{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3TEOQFSXZWFEV6EQWZZVPBVDBR","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":"33e80eb51c05b9ee9ad755dd8ea931b39b9b095b6850641da876f9d7375a78b8","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:07:17Z","title_canon_sha256":"b3652c2e11c06163504eb9b20507d2ba8f180f10fc67fb01db6d37ba2815ae3d"},"schema_version":"1.0","source":{"id":"1209.1457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1457","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1457v1","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1457","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"3TEOQFSXZWFE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3TEOQFSXZWFEV6EQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3TEOQFSX","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:01be408c147fec6753ecc65b3a5e8994ad617240e0053b9a568cbfe4049b01d2","target":"graph","created_at":"2026-05-18T03:46:04Z","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":"It is proved that for any separable infinite dimensional Banach space $X$, there is a bounded linear operator $T$ on $X$ such that $T$ satisfies the Kitai Criterion. The proof is based on quasisimilarity argument and on showing that $I+T$ satisfies the Kitai Criterion for certain backward weighted shifts $T$.","authors_text":"Stanislav Shkarin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:07:17Z","title":"The Kitai Criterion and backward shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1457","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":"sha256:6fb8459ea35370861067908f8bb04bb8a856209e08f5081f48774de252392647","target":"record","created_at":"2026-05-18T03:46:04Z","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":"33e80eb51c05b9ee9ad755dd8ea931b39b9b095b6850641da876f9d7375a78b8","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:07:17Z","title_canon_sha256":"b3652c2e11c06163504eb9b20507d2ba8f180f10fc67fb01db6d37ba2815ae3d"},"schema_version":"1.0","source":{"id":"1209.1457","kind":"arxiv","version":1}},"canonical_sha256":"dcc8e81657cd8a4af890b6735786a30c5d6cd3fab393995df74827d4c6aacb69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcc8e81657cd8a4af890b6735786a30c5d6cd3fab393995df74827d4c6aacb69","first_computed_at":"2026-05-18T03:46:04.745640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:04.745640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Znyl043M6cGuySsZO/RQUjg9dfcXde3TOFN/L90M9vrwmxAuAvJigcBVZspALUelv6U3aTecm3sgDSmGU1g9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:04.746538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fb8459ea35370861067908f8bb04bb8a856209e08f5081f48774de252392647","sha256:01be408c147fec6753ecc65b3a5e8994ad617240e0053b9a568cbfe4049b01d2"],"state_sha256":"12d8bc6c934b48642b2ad07c9f64490e457267fc1fcaf338000fd6e729a3e528"}