{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MSGU3HX72WFGPOBFVOGJ4TXS6K","short_pith_number":"pith:MSGU3HX7","canonical_record":{"source":{"id":"2508.20956","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-28T16:18:14Z","cross_cats_sorted":[],"title_canon_sha256":"d9ffb3a207ac5904817bc0105fc00dd1ec2e418e76ca4ae47ffec798dc58d78d","abstract_canon_sha256":"bc26f2255bd00fefdfeaa82c307d02c4b5044003df6a67639a092bafa80d9f75"},"schema_version":"1.0"},"canonical_sha256":"648d4d9effd58a67b825ab8c9e4ef2f296f85e0fca2b03d47e405971ccafde63","source":{"kind":"arxiv","id":"2508.20956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.20956","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"2508.20956v2","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20956","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"MSGU3HX72WFG","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_16","alias_value":"MSGU3HX72WFGPOBF","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_8","alias_value":"MSGU3HX7","created_at":"2026-05-28T01:04:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MSGU3HX72WFGPOBFVOGJ4TXS6K","target":"record","payload":{"canonical_record":{"source":{"id":"2508.20956","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-28T16:18:14Z","cross_cats_sorted":[],"title_canon_sha256":"d9ffb3a207ac5904817bc0105fc00dd1ec2e418e76ca4ae47ffec798dc58d78d","abstract_canon_sha256":"bc26f2255bd00fefdfeaa82c307d02c4b5044003df6a67639a092bafa80d9f75"},"schema_version":"1.0"},"canonical_sha256":"648d4d9effd58a67b825ab8c9e4ef2f296f85e0fca2b03d47e405971ccafde63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:30.050855Z","signature_b64":"Cdmu7Y07k9FEV8tuRPRE5NdYiLsvH/oIlkckp8h6DtLMLbngTWQv8rRdjjaIDV38SCEXmDUuG1iaxpEAKHeUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648d4d9effd58a67b825ab8c9e4ef2f296f85e0fca2b03d47e405971ccafde63","last_reissued_at":"2026-05-28T01:04:30.050307Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:30.050307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.20956","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+uU4rxjNt1kmERiNyi1T3gZjmVvJLKQ2amgSbyWLLkoreG+QjbCgARnH2Zj2564CumSmRMMr2Zc8y4mblUZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:58:41.699235Z"},"content_sha256":"dfd00e7b70f2b2b5d6f61a967ae26b672b9b3e2984817bbc021eb8bdb197b81c","schema_version":"1.0","event_id":"sha256:dfd00e7b70f2b2b5d6f61a967ae26b672b9b3e2984817bbc021eb8bdb197b81c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MSGU3HX72WFGPOBFVOGJ4TXS6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invertible completions of FLI and FRI upper triangular operator matrices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nikola Sarajlija","submitted_at":"2025-08-28T16:18:14Z","abstract_excerpt":"If $A\\in\\mathcal{B}(\\mathcal{H})$ and $B\\in\\mathcal{B}(\\mathcal{K})$ are given operators, denote by $M_C$ an operator matrix of the form $$M_C=\\begin{pmatrix}\n  A & C\\\\ 0 & B \\end{pmatrix}\\in\\mathcal{B}(\\mathcal{H}\\oplus\\mathcal{K})$$ acting on a direct sum of infinite dimensional separable Hilbert spaces $\\mathcal{H}$ and $\\mathcal{K}$, where $C\\in\\mathcal{B}(\\mathcal{K},\\mathcal{H})$ is unknown. In this article we solve the completion problem of $M_C$ to Fredholm left and Fredholm right invertibility, and we obtain appropriate perturbation results as consequences. We illustrate our results b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20956","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.20956/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAzyMBWzEXYl7yYY9VFlXnex+2ihF9On5zcdSO8PQq1dNvNiavmHR6D/RStb3lI0mHHC/mHiI0kk1xaLhjTYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:58:41.699906Z"},"content_sha256":"45301adff47baf4df09c0f58abe58ffa1c7c8f62bed3a374f89db8bf7a9d32e5","schema_version":"1.0","event_id":"sha256:45301adff47baf4df09c0f58abe58ffa1c7c8f62bed3a374f89db8bf7a9d32e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/bundle.json","state_url":"https://pith.science/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