{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:H3HZKJRD7HCCT64ZO6QLWUHDLM","short_pith_number":"pith:H3HZKJRD","schema_version":"1.0","canonical_sha256":"3ecf952623f9c429fb9977a0bb50e35b1ad5e5f709cec4d26bac5beba1bf7dfa","source":{"kind":"arxiv","id":"1602.01163","version":1},"attestation_state":"computed","paper":{"title":"Operators $L^1 (\\mathbb R_+ )\\to X$ and the norm continuity problem for semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"R. Chill, Yu. Tomilov","submitted_at":"2016-02-03T01:24:06Z","abstract_excerpt":"We present a new method for constructing $C_0$-semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm topology are controlled simultaneously. It allows us to show that a) there exists a $C_0$-semigroup which is continuous in the operator-norm topology for no $t \\in [0,1]$ such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines; b) there exists a $C_0$-semigroup which is continuous in the operator-norm topology for no $t \\in \\mathbb R_+$ such that the resolvent of its generator h"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.01163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-03T01:24:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"684a9ad1ac889fd51e7cdfca9c5c4b68bc6f395abab3394b8d757bb23e09e13b","abstract_canon_sha256":"02824897db9826d0fcc698bdd2acdde97dd85208e8dd432b88c9a3f83a2def1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:23.440994Z","signature_b64":"ICdQ37MHAsshmVvkr8yrAHJcn9la0xWunwl/cv3+UE1rBIOY2SyzXwsCLGKKy3k7rwMw0jbIJOkPQAaw+W5bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ecf952623f9c429fb9977a0bb50e35b1ad5e5f709cec4d26bac5beba1bf7dfa","last_reissued_at":"2026-05-18T01:21:23.440483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:23.440483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operators $L^1 (\\mathbb R_+ )\\to X$ and the norm continuity problem for semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"R. Chill, Yu. Tomilov","submitted_at":"2016-02-03T01:24:06Z","abstract_excerpt":"We present a new method for constructing $C_0$-semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm topology are controlled simultaneously. It allows us to show that a) there exists a $C_0$-semigroup which is continuous in the operator-norm topology for no $t \\in [0,1]$ such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines; b) there exists a $C_0$-semigroup which is continuous in the operator-norm topology for no $t \\in \\mathbb R_+$ such that the resolvent of its generator h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01163","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.01163","created_at":"2026-05-18T01:21:23.440571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.01163v1","created_at":"2026-05-18T01:21:23.440571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01163","created_at":"2026-05-18T01:21:23.440571+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3HZKJRD7HCC","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3HZKJRD7HCCT64Z","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3HZKJRD","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM","json":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM.json","graph_json":"https://pith.science/api/pith-number/H3HZKJRD7HCCT64ZO6QLWUHDLM/graph.json","events_json":"https://pith.science/api/pith-number/H3HZKJRD7HCCT64ZO6QLWUHDLM/events.json","paper":"https://pith.science/paper/H3HZKJRD"},"agent_actions":{"view_html":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM","download_json":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM.json","view_paper":"https://pith.science/paper/H3HZKJRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.01163&json=true","fetch_graph":"https://pith.science/api/pith-number/H3HZKJRD7HCCT64ZO6QLWUHDLM/graph.json","fetch_events":"https://pith.science/api/pith-number/H3HZKJRD7HCCT64ZO6QLWUHDLM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM/action/storage_attestation","attest_author":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM/action/author_attestation","sign_citation":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM/action/citation_signature","submit_replication":"https://pith.science/pith/H3HZKJRD7HCCT64ZO6QLWUHDLM/action/replication_record"}},"created_at":"2026-05-18T01:21:23.440571+00:00","updated_at":"2026-05-18T01:21:23.440571+00:00"}