{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:724QNIAQHK2LSD5FEUT26UFG52","short_pith_number":"pith:724QNIAQ","canonical_record":{"source":{"id":"2606.00865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-30T19:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"92e32b74d53df4759d787525a1b797a633fda72c8394f1865ddd9e5dcafd31b4","abstract_canon_sha256":"5bffd876ff044c0c0db3e1949f7767c08aa6cebc6604431a4a56d78b687cd7b9"},"schema_version":"1.0"},"canonical_sha256":"feb906a0103ab4b90fa52527af50a6eeba82bc607be646af811cefce876b24a5","source":{"kind":"arxiv","id":"2606.00865","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00865","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00865v1","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00865","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"724QNIAQHK2L","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"724QNIAQHK2LSD5F","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"724QNIAQ","created_at":"2026-06-02T01:04:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:724QNIAQHK2LSD5FEUT26UFG52","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-30T19:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"92e32b74d53df4759d787525a1b797a633fda72c8394f1865ddd9e5dcafd31b4","abstract_canon_sha256":"5bffd876ff044c0c0db3e1949f7767c08aa6cebc6604431a4a56d78b687cd7b9"},"schema_version":"1.0"},"canonical_sha256":"feb906a0103ab4b90fa52527af50a6eeba82bc607be646af811cefce876b24a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:08.268475Z","signature_b64":"PlRf8iAK7j7YgLyPlCHDro92ntSZLUCIiM1aMrjPyxZIZ6jtEr/vKdGTgxU1oz2d7XnZzE1y4FkBFRqzuwEtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feb906a0103ab4b90fa52527af50a6eeba82bc607be646af811cefce876b24a5","last_reissued_at":"2026-06-02T01:04:08.268127Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:08.268127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00865","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ll/3X4bBeRt1ZvJci1ROh3NvhrBKHFAxwMYRpSJUTs1qA1RmDrVM5LeKTQLXn+nY7qDzjcCy+iM4sIPB48JADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:31:00.209113Z"},"content_sha256":"6b7ec164537d923d014bf9ad73e5333007de6782e1610633f875cda64f05fbce","schema_version":"1.0","event_id":"sha256:6b7ec164537d923d014bf9ad73e5333007de6782e1610633f875cda64f05fbce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:724QNIAQHK2LSD5FEUT26UFG52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperinvariant subspaces of hyponormal operators: A constructive decomposition approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eva A. Gallardo-Guti\\'errez, Norberto Clemente","submitted_at":"2026-05-30T19:40:40Z","abstract_excerpt":"It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \\( T = R + V \\), where \\( R \\) is tridiagonal and \\( V \\) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators answering, in particular, negatively to a question raised by Kim and Lee \\cite{kimlee} regarding an explicit approach to such a problem. Finally, we characterize the existence of reducing subspaces for hyp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00865","kind":"arxiv","version":1},"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/2606.00865/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":"2026-06-02T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s3OhYkaqxOD1paXSwyETzBfnz1YaO4DutBxDt8s3aFX1i9OX+LaHSGGs3kixQ+jw49z+pN4/j1fSNyrDkeweDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:31:00.209509Z"},"content_sha256":"7d4c4ba99614008da9dfbbc4769135ec1abe545fb6bcc992e81ebda7752982fb","schema_version":"1.0","event_id":"sha256:7d4c4ba99614008da9dfbbc4769135ec1abe545fb6bcc992e81ebda7752982fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/724QNIAQHK2LSD5FEUT26UFG52/bundle.json","state_url":"https://pith.science/pith/724QNIAQHK2LSD5FEUT26UFG52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/724QNIAQHK2LSD5FEUT26UFG52/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":"2026-06-27T16:31:00Z","links":{"resolver":"https://pith.science/pith/724QNIAQHK2LSD5FEUT26UFG52","bundle":"https://pith.science/pith/724QNIAQHK2LSD5FEUT26UFG52/bundle.json","state":"https://pith.science/pith/724QNIAQHK2LSD5FEUT26UFG52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/724QNIAQHK2LSD5FEUT26UFG52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:724QNIAQHK2LSD5FEUT26UFG52","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":"5bffd876ff044c0c0db3e1949f7767c08aa6cebc6604431a4a56d78b687cd7b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-30T19:40:40Z","title_canon_sha256":"92e32b74d53df4759d787525a1b797a633fda72c8394f1865ddd9e5dcafd31b4"},"schema_version":"1.0","source":{"id":"2606.00865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00865","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00865v1","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00865","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"724QNIAQHK2L","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"724QNIAQHK2LSD5F","created_at":"2026-06-02T01:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"724QNIAQ","created_at":"2026-06-02T01:04:08Z"}],"graph_snapshots":[{"event_id":"sha256:7d4c4ba99614008da9dfbbc4769135ec1abe545fb6bcc992e81ebda7752982fb","target":"graph","created_at":"2026-06-02T01:04:08Z","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/2606.00865/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \\( T = R + V \\), where \\( R \\) is tridiagonal and \\( V \\) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators answering, in particular, negatively to a question raised by Kim and Lee \\cite{kimlee} regarding an explicit approach to such a problem. Finally, we characterize the existence of reducing subspaces for hyp","authors_text":"Eva A. Gallardo-Guti\\'errez, Norberto Clemente","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-30T19:40:40Z","title":"Hyperinvariant subspaces of hyponormal operators: A constructive decomposition approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00865","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":"sha256:6b7ec164537d923d014bf9ad73e5333007de6782e1610633f875cda64f05fbce","target":"record","created_at":"2026-06-02T01:04:08Z","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":"5bffd876ff044c0c0db3e1949f7767c08aa6cebc6604431a4a56d78b687cd7b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-30T19:40:40Z","title_canon_sha256":"92e32b74d53df4759d787525a1b797a633fda72c8394f1865ddd9e5dcafd31b4"},"schema_version":"1.0","source":{"id":"2606.00865","kind":"arxiv","version":1}},"canonical_sha256":"feb906a0103ab4b90fa52527af50a6eeba82bc607be646af811cefce876b24a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feb906a0103ab4b90fa52527af50a6eeba82bc607be646af811cefce876b24a5","first_computed_at":"2026-06-02T01:04:08.268127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:08.268127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlRf8iAK7j7YgLyPlCHDro92ntSZLUCIiM1aMrjPyxZIZ6jtEr/vKdGTgxU1oz2d7XnZzE1y4FkBFRqzuwEtCg==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:08.268475Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b7ec164537d923d014bf9ad73e5333007de6782e1610633f875cda64f05fbce","sha256:7d4c4ba99614008da9dfbbc4769135ec1abe545fb6bcc992e81ebda7752982fb"],"state_sha256":"fa62b1c86c7db49a653cc84289cff3459f58473ab87567dd7950546e005e0a8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WlXERUUddDNkcUadqfqO1Lbhd/vpbfqH+nv3E3FgOiFwDVk0LJZ/TOpLEefWJIjydsP+/r42nxXOc4+lxdGQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:31:00.211439Z","bundle_sha256":"8edf6e34c6c12b3d6b1d7e5c64f4cb9d0d243c6eadf47a090b1a210290bf4924"}}