273a76d5219e07876c4785cb2c0cf5b3ee2b26f9234676e"},"schema_version":"1.0","source":{"id":"1811.10071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10071","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10071v1","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10071","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"AK2ABZFEOPXC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AK2ABZFEOPXC3SU3","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AK2ABZFE","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:0a8aef4187bd5741e5e3e11b9f7042cd231a34712fb67a4c68a03cd035802906","target":"graph","created_at":"2026-05-17T23:59:57Z","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":"Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is always feasible for innovation processes taking values over a continuous set. However, the problem becomes more challenging when the alphabet size of the innovation is finite. In this case, we introduce both lossless and lossy frameworks, and provide closed-form solutions and practical algorithmic methods. In addition, we discuss the properties and uniqueness o","authors_text":"Amichai Painsky, Meir Feder, Saharon Rosset","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-25T18:50:04Z","title":"Innovation Representation of Stochastic Processes with Application to Causal Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10071","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:ee9ea41e215358e798e5808c2f9c61543d94d624fbad16348e6b5a8f659fb745","target":"record","created_at":"2026-05-17T23:59:57Z","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":"af490478895af211cc6433a6bd43fb8b1815383d82915a0b59ce2889225c1264","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-25T18:50:04Z","title_canon_sha256":"ceb2358e2985d7ec0273a76d5219e07876c4785cb2c0cf5b3ee2b26f9234676e"},"schema_version":"1.0","source":{"id":"1811.10071","kind":"arxiv","version":1}},"canonical_sha256":"02b400e4a473ee2dca9bf3d5cf173be8a7b1ebf525bc119eb6888edc51abf502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02b400e4a473ee2dca9bf3d5cf173be8a7b1ebf525bc119eb6888edc51abf502","first_computed_at":"2026-05-17T23:59:57.214619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:57.214619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ppiJ/W+ReHMMrHQQhZpTzPNMb24+qSNThiF6t3lHwIx8g5SK7B/DUguZ44/jv5mTZdSRyeSDRBoCWU3pSiBlAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:57.215352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee9ea41e215358e798e5808c2f9c61543d94d624fbad16348e6b5a8f659fb745","sha256:0a8aef4187bd5741e5e3e11b9f7042cd231a34712fb67a4c68a03cd035802906"],"state_sha256":"54db2745c819c524fa82e275eca92a7368e5414483ebecc851eda1353f809887"}