{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UMFP7BS5EIJZGLRLLDH6JVLXFE","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":"78a9ab5484cca610fdd8b147408e2ecc00cbd0f889b8be9eb0caf2a7eeb3035b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-02T19:51:46Z","title_canon_sha256":"e8a3e04b6b90eb76186877145e60152d60cc84885a91603745d505338f01dec1"},"schema_version":"1.0","source":{"id":"1906.00473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00473","created_at":"2026-05-17T23:44:26Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00473v1","created_at":"2026-05-17T23:44:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00473","created_at":"2026-05-17T23:44:26Z"},{"alias_kind":"pith_short_12","alias_value":"UMFP7BS5EIJZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UMFP7BS5EIJZGLRL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UMFP7BS5","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c0358644c00b874f75dc272e8aa2d3b39ee62dbf8660f8ad00f4a6e113d87169","target":"graph","created_at":"2026-05-17T23:44:26Z","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":"The stability of an Auto-Regressive (AR) time sequence of finite order $L$, is determined by the maximal modulus $r^\\star$ among all zeros of its generating polynomial. If $r^\\star<1$ then the effect of input and initial conditions decays rapidly in time, whereas for $r^\\star>1$ it is exponentially magnified (with constant or polynomially growing oscillations when $r^\\star=1$). Persistence of such AR sequence (namely staying non-negative throughout $[0,N]$) with decent probability, requires the largest positive zero of the generating polynomial to have the largest multiplicity among all zeros ","authors_text":"Amir Dembo, Jian Ding, Jun Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-02T19:51:46Z","title":"Persistence versus stability for auto-regressive processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00473","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":"sha256:49fa7b19fb6a98b3a709f290e9b8a3dcb14941e3aa75e4464fcc5044bd98cbce","target":"record","created_at":"2026-05-17T23:44:26Z","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":"78a9ab5484cca610fdd8b147408e2ecc00cbd0f889b8be9eb0caf2a7eeb3035b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-02T19:51:46Z","title_canon_sha256":"e8a3e04b6b90eb76186877145e60152d60cc84885a91603745d505338f01dec1"},"schema_version":"1.0","source":{"id":"1906.00473","kind":"arxiv","version":1}},"canonical_sha256":"a30aff865d2213932e2b58cfe4d5772938ba0762144b7ff07ee73792515a54f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a30aff865d2213932e2b58cfe4d5772938ba0762144b7ff07ee73792515a54f8","first_computed_at":"2026-05-17T23:44:26.986221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:26.986221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQfD5RE6tdhwnlrIqlEH99ROrFvnisTiE/4IzFwlON4dUrsj51JuuPm90/KRPEawf2JDn43TRZrgivdYCep9AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:26.986843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.00473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49fa7b19fb6a98b3a709f290e9b8a3dcb14941e3aa75e4464fcc5044bd98cbce","sha256:c0358644c00b874f75dc272e8aa2d3b39ee62dbf8660f8ad00f4a6e113d87169"],"state_sha256":"7c0f27e8f2cf620bf622280ee3cacde8edd03ae48c52b3b997e3ba81ba224dd7"}