{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QEHYN6QQKTBTAPJWXUKC5GEUD5","short_pith_number":"pith:QEHYN6QQ","canonical_record":{"source":{"id":"1711.08391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-22T17:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"dc8d53c1cb2a7770b8ee123551b25f61480a1d7f7e11df2fcc4546daca193c71","abstract_canon_sha256":"9c3515d27bb2e035316c4dce88e090f8d2e6bb938ae61c82f7a17ec9e193f854"},"schema_version":"1.0"},"canonical_sha256":"810f86fa1054c3303d36bd142e98941f7d701f58e7c7712e2a51f24d94ee5779","source":{"kind":"arxiv","id":"1711.08391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08391","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08391v1","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08391","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"QEHYN6QQKTBT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QEHYN6QQKTBTAPJW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QEHYN6QQ","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QEHYN6QQKTBTAPJWXUKC5GEUD5","target":"record","payload":{"canonical_record":{"source":{"id":"1711.08391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-22T17:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"dc8d53c1cb2a7770b8ee123551b25f61480a1d7f7e11df2fcc4546daca193c71","abstract_canon_sha256":"9c3515d27bb2e035316c4dce88e090f8d2e6bb938ae61c82f7a17ec9e193f854"},"schema_version":"1.0"},"canonical_sha256":"810f86fa1054c3303d36bd142e98941f7d701f58e7c7712e2a51f24d94ee5779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:49.974874Z","signature_b64":"M7Uu3Ro3IVhrq/fSGi6UHA6KtR3iG54uPNa/EpU4Y87sViNC+SjeI7uS/pvGCSe0JlrfZGFnuzVAUry5BaZEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"810f86fa1054c3303d36bd142e98941f7d701f58e7c7712e2a51f24d94ee5779","last_reissued_at":"2026-05-18T00:29:49.974405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:49.974405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.08391","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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xm92DrkJEkZ3QSq5LkwPAfHwggrxCtS7FzWF/Mbl4wOaW3PhO50nAA8BncD8Pwq+OvF69xRjt3SbsvCInbnTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:13:03.288779Z"},"content_sha256":"63e7cf5636f23a6eb38f6459d76c8f92f87c5aaab2a9db13575b14db0efe3bc3","schema_version":"1.0","event_id":"sha256:63e7cf5636f23a6eb38f6459d76c8f92f87c5aaab2a9db13575b14db0efe3bc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QEHYN6QQKTBTAPJWXUKC5GEUD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the adjoint of Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Zolt\\'an Sebesty\\'en, Zsigmond Tarcsay","submitted_at":"2017-11-22T17:00:29Z","abstract_excerpt":"In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our considerations, a central role is played by the operator matrix $M_{S,T}=\\left(\\begin{array}{cc} I & -T\\\\ S & I\\end{array}\\right)$. Our approach has several consequences such as characterizations of closed, normal, skew- and selfadjoint, unitary and orthogonal projection operators in real or complex Hilbert spaces. We also give a self-contained proof of the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08391","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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5N78MQfvBbl7F/9RUfyPrLfuBaYo+0K9MiLV3OXsqvu0xzM45EpihUEvUzYaQiiZQYasZBkSMHvgjXYK2XtvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:13:03.289434Z"},"content_sha256":"a142e07f19a7ffd99d0f18ec203ff64730c0b1c5230a3fcd978c76856922e4cb","schema_version":"1.0","event_id":"sha256:a142e07f19a7ffd99d0f18ec203ff64730c0b1c5230a3fcd978c76856922e4cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/bundle.json","state_url":"https://pith.science/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/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":"2026-05-31T02:13:03Z","links":{"resolver":"https://pith.science/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5","bundle":"https://pith.science/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/bundle.json","state":"https://pith.science/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEHYN6QQKTBTAPJWXUKC5GEUD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QEHYN6QQKTBTAPJWXUKC5GEUD5","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":"9c3515d27bb2e035316c4dce88e090f8d2e6bb938ae61c82f7a17ec9e193f854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-22T17:00:29Z","title_canon_sha256":"dc8d53c1cb2a7770b8ee123551b25f61480a1d7f7e11df2fcc4546daca193c71"},"schema_version":"1.0","source":{"id":"1711.08391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08391","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08391v1","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08391","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"QEHYN6QQKTBT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QEHYN6QQKTBTAPJW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QEHYN6QQ","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:a142e07f19a7ffd99d0f18ec203ff64730c0b1c5230a3fcd978c76856922e4cb","target":"graph","created_at":"2026-05-18T00:29:49Z","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":"In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our considerations, a central role is played by the operator matrix $M_{S,T}=\\left(\\begin{array}{cc} I & -T\\\\ S & I\\end{array}\\right)$. Our approach has several consequences such as characterizations of closed, normal, skew- and selfadjoint, unitary and orthogonal projection operators in real or complex Hilbert spaces. We also give a self-contained proof of the f","authors_text":"Zolt\\'an Sebesty\\'en, Zsigmond Tarcsay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-22T17:00:29Z","title":"On the adjoint of Hilbert space operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08391","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":"sha256:63e7cf5636f23a6eb38f6459d76c8f92f87c5aaab2a9db13575b14db0efe3bc3","target":"record","created_at":"2026-05-18T00:29:49Z","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":"9c3515d27bb2e035316c4dce88e090f8d2e6bb938ae61c82f7a17ec9e193f854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-22T17:00:29Z","title_canon_sha256":"dc8d53c1cb2a7770b8ee123551b25f61480a1d7f7e11df2fcc4546daca193c71"},"schema_version":"1.0","source":{"id":"1711.08391","kind":"arxiv","version":1}},"canonical_sha256":"810f86fa1054c3303d36bd142e98941f7d701f58e7c7712e2a51f24d94ee5779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"810f86fa1054c3303d36bd142e98941f7d701f58e7c7712e2a51f24d94ee5779","first_computed_at":"2026-05-18T00:29:49.974405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:49.974405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7Uu3Ro3IVhrq/fSGi6UHA6KtR3iG54uPNa/EpU4Y87sViNC+SjeI7uS/pvGCSe0JlrfZGFnuzVAUry5BaZEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:49.974874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63e7cf5636f23a6eb38f6459d76c8f92f87c5aaab2a9db13575b14db0efe3bc3","sha256:a142e07f19a7ffd99d0f18ec203ff64730c0b1c5230a3fcd978c76856922e4cb"],"state_sha256":"a333364d47b1f7d997c1b6486349c8c76cba0657103ea382e0e32528d6447c0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GN9IO5df5Bf1WXJKl5L8mDnKp4Xcd4ViNiZvNZPjBT2jU2tSCdroW+pWS5WtXEAJnRXEKFRnfJ3bS8xxCqaeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:13:03.292559Z","bundle_sha256":"90ff472ce5f2ff92429e65138611e51f2c8ebed57d1598aa374e65c9735fe058"}}