{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YZTAZRB6VGJS2KLKBENUQ2EFCZ","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":"b3e36532dd9da0f5e50f1dd4cf4c4af88dbdc2cc2a291e41981afb274b6774c8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-30T15:10:45Z","title_canon_sha256":"5e3a9c0ea3bc196d7b45255af68ee13c57e4e0d32c0aa3da66af28c55e3bcee8"},"schema_version":"1.0","source":{"id":"1009.6163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.6163","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1009.6163v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6163","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"YZTAZRB6VGJS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YZTAZRB6VGJS2KLK","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YZTAZRB6","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:74cf4d2fd49f6e51e646ff91ddaa3c627ee74d58ca9a85f18e695112f0747f0c","target":"graph","created_at":"2026-05-18T03:39:51Z","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":"Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) $\\l^p$-input $\\l^q$-state stability (sometimes is called Perron's property). The latter means that solutions of the non-homogeneous equation with zero initial data belong to $\\l^q$ when non-homogeneous terms are in $\\l^p$. It is assumed that at each moment the prehistory (the sequence of preceding states) belongs to some weighted $\\l^r$-space with an exponentially fading weight (the phase space). Our main result states that (i) $\\Leftrightarrow$ (ii) whenever $(p,","authors_text":"Elena Braverman, Illya M. Karabash","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-30T15:10:45Z","title":"Bohl-Perron type stability theorems for linear difference equations with infinite delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6163","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:b201b05569f9fad8b724db4436d288f10f34d80de16616e9c15e10ea712f302d","target":"record","created_at":"2026-05-18T03:39:51Z","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":"b3e36532dd9da0f5e50f1dd4cf4c4af88dbdc2cc2a291e41981afb274b6774c8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-30T15:10:45Z","title_canon_sha256":"5e3a9c0ea3bc196d7b45255af68ee13c57e4e0d32c0aa3da66af28c55e3bcee8"},"schema_version":"1.0","source":{"id":"1009.6163","kind":"arxiv","version":1}},"canonical_sha256":"c6660cc43ea9932d296a091b48688516671e99866366240be771f060c9df6bcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6660cc43ea9932d296a091b48688516671e99866366240be771f060c9df6bcc","first_computed_at":"2026-05-18T03:39:51.219206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.219206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sK/nmP5u2tcuDpCViwZJBfIRu62+7M1VQxUYZveKZmId9qYyM+ehlYknlBgIKX/Kb56GlU1MMNsl8MFsY8esDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.219651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.6163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b201b05569f9fad8b724db4436d288f10f34d80de16616e9c15e10ea712f302d","sha256:74cf4d2fd49f6e51e646ff91ddaa3c627ee74d58ca9a85f18e695112f0747f0c"],"state_sha256":"6f939ddc2b8d536cc824c5daee3d87355afa3e772c9cdfd53f26da346e8673fd"}