{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YUCTRK5OVD2KAKQ5ICYETV4AUM","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":"1a32931ed76106bf517e40b066236c12e91bb04bf276acf439f6729fe035c57d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-03T18:43:54Z","title_canon_sha256":"7b74bbc0fd5e60354d85aae12c9c67d145647ece6588c760bb970e6cd724c471"},"schema_version":"1.0","source":{"id":"1703.01283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01283","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01283v1","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01283","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"pith_short_12","alias_value":"YUCTRK5OVD2K","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YUCTRK5OVD2KAKQ5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YUCTRK5O","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:7bf4b39700cae568f075ee6c842df5f57580658cf9fe5b28a4e8494da8b6efe7","target":"graph","created_at":"2026-05-18T00:49:35Z","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":"In this paper we present a general method for generation of uniformly continuous groups on abstract Fr\\'{e}chet spaces (without appealing to spectral theory) and apply it to a such space of distributions, namely ${\\mathscr F}L^{2}_{loc}(\\mathbb{R}^{n})$, so that the linear evolution problem \\begin{equation*} \\left\\{\\begin{array}{l} u_{t} = a(D)u, t \\in \\mathbb{R} \\\\ u(0) = u_0 \\end{array} \\right. \\end{equation*}always has a unique solution in such a space, for every pseudodifferential operator $a(D)$ with constant coefficients. We also provide necessary and sufficient conditions so that the sp","authors_text":"Alex Pereira da Silva, \\'Eder R\\'itis Arag\\~ao Costa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-03T18:43:54Z","title":"On the generation of groups of bounded linear operators on Fr\\'{e}chet spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01283","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:b833f7d1644e55253e5937cbd10a162cff7707cb52578f353e1cc949ce51a786","target":"record","created_at":"2026-05-18T00:49:35Z","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":"1a32931ed76106bf517e40b066236c12e91bb04bf276acf439f6729fe035c57d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-03T18:43:54Z","title_canon_sha256":"7b74bbc0fd5e60354d85aae12c9c67d145647ece6588c760bb970e6cd724c471"},"schema_version":"1.0","source":{"id":"1703.01283","kind":"arxiv","version":1}},"canonical_sha256":"c50538abaea8f4a02a1d40b049d780a32d79d38d251d9948041bc4bc6e598cb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c50538abaea8f4a02a1d40b049d780a32d79d38d251d9948041bc4bc6e598cb0","first_computed_at":"2026-05-18T00:49:35.501621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:35.501621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCWrkJpd7MFhfqqCJVL8gZkpZidUIcFzF13hRgnuXSQW2ECwiz3OYYTQ7oQz4l5WyGNx/2+4+2YzxJ3lm/STAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:35.502310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b833f7d1644e55253e5937cbd10a162cff7707cb52578f353e1cc949ce51a786","sha256:7bf4b39700cae568f075ee6c842df5f57580658cf9fe5b28a4e8494da8b6efe7"],"state_sha256":"355a84a7a4ec2ef723779fe0c6f8a5301247ac0807e4fc31ac64d516f8dca662"}