{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VCYIME6YPLO2FHRTHIC5XXEQLP","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":"b19945f0dccf6e4e79ed601fed0ef3e0012a810bab651264ace49e27b9be840e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-06-10T02:18:49Z","title_canon_sha256":"c1d124927f1895dbb3062fa5b5c8dea926a2cf9a7d8d2a8152a0cc72a3fdf678"},"schema_version":"1.0","source":{"id":"1006.1940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1940","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1940v1","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1940","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"VCYIME6YPLO2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VCYIME6YPLO2FHRT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VCYIME6Y","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:3050572b14cd9b701741e2951467917a04c26460ba771213e149cad0ac7b11e3","target":"graph","created_at":"2026-05-18T03:59:38Z","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":"Suppose that $\\mathcal{X}$ is a sequentially complete Hausdorff locally convex space over a scalar field $\\mathbb{K}$, $V$ is a bounded subset of $\\mathcal{X}$, $(a_n)_{n\\ge 0}$ is a sequence in $\\mathbb{K}\\setminus\\{0\\}$ with the property\\ $\\ds\\liminf_{n\\to\\infty} |a_n|>1$ and $(b_n)_{n\\ge 0}$ is a sequence in $\\mathcal{X}$. We show that for every sequence $(x_n)_{n\\ge 0}$ in $\\mathcal{X}$ satisfying \\begin{eqnarray*} x_{n+1}-a_nx_n-b_n\\in V\\q(n\\geq 0) \\end{eqnarray*} there exists a unique sequence $(y_n)_{n\\ge 0}$ satisfying the recurrence $y_{n+1}=a_ny_n+b_n\\,\\,(n\\geq 0)$ and for every $q$ ","authors_text":"Dorian Popa, Mohammad Sal Moslehian","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-06-10T02:18:49Z","title":"On the stability of the first order linear recurrence in topological vector spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1940","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":"sha256:16d4507b8f2441fa04b00c9e5b5cbfe5e19856691e0222f3e7b9ac2cf72680d3","target":"record","created_at":"2026-05-18T03:59:38Z","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":"b19945f0dccf6e4e79ed601fed0ef3e0012a810bab651264ace49e27b9be840e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-06-10T02:18:49Z","title_canon_sha256":"c1d124927f1895dbb3062fa5b5c8dea926a2cf9a7d8d2a8152a0cc72a3fdf678"},"schema_version":"1.0","source":{"id":"1006.1940","kind":"arxiv","version":1}},"canonical_sha256":"a8b08613d87adda29e333a05dbdc905bd42896409d0e70a588ddd774474f14e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b08613d87adda29e333a05dbdc905bd42896409d0e70a588ddd774474f14e0","first_computed_at":"2026-05-18T03:59:38.546909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:38.546909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iM1oyEk4qxROTSx0nPgbWr9GLuDdFDFpSknbYCAEvHIZU2DpIRkPnSNFChYNXPIw8xJF5xPpbhmG9aDkPlM7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:38.547640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16d4507b8f2441fa04b00c9e5b5cbfe5e19856691e0222f3e7b9ac2cf72680d3","sha256:3050572b14cd9b701741e2951467917a04c26460ba771213e149cad0ac7b11e3"],"state_sha256":"bf68da2813d422ce67fa17ce60e83e96dc2593c782052287b9c334d183e99abd"}