{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3667LKVHI4ZKU2YPDXGVQ6MVDT","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":"b86589c8ccfda243db0a6ca2577bbf68b9e23c4d2977d00ea1c7a64f5a582897","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-29T19:51:50Z","title_canon_sha256":"4636aeef1c82ce149684629e2950cef42dd139f7a7a9a1a2201489ed7636f932"},"schema_version":"1.0","source":{"id":"1801.09733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09733","created_at":"2026-05-18T00:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09733v1","created_at":"2026-05-18T00:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09733","created_at":"2026-05-18T00:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"3667LKVHI4ZK","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3667LKVHI4ZKU2YP","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3667LKVH","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:d4407fb4db1a364c6f90728db97046ace9bd963ea76b1ce388ae77784b3af976","target":"graph","created_at":"2026-05-18T00:24:54Z","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 describe the different spectrums of the {\\alpha}-times integrated semigroups by the spectrums of their generators. Specially, essential ascent and descent, upper and lower semi-Fredholm and semi-Browder spectrums.","authors_text":"Abdelaziz Tajmouati, Abdeslam El Bakkali, Hamid Boua, Mohamed Baba Mohamed Ahmed","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-29T19:51:50Z","title":"Semi-Fredholm and semi-Browder spectrums for the ${\\alpha}$-times integrated semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09733","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:dfb5601ff274fc5c4e52134db0c6ecab6635da82b768de8d806ee6e81f48223d","target":"record","created_at":"2026-05-18T00:24:54Z","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":"b86589c8ccfda243db0a6ca2577bbf68b9e23c4d2977d00ea1c7a64f5a582897","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-29T19:51:50Z","title_canon_sha256":"4636aeef1c82ce149684629e2950cef42dd139f7a7a9a1a2201489ed7636f932"},"schema_version":"1.0","source":{"id":"1801.09733","kind":"arxiv","version":1}},"canonical_sha256":"dfbdf5aaa74732aa6b0f1dcd5879951ce1eca96a2a348a7a789d99cfbbbe44b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfbdf5aaa74732aa6b0f1dcd5879951ce1eca96a2a348a7a789d99cfbbbe44b4","first_computed_at":"2026-05-18T00:24:54.010044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:54.010044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U//tkjPvv1YAYLC9biJxUZlbFNImzICjVp979eqPgosjltFvq3N94MFkuFDePmtOcAJAthgPXjdWjgYbLJ5DCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:54.010885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfb5601ff274fc5c4e52134db0c6ecab6635da82b768de8d806ee6e81f48223d","sha256:d4407fb4db1a364c6f90728db97046ace9bd963ea76b1ce388ae77784b3af976"],"state_sha256":"ce9d2dd7b085861f98f8553001dd94386c4caa4388e34a9303b357888c3d5420"}