{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6324OYDNGQCRWALNVIZODQDUCR","short_pith_number":"pith:6324OYDN","canonical_record":{"source":{"id":"1711.08787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-23T17:40:30Z","cross_cats_sorted":[],"title_canon_sha256":"edb4c1acb75dfe69171768af08f0e18ce64e63bac7b067f44dd8e478457fc2f5","abstract_canon_sha256":"6477edbc1d97d84254857760fd8572fdb1b4b26c97d91e906ee59f5419c68119"},"schema_version":"1.0"},"canonical_sha256":"f6f5c7606d34051b016daa32e1c074145120e32cb001c74aa33818d87e8f1211","source":{"kind":"arxiv","id":"1711.08787","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08787","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08787v1","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08787","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"6324OYDNGQCR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6324OYDNGQCRWALN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6324OYDN","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6324OYDNGQCRWALNVIZODQDUCR","target":"record","payload":{"canonical_record":{"source":{"id":"1711.08787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-23T17:40:30Z","cross_cats_sorted":[],"title_canon_sha256":"edb4c1acb75dfe69171768af08f0e18ce64e63bac7b067f44dd8e478457fc2f5","abstract_canon_sha256":"6477edbc1d97d84254857760fd8572fdb1b4b26c97d91e906ee59f5419c68119"},"schema_version":"1.0"},"canonical_sha256":"f6f5c7606d34051b016daa32e1c074145120e32cb001c74aa33818d87e8f1211","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:44.104788Z","signature_b64":"gm7rxhtRoGbdBTBpcBXYhqZPiHxkt48efTgKJg+Jt1oJkJZEE/P23fyvH7OtrceURhmXnKMoCb82BMDfDIfDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6f5c7606d34051b016daa32e1c074145120e32cb001c74aa33818d87e8f1211","last_reissued_at":"2026-05-18T00:29:44.104380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:44.104380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.08787","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":"2026-05-18T00:29:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6UzKBVAZPvVPjEk7h5l5jM1nU6tLkVtmlD4SH4LSG6itDZAGZgpZ3gIsOjsCscue7EuTymGf8dlIPSaKz6DgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:09:19.384382Z"},"content_sha256":"7be778d2fefa817a1a817e7bd73879ccb67370b5c3ace72ee9cbffd0ad35f3d3","schema_version":"1.0","event_id":"sha256:7be778d2fefa817a1a817e7bd73879ccb67370b5c3ace72ee9cbffd0ad35f3d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6324OYDNGQCRWALNVIZODQDUCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator least squares problems and Moore-Penrose inverses in Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandra Maestripieri, Maximiliano Contino, Stefania Marcantognini","submitted_at":"2017-11-23T17:40:30Z","abstract_excerpt":"A Krein space H and bounded linear operators B, C on H are given. Then, some min and max problems about the operators (BX - C)^{#}(BX -C), where X runs over the space of all bounded linear operators on H, are discussed. In each case, a complete answer to the problem, including solvability conditions and characterization of the solutions, is presented. Also, an adequate decomposition of B is considered and the min-max problem is addressed. As a by-product the Moore-Penrose inverse of B is characterized as the only solution of a variational problem. Other generalized inverses are described in a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08787","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":""},"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":"2026-05-18T00:29:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNEzxJgIFbn0NmrL7bz6QumgXZ7Nc3JCy4dCN2ARJD+GAQa50gZVQioNIHHFvGNTUP3e1DvaDsgf1wyi8PWmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:09:19.385040Z"},"content_sha256":"fd64b262defdbbba176f64f9dcb2a60dea0b5ec065a7181f0c8a8079bd3f7fc4","schema_version":"1.0","event_id":"sha256:fd64b262defdbbba176f64f9dcb2a60dea0b5ec065a7181f0c8a8079bd3f7fc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6324OYDNGQCRWALNVIZODQDUCR/bundle.json","state_url":"https://pith.science/pith/6324OYDNGQCRWALNVIZODQDUCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6324OYDNGQCRWALNVIZODQDUCR/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":"2026-06-07T08:09:19Z","links":{"resolver":"https://pith.science/pith/6324OYDNGQCRWALNVIZODQDUCR","bundle":"https://pith.science/pith/6324OYDNGQCRWALNVIZODQDUCR/bundle.json","state":"https://pith.science/pith/6324OYDNGQCRWALNVIZODQDUCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6324OYDNGQCRWALNVIZODQDUCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6324OYDNGQCRWALNVIZODQDUCR","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":"6477edbc1d97d84254857760fd8572fdb1b4b26c97d91e906ee59f5419c68119","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-23T17:40:30Z","title_canon_sha256":"edb4c1acb75dfe69171768af08f0e18ce64e63bac7b067f44dd8e478457fc2f5"},"schema_version":"1.0","source":{"id":"1711.08787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08787","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08787v1","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08787","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"6324OYDNGQCR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6324OYDNGQCRWALN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6324OYDN","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:fd64b262defdbbba176f64f9dcb2a60dea0b5ec065a7181f0c8a8079bd3f7fc4","target":"graph","created_at":"2026-05-18T00:29:44Z","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":"A Krein space H and bounded linear operators B, C on H are given. Then, some min and max problems about the operators (BX - C)^{#}(BX -C), where X runs over the space of all bounded linear operators on H, are discussed. In each case, a complete answer to the problem, including solvability conditions and characterization of the solutions, is presented. Also, an adequate decomposition of B is considered and the min-max problem is addressed. As a by-product the Moore-Penrose inverse of B is characterized as the only solution of a variational problem. Other generalized inverses are described in a ","authors_text":"Alejandra Maestripieri, Maximiliano Contino, Stefania Marcantognini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-23T17:40:30Z","title":"Operator least squares problems and Moore-Penrose inverses in Krein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08787","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":"sha256:7be778d2fefa817a1a817e7bd73879ccb67370b5c3ace72ee9cbffd0ad35f3d3","target":"record","created_at":"2026-05-18T00:29:44Z","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":"6477edbc1d97d84254857760fd8572fdb1b4b26c97d91e906ee59f5419c68119","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-23T17:40:30Z","title_canon_sha256":"edb4c1acb75dfe69171768af08f0e18ce64e63bac7b067f44dd8e478457fc2f5"},"schema_version":"1.0","source":{"id":"1711.08787","kind":"arxiv","version":1}},"canonical_sha256":"f6f5c7606d34051b016daa32e1c074145120e32cb001c74aa33818d87e8f1211","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6f5c7606d34051b016daa32e1c074145120e32cb001c74aa33818d87e8f1211","first_computed_at":"2026-05-18T00:29:44.104380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:44.104380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gm7rxhtRoGbdBTBpcBXYhqZPiHxkt48efTgKJg+Jt1oJkJZEE/P23fyvH7OtrceURhmXnKMoCb82BMDfDIfDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:44.104788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7be778d2fefa817a1a817e7bd73879ccb67370b5c3ace72ee9cbffd0ad35f3d3","sha256:fd64b262defdbbba176f64f9dcb2a60dea0b5ec065a7181f0c8a8079bd3f7fc4"],"state_sha256":"e504ff6816e3a5d6902f232b9b98faafafb1614afbd5be1d355a4136bbe20e1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ssdrTn8srFH3rm1lQusJ0KB6eevhSDtwI0e8B9lwsUrTO2BsEcTn/ijfPh+wcc21qJmEYa6eZlASQEntBmcMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:09:19.388057Z","bundle_sha256":"0b416427aa909353aa7eebe2b8e60457cc0fb5eb9947f4ef809ee61a5c05723b"}}