T09:58:41Z","links":{"resolver":"https://pith.science/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K","bundle":"https://pith.science/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/bundle.json","state":"https://pith.science/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSGU3HX72WFGPOBFVOGJ4TXS6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MSGU3HX72WFGPOBFVOGJ4TXS6K","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":"bc26f2255bd00fefdfeaa82c307d02c4b5044003df6a67639a092bafa80d9f75","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-28T16:18:14Z","title_canon_sha256":"d9ffb3a207ac5904817bc0105fc00dd1ec2e418e76ca4ae47ffec798dc58d78d"},"schema_version":"1.0","source":{"id":"2508.20956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.20956","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"2508.20956v2","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20956","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"MSGU3HX72WFG","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_16","alias_value":"MSGU3HX72WFGPOBF","created_at":"2026-05-28T01:04:30Z"},{"alias_kind":"pith_short_8","alias_value":"MSGU3HX7","created_at":"2026-05-28T01:04:30Z"}],"graph_snapshots":[{"event_id":"sha256:45301adff47baf4df09c0f58abe58ffa1c7c8f62bed3a374f89db8bf7a9d32e5","target":"graph","created_at":"2026-05-28T01:04:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.20956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If $A\\in\\mathcal{B}(\\mathcal{H})$ and $B\\in\\mathcal{B}(\\mathcal{K})$ are given operators, denote by $M_C$ an operator matrix of the form $$M_C=\\begin{pmatrix}\n  A & C\\\\ 0 & B \\end{pmatrix}\\in\\mathcal{B}(\\mathcal{H}\\oplus\\mathcal{K})$$ acting on a direct sum of infinite dimensional separable Hilbert spaces $\\mathcal{H}$ and $\\mathcal{K}$, where $C\\in\\mathcal{B}(\\mathcal{K},\\mathcal{H})$ is unknown. In this article we solve the completion problem of $M_C$ to Fredholm left and Fredholm right invertibility, and we obtain appropriate perturbation results as consequences. We illustrate our results b","authors_text":"Nikola Sarajlija","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-28T16:18:14Z","title":"Invertible completions of FLI and FRI upper triangular operator matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20956","kind":"arxiv","version":2},"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:dfd00e7b70f2b2b5d6f61a967ae26b672b9b3e2984817bbc021eb8bdb197b81c","target":"record","created_at":"2026-05-28T01:04:30Z","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":"bc26f2255bd00fefdfeaa82c307d02c4b5044003df6a67639a092bafa80d9f75","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-28T16:18:14Z","title_canon_sha256":"d9ffb3a207ac5904817bc0105fc00dd1ec2e418e76ca4ae47ffec798dc58d78d"},"schema_version":"1.0","source":{"id":"2508.20956","kind":"arxiv","version":2}},"canonical_sha256":"648d4d9effd58a67b825ab8c9e4ef2f296f85e0fca2b03d47e405971ccafde63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"648d4d9effd58a67b825ab8c9e4ef2f296f85e0fca2b03d47e405971ccafde63","first_computed_at":"2026-05-28T01:04:30.050307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:30.050307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cdmu7Y07k9FEV8tuRPRE5NdYiLsvH/oIlkckp8h6DtLMLbngTWQv8rRdjjaIDV38SCEXmDUuG1iaxpEAKHeUCA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:30.050855Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.20956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfd00e7b70f2b2b5d6f61a967ae26b672b9b3e2984817bbc021eb8bdb197b81c","sha256:45301adff47baf4df09c0f58abe58ffa1c7c8f62bed3a374f89db8bf7a9d32e5"],"state_sha256":"c53ca29f8f166fa8ed50e189a92e27b3b6ad277ec8173ec3313e549ce47a5830"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQJE34QGY/iPSk0CaTMTsT8dFCrVObsMbfyjomeMknloFkG5uRyK68dVpPr3gbK+NwWQhSKDySNUsvAdawP1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:58:41.703580Z","bundle_sha256":"28f4b983a707cfec00a0f58ec8747723533bd77d2c7855b3ab091933c7903b82"}}