{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GSO6PTF74F6N4GHOO3DAPUJ6TQ","short_pith_number":"pith:GSO6PTF7","schema_version":"1.0","canonical_sha256":"349de7ccbfe17cde18ee76c607d13e9c3b021afeab0d4e52ddd73f7e7915a1f5","source":{"kind":"arxiv","id":"1505.02719","version":2},"attestation_state":"computed","paper":{"title":"Right (Or Left) Invertibility of Bounded and Unbounded Operators and Applications to the Spectrum of Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammed Hichem Mortad, Souheyb Dehimi","submitted_at":"2015-05-11T18:14:51Z","abstract_excerpt":"This paper is mainly concerned with proving $\\sigma(AB)=\\sigma(BA)$ for two linear and non necessarily bounded operators $A$ and $B$. The main tool is left and right invertibility of bounded and unbounded operators."},"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":"1505.02719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-11T18:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"ca9d44894350052812bfae6cc758c0e456ec00822937b185708e9f040d4f39d8","abstract_canon_sha256":"161359231f691ae3bbca07de6110163ae2509988a52229313dd62cd58de829b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:02.047294Z","signature_b64":"dtZzY56Ro8mUAqxpfCVeYSiUFxF5M0IMoqvYyPT3RK/8VyMRH7NPb+4yHu4WCOQ/9n6/EtosJuEfHK318xEbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349de7ccbfe17cde18ee76c607d13e9c3b021afeab0d4e52ddd73f7e7915a1f5","last_reissued_at":"2026-05-18T00:50:02.046421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:02.046421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Right (Or Left) Invertibility of Bounded and Unbounded Operators and Applications to the Spectrum of Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammed Hichem Mortad, Souheyb Dehimi","submitted_at":"2015-05-11T18:14:51Z","abstract_excerpt":"This paper is mainly concerned with proving $\\sigma(AB)=\\sigma(BA)$ for two linear and non necessarily bounded operators $A$ and $B$. The main tool is left and right invertibility of bounded and unbounded operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02719","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":"1505.02719","created_at":"2026-05-18T00:50:02.046572+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.02719v2","created_at":"2026-05-18T00:50:02.046572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02719","created_at":"2026-05-18T00:50:02.046572+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSO6PTF74F6N","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSO6PTF74F6N4GHO","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSO6PTF7","created_at":"2026-05-18T12:29:22.688609+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/GSO6PTF74F6N4GHOO3DAPUJ6TQ","json":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ.json","graph_json":"https://pith.science/api/pith-number/GSO6PTF74F6N4GHOO3DAPUJ6TQ/graph.json","events_json":"https://pith.science/api/pith-number/GSO6PTF74F6N4GHOO3DAPUJ6TQ/events.json","paper":"https://pith.science/paper/GSO6PTF7"},"agent_actions":{"view_html":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ","download_json":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ.json","view_paper":"https://pith.science/paper/GSO6PTF7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.02719&json=true","fetch_graph":"https://pith.science/api/pith-number/GSO6PTF74F6N4GHOO3DAPUJ6TQ/graph.json","fetch_events":"https://pith.science/api/pith-number/GSO6PTF74F6N4GHOO3DAPUJ6TQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ/action/storage_attestation","attest_author":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ/action/author_attestation","sign_citation":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ/action/citation_signature","submit_replication":"https://pith.science/pith/GSO6PTF74F6N4GHOO3DAPUJ6TQ/action/replication_record"}},"created_at":"2026-05-18T00:50:02.046572+00:00","updated_at":"2026-05-18T00:50:02.046572+00:00"}