{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BTRCE7CKB3MG4ULH7DUOHW3DHE","short_pith_number":"pith:BTRCE7CK","schema_version":"1.0","canonical_sha256":"0ce2227c4a0ed86e5167f8e8e3db63393fbc691d8a8b0f32ea97df63790ac579","source":{"kind":"arxiv","id":"1309.4946","version":2},"attestation_state":"computed","paper":{"title":"Strongly continuous semigroups on some Fr\\'echet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrique Jord\\'a, Jochen Wengenroth, Leonhrd Frerick, Thomas Kalmes","submitted_at":"2013-09-19T11:58:25Z","abstract_excerpt":"We prove that for a strongly continuous semigroup on the Fr\\'echet space of all scalar sequences, its generator is a continuous linear operator and that the semigroup can be represented as exp(tA) where the exponential series converges in a very strong sense. This solves a problem posed by Conejero. Moreover, we improve recent results of Albanese, Bonet, and Ricker about semigroups on strict projective limits of Banach spaces."},"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":"1309.4946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T11:58:25Z","cross_cats_sorted":[],"title_canon_sha256":"6abb03a760e81bd7ad96578b0d8b644d46594d36bf0362cb494bcc429ab3a809","abstract_canon_sha256":"8057e5a968911744d29c28f08f804c01782518c4829f865824a0774f3890882e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:47.814874Z","signature_b64":"3TrGZqcDJtbKoimeP5yJzedS08DZQQNMPe9JOvz3JyxpNjQP/QtFj6ckup/k4oEduACm6mh9r03FupBsBrLbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ce2227c4a0ed86e5167f8e8e3db63393fbc691d8a8b0f32ea97df63790ac579","last_reissued_at":"2026-05-18T03:12:47.814029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:47.814029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly continuous semigroups on some Fr\\'echet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrique Jord\\'a, Jochen Wengenroth, Leonhrd Frerick, Thomas Kalmes","submitted_at":"2013-09-19T11:58:25Z","abstract_excerpt":"We prove that for a strongly continuous semigroup on the Fr\\'echet space of all scalar sequences, its generator is a continuous linear operator and that the semigroup can be represented as exp(tA) where the exponential series converges in a very strong sense. This solves a problem posed by Conejero. Moreover, we improve recent results of Albanese, Bonet, and Ricker about semigroups on strict projective limits of Banach spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4946","kind":"arxiv","version":2},"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":"1309.4946","created_at":"2026-05-18T03:12:47.814181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.4946v2","created_at":"2026-05-18T03:12:47.814181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4946","created_at":"2026-05-18T03:12:47.814181+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTRCE7CKB3MG","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTRCE7CKB3MG4ULH","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTRCE7CK","created_at":"2026-05-18T12:27:40.988391+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/BTRCE7CKB3MG4ULH7DUOHW3DHE","json":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE.json","graph_json":"https://pith.science/api/pith-number/BTRCE7CKB3MG4ULH7DUOHW3DHE/graph.json","events_json":"https://pith.science/api/pith-number/BTRCE7CKB3MG4ULH7DUOHW3DHE/events.json","paper":"https://pith.science/paper/BTRCE7CK"},"agent_actions":{"view_html":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE","download_json":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE.json","view_paper":"https://pith.science/paper/BTRCE7CK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.4946&json=true","fetch_graph":"https://pith.science/api/pith-number/BTRCE7CKB3MG4ULH7DUOHW3DHE/graph.json","fetch_events":"https://pith.science/api/pith-number/BTRCE7CKB3MG4ULH7DUOHW3DHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE/action/storage_attestation","attest_author":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE/action/author_attestation","sign_citation":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE/action/citation_signature","submit_replication":"https://pith.science/pith/BTRCE7CKB3MG4ULH7DUOHW3DHE/action/replication_record"}},"created_at":"2026-05-18T03:12:47.814181+00:00","updated_at":"2026-05-18T03:12:47.814181+00:00"}