{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YSUOKHIH2SPQ7NM3P4FMHAPF3G","short_pith_number":"pith:YSUOKHIH","canonical_record":{"source":{"id":"2506.01161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-01T20:43:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c1fc093ad134811dc643588ab8ce9776f6365f3a278ec4e80505a0b995bde6b3","abstract_canon_sha256":"c47958cf2b3a77c2f2e8c25345950923b85d2fb7110e95af3a07b4ff2f900cee"},"schema_version":"1.0"},"canonical_sha256":"c4a8e51d07d49f0fb59b7f0ac381e5d995223c541758d44f77015be27fb81f3f","source":{"kind":"arxiv","id":"2506.01161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01161","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01161v1","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01161","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"YSUOKHIH2SPQ","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_16","alias_value":"YSUOKHIH2SPQ7NM3","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_8","alias_value":"YSUOKHIH","created_at":"2026-07-05T11:13:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YSUOKHIH2SPQ7NM3P4FMHAPF3G","target":"record","payload":{"canonical_record":{"source":{"id":"2506.01161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-01T20:43:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c1fc093ad134811dc643588ab8ce9776f6365f3a278ec4e80505a0b995bde6b3","abstract_canon_sha256":"c47958cf2b3a77c2f2e8c25345950923b85d2fb7110e95af3a07b4ff2f900cee"},"schema_version":"1.0"},"canonical_sha256":"c4a8e51d07d49f0fb59b7f0ac381e5d995223c541758d44f77015be27fb81f3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:47.481451Z","signature_b64":"zDiTxXoJFmxIq0rUF4kBstw1UUKCVmtnTjKMWeCMb6Xapj8VNXHMBt3ZMNeNs26nCIOgNk6QJxCXcZOL8bLsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4a8e51d07d49f0fb59b7f0ac381e5d995223c541758d44f77015be27fb81f3f","last_reissued_at":"2026-07-05T11:13:47.481029Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:47.481029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.01161","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":"2026-07-05T11:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ID264aOLzN5KhXQIFhl1msbo07Ve6SozxBkwsqfhYKKDsQkHju+mods8oYpFk+QCJoGFifDvEcR8CxE+UeOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:33:52.309808Z"},"content_sha256":"33f0e9ffed5d536587cc701b97e8d922c839ccb06a21f148e61ec1507df229f3","schema_version":"1.0","event_id":"sha256:33f0e9ffed5d536587cc701b97e8d922c839ccb06a21f148e61ec1507df229f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YSUOKHIH2SPQ7NM3P4FMHAPF3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Kamran Sharifi","submitted_at":"2025-06-01T20:43:31Z","abstract_excerpt":"In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We demonstrate the representation of the solution set of an operator equation on Hilbert C*-modules by taking advantage of invariant submodules. In particular, we consider the special cases of finite dimensional C*-algebras and C*-algebras of compact operators as the underling C*-algebra to simplify our results, and obtain a Lomonosov type theorem for compact "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01161","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/2506.01161/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":"2026-07-05T11:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTD2NckDjPtx0MQo6qHXzJFWFOlk4cf0mK7JaoPtp/iQqmT2uVPYlId2RO8DnLMIprbb8IAywYclJlErx00KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:33:52.310304Z"},"content_sha256":"8c30147003e683445f1d762bbf27c9392123d5e5edc2c01601e7ec2cf3ef071e","schema_version":"1.0","event_id":"sha256:8c30147003e683445f1d762bbf27c9392123d5e5edc2c01601e7ec2cf3ef071e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/bundle.json","state_url":"https://pith.science/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/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":"2026-08-09T09:33:52Z","links":{"resolver":"https://pith.science/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G","bundle":"https://pith.science/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/bundle.json","state":"https://pith.science/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSUOKHIH2SPQ7NM3P4FMHAPF3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YSUOKHIH2SPQ7NM3P4FMHAPF3G","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":"c47958cf2b3a77c2f2e8c25345950923b85d2fb7110e95af3a07b4ff2f900cee","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-01T20:43:31Z","title_canon_sha256":"c1fc093ad134811dc643588ab8ce9776f6365f3a278ec4e80505a0b995bde6b3"},"schema_version":"1.0","source":{"id":"2506.01161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01161","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01161v1","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01161","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"YSUOKHIH2SPQ","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_16","alias_value":"YSUOKHIH2SPQ7NM3","created_at":"2026-07-05T11:13:47Z"},{"alias_kind":"pith_short_8","alias_value":"YSUOKHIH","created_at":"2026-07-05T11:13:47Z"}],"graph_snapshots":[{"event_id":"sha256:8c30147003e683445f1d762bbf27c9392123d5e5edc2c01601e7ec2cf3ef071e","target":"graph","created_at":"2026-07-05T11:13:47Z","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/2506.01161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We demonstrate the representation of the solution set of an operator equation on Hilbert C*-modules by taking advantage of invariant submodules. In particular, we consider the special cases of finite dimensional C*-algebras and C*-algebras of compact operators as the underling C*-algebra to simplify our results, and obtain a Lomonosov type theorem for compact ","authors_text":"Kamran Sharifi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-01T20:43:31Z","title":"Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01161","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":"sha256:33f0e9ffed5d536587cc701b97e8d922c839ccb06a21f148e61ec1507df229f3","target":"record","created_at":"2026-07-05T11:13:47Z","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":"c47958cf2b3a77c2f2e8c25345950923b85d2fb7110e95af3a07b4ff2f900cee","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-01T20:43:31Z","title_canon_sha256":"c1fc093ad134811dc643588ab8ce9776f6365f3a278ec4e80505a0b995bde6b3"},"schema_version":"1.0","source":{"id":"2506.01161","kind":"arxiv","version":1}},"canonical_sha256":"c4a8e51d07d49f0fb59b7f0ac381e5d995223c541758d44f77015be27fb81f3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4a8e51d07d49f0fb59b7f0ac381e5d995223c541758d44f77015be27fb81f3f","first_computed_at":"2026-07-05T11:13:47.481029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:47.481029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zDiTxXoJFmxIq0rUF4kBstw1UUKCVmtnTjKMWeCMb6Xapj8VNXHMBt3ZMNeNs26nCIOgNk6QJxCXcZOL8bLsCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:47.481451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f0e9ffed5d536587cc701b97e8d922c839ccb06a21f148e61ec1507df229f3","sha256:8c30147003e683445f1d762bbf27c9392123d5e5edc2c01601e7ec2cf3ef071e"],"state_sha256":"e30ab7e318ea15f876f07f2520f4d211e7306cf72bd707804cff42791b0201cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLRKPx+fgVEVlwvuDkZT62SphjQq7GzASX5Jt2IbO7tQ7gFhTvUu+RDmvWoW+m4u+rm3gQoq1PA2LY0XoUNPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:33:52.313720Z","bundle_sha256":"e62496096029d3c8906cff61fece8984d6d68c300e4320ecfb4767da54c0f445"}}