{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SKHIKSP2ZMOTAYZZAKSFITT4XN","short_pith_number":"pith:SKHIKSP2","canonical_record":{"source":{"id":"1804.06766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-18T14:46:11Z","cross_cats_sorted":["math.FA","math.MP","math.SP","quant-ph"],"title_canon_sha256":"fc3dbf1b5d769a82fed1290f5ad0e0d71da6471af6a784a0e8aad744a1707bef","abstract_canon_sha256":"f0050a0e23c112ee9ecf288e3869857bc73eef9564a4c26a3ae15dc4dd875c4e"},"schema_version":"1.0"},"canonical_sha256":"928e8549facb1d30633902a4544e7cbb5b4fd891b61a7464733df4e278affbd6","source":{"kind":"arxiv","id":"1804.06766","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06766","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06766v1","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06766","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"SKHIKSP2ZMOT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SKHIKSP2ZMOTAYZZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SKHIKSP2","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SKHIKSP2ZMOTAYZZAKSFITT4XN","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-18T14:46:11Z","cross_cats_sorted":["math.FA","math.MP","math.SP","quant-ph"],"title_canon_sha256":"fc3dbf1b5d769a82fed1290f5ad0e0d71da6471af6a784a0e8aad744a1707bef","abstract_canon_sha256":"f0050a0e23c112ee9ecf288e3869857bc73eef9564a4c26a3ae15dc4dd875c4e"},"schema_version":"1.0"},"canonical_sha256":"928e8549facb1d30633902a4544e7cbb5b4fd891b61a7464733df4e278affbd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:31.519030Z","signature_b64":"UmehZon49TPG5WVMCa4R7WDWmsrVSOuGk06zucnhFbPukivTEWVon5Z9gF7/v7BECwpBc5kcA64IEeNx0V6uAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"928e8549facb1d30633902a4544e7cbb5b4fd891b61a7464733df4e278affbd6","last_reissued_at":"2026-05-18T00:05:31.518433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:31.518433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06766","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":"2026-05-18T00:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Fyf5AGFNBXnWITPA4JQovCcxqcqNF7jj2bOFpKFt7BTSr40A/T2vNXHGpt/BsMJT/diugj10C1w/4BLWNq5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:19:33.377000Z"},"content_sha256":"53c6031ce298d2f67eb99d6e5b150f1891c2749a55c66d2ceb858d27d5131368","schema_version":"1.0","event_id":"sha256:53c6031ce298d2f67eb99d6e5b150f1891c2749a55c66d2ceb858d27d5131368"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SKHIKSP2ZMOTAYZZAKSFITT4XN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"David Krejcirik, Miloslav Znojil, Vladimir Lotoreichik","submitted_at":"2018-04-18T14:46:11Z","abstract_excerpt":"We propose a unique way how to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator becomes self-adjoint. Our construction is based on minimising a 'Hilbert-Schmidt distance' to the original inner product among the entire class of admissible inner products. We prove that either the minimiser exists and is unique, or it does not exist at all. In the former case we derive a system of Euler-Lagrange equations by which the optimal inner product is determined. A sufficient condition for the existence of the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06766","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":"2026-05-18T00:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2jt5Ja52nydPUGmpGkI+FH2EbgrUVgCCeKf4AbqWBxUzOnwA9XQcf5Z7+hi51px/ljuYkqOLZMFIDRPyDpRAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:19:33.377368Z"},"content_sha256":"7bbfc55712acd02197261a38e2a8ca67a372d8cb7cdf6f52843929cd0c6b2a9c","schema_version":"1.0","event_id":"sha256:7bbfc55712acd02197261a38e2a8ca67a372d8cb7cdf6f52843929cd0c6b2a9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/bundle.json","state_url":"https://pith.science/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/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":"2026-05-27T14:19:33Z","links":{"resolver":"https://pith.science/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN","bundle":"https://pith.science/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/bundle.json","state":"https://pith.science/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKHIKSP2ZMOTAYZZAKSFITT4XN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SKHIKSP2ZMOTAYZZAKSFITT4XN","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":"f0050a0e23c112ee9ecf288e3869857bc73eef9564a4c26a3ae15dc4dd875c4e","cross_cats_sorted":["math.FA","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-18T14:46:11Z","title_canon_sha256":"fc3dbf1b5d769a82fed1290f5ad0e0d71da6471af6a784a0e8aad744a1707bef"},"schema_version":"1.0","source":{"id":"1804.06766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06766","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06766v1","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06766","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"SKHIKSP2ZMOT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SKHIKSP2ZMOTAYZZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SKHIKSP2","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:7bbfc55712acd02197261a38e2a8ca67a372d8cb7cdf6f52843929cd0c6b2a9c","target":"graph","created_at":"2026-05-18T00:05:31Z","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":"We propose a unique way how to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator becomes self-adjoint. Our construction is based on minimising a 'Hilbert-Schmidt distance' to the original inner product among the entire class of admissible inner products. We prove that either the minimiser exists and is unique, or it does not exist at all. In the former case we derive a system of Euler-Lagrange equations by which the optimal inner product is determined. A sufficient condition for the existence of the un","authors_text":"David Krejcirik, Miloslav Znojil, Vladimir Lotoreichik","cross_cats":["math.FA","math.MP","math.SP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-18T14:46:11Z","title":"The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06766","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":"sha256:53c6031ce298d2f67eb99d6e5b150f1891c2749a55c66d2ceb858d27d5131368","target":"record","created_at":"2026-05-18T00:05:31Z","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":"f0050a0e23c112ee9ecf288e3869857bc73eef9564a4c26a3ae15dc4dd875c4e","cross_cats_sorted":["math.FA","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-18T14:46:11Z","title_canon_sha256":"fc3dbf1b5d769a82fed1290f5ad0e0d71da6471af6a784a0e8aad744a1707bef"},"schema_version":"1.0","source":{"id":"1804.06766","kind":"arxiv","version":1}},"canonical_sha256":"928e8549facb1d30633902a4544e7cbb5b4fd891b61a7464733df4e278affbd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"928e8549facb1d30633902a4544e7cbb5b4fd891b61a7464733df4e278affbd6","first_computed_at":"2026-05-18T00:05:31.518433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:31.518433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UmehZon49TPG5WVMCa4R7WDWmsrVSOuGk06zucnhFbPukivTEWVon5Z9gF7/v7BECwpBc5kcA64IEeNx0V6uAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:31.519030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53c6031ce298d2f67eb99d6e5b150f1891c2749a55c66d2ceb858d27d5131368","sha256:7bbfc55712acd02197261a38e2a8ca67a372d8cb7cdf6f52843929cd0c6b2a9c"],"state_sha256":"4abdebd5b9d4c3d96ad1401d2fc1d4653fe9d1c48445799b52fd7808a61a3624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuAw9m+cKw5CtNXKjbyP9bnobLdIRE16BpDXjwbbZJt9vas1C8tQY5ldyU/WxwT/SxyGVyserySZVbuGrTEaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:19:33.379614Z","bundle_sha256":"045d92374c31f5bf21b470abcb354b5e5f40d45900b05bf880acff6e51993511"}}