{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5AWWBHITU5KNGYI4VMBKZRLLTB","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":"c3b0d32352975a01c90341baa2efe391893bb50926b6af394ed018368589093c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T15:15:22Z","title_canon_sha256":"55f901bfeb84bfebd07760a103242ae216da4fa680e7681aba45bde8b7cb3c13"},"schema_version":"1.0","source":{"id":"1802.00335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00335","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00335v1","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00335","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"5AWWBHITU5KN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5AWWBHITU5KNGYI4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5AWWBHIT","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:758d2cb3ef2b3cc09700d96b6c29775700031136a671971e0e727808e97cee2b","target":"graph","created_at":"2026-05-18T00:24:36Z","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":"This article deals with a variation of constants type inequality for semigroups acting consistently on a scale of Banach spaces. This inequality can be characterized by a corresponding (easy to verify) inequality for their generators. The results have applications to heat kernel estimates and provide a unified perspective to estimates of these type. Moreover, bi-continuous semigroups can be treated as well.","authors_text":"Christian Seifert, Hendrik Vogt, Marcus Waurick","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T15:15:22Z","title":"A note on perturbations of $C_0$-semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00335","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":"sha256:72bc654d1a16652e8cb318a5e25c43fb23dba67ab6b0e3e1452e6daab376fc49","target":"record","created_at":"2026-05-18T00:24:36Z","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":"c3b0d32352975a01c90341baa2efe391893bb50926b6af394ed018368589093c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T15:15:22Z","title_canon_sha256":"55f901bfeb84bfebd07760a103242ae216da4fa680e7681aba45bde8b7cb3c13"},"schema_version":"1.0","source":{"id":"1802.00335","kind":"arxiv","version":1}},"canonical_sha256":"e82d609d13a754d3611cab02acc56b98628bd7a47925185ec00d3efacbd227de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e82d609d13a754d3611cab02acc56b98628bd7a47925185ec00d3efacbd227de","first_computed_at":"2026-05-18T00:24:36.210831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:36.210831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BArrqXqvtezTCQZy7GtTb0P+qixRWnZl+HYxJ3G+G45BhoJk367kVO37bXfKytEy+QdM16v8D8JehNGuZNPhAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:36.211236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72bc654d1a16652e8cb318a5e25c43fb23dba67ab6b0e3e1452e6daab376fc49","sha256:758d2cb3ef2b3cc09700d96b6c29775700031136a671971e0e727808e97cee2b"],"state_sha256":"86af37928ce885283cf2685cf30e67dca3d840ff02cd659c0566e85024ad6160"}