{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:AWW4SYIWY7P5XOOWITV2DXXO2X","short_pith_number":"pith:AWW4SYIW","canonical_record":{"source":{"id":"0901.0700","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2009-01-06T19:42:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1a1e27209f78672246841fd7e34ab6ff29c3f8119c35df99a04df61a5168fb9c","abstract_canon_sha256":"7a44a7524e176f140f4c579d102117d28a07f84a9328a4f0c813fc84b97c757f"},"schema_version":"1.0"},"canonical_sha256":"05adc96116c7dfdbb9d644eba1deeed5f4b7cf0b56a47815f497a4b7a8060eda","source":{"kind":"arxiv","id":"0901.0700","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0700","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0700v1","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0700","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_12","alias_value":"AWW4SYIWY7P5","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_16","alias_value":"AWW4SYIWY7P5XOOW","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_8","alias_value":"AWW4SYIW","created_at":"2026-07-04T15:35:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:AWW4SYIWY7P5XOOWITV2DXXO2X","target":"record","payload":{"canonical_record":{"source":{"id":"0901.0700","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2009-01-06T19:42:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1a1e27209f78672246841fd7e34ab6ff29c3f8119c35df99a04df61a5168fb9c","abstract_canon_sha256":"7a44a7524e176f140f4c579d102117d28a07f84a9328a4f0c813fc84b97c757f"},"schema_version":"1.0"},"canonical_sha256":"05adc96116c7dfdbb9d644eba1deeed5f4b7cf0b56a47815f497a4b7a8060eda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:35:31.692698Z","signature_b64":"2mrlGrULAYEeKUD5QFTwGZih+YXeVCBYfbHPM2knhVdSS9h40nJMaV24EeJtKnJN8CkSZsSyhJhOf+oMIoJ8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05adc96116c7dfdbb9d644eba1deeed5f4b7cf0b56a47815f497a4b7a8060eda","last_reissued_at":"2026-07-04T15:35:31.692309Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:35:31.692309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.0700","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":"2026-07-04T15:35:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gauF37Xh6uDS4ai3BhxC5RMwDPT0II2gSxo5H5TZDyhsC9w3nBmidE7myzvYLLz7ZnbvcKz7IfX3oo9AXhePAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:12:24.548055Z"},"content_sha256":"9d4811305b7098cf6e0f5dad5b8502a2990f49623a9c02e7984d851cc42a0312","schema_version":"1.0","event_id":"sha256:9d4811305b7098cf6e0f5dad5b8502a2990f49623a9c02e7984d851cc42a0312"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:AWW4SYIWY7P5XOOWITV2DXXO2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-Hilbert-Space Formulation of Quantum Mechanics","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Miloslav Znojil","submitted_at":"2009-01-06T19:42:37Z","abstract_excerpt":"In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as ${\\cal H}^{\\rm (auxiliary)}$ and ${\\cal H}^{\\rm (standard)}$) we spot a weak point of the 2HS formalism which lies in the double role played by ${\\cal H}^{\\rm (auxiliary)}$. As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0700","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/0901.0700/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":"2026-07-04T15:35:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkBRFXHOqmRDcgs5p5O8nnmw7MIOXeBi3Ww/4Y2hbioFARAFlOiNkQL8fXv7rA4iR2F4m2W9FovtpCZY9qPHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:12:24.548749Z"},"content_sha256":"342003cee8498940f6c234da38b77af6622883987b50b6f390d45fa29a547bab","schema_version":"1.0","event_id":"sha256:342003cee8498940f6c234da38b77af6622883987b50b6f390d45fa29a547bab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/bundle.json","state_url":"https://pith.science/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/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":"2026-08-17T03:12:24Z","links":{"resolver":"https://pith.science/pith/AWW4SYIWY7P5XOOWITV2DXXO2X","bundle":"https://pith.science/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/bundle.json","state":"https://pith.science/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWW4SYIWY7P5XOOWITV2DXXO2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AWW4SYIWY7P5XOOWITV2DXXO2X","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":"7a44a7524e176f140f4c579d102117d28a07f84a9328a4f0c813fc84b97c757f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2009-01-06T19:42:37Z","title_canon_sha256":"1a1e27209f78672246841fd7e34ab6ff29c3f8119c35df99a04df61a5168fb9c"},"schema_version":"1.0","source":{"id":"0901.0700","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0700","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0700v1","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0700","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_12","alias_value":"AWW4SYIWY7P5","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_16","alias_value":"AWW4SYIWY7P5XOOW","created_at":"2026-07-04T15:35:31Z"},{"alias_kind":"pith_short_8","alias_value":"AWW4SYIW","created_at":"2026-07-04T15:35:31Z"}],"graph_snapshots":[{"event_id":"sha256:342003cee8498940f6c234da38b77af6622883987b50b6f390d45fa29a547bab","target":"graph","created_at":"2026-07-04T15:35:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0901.0700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as ${\\cal H}^{\\rm (auxiliary)}$ and ${\\cal H}^{\\rm (standard)}$) we spot a weak point of the 2HS formalism which lies in the double role played by ${\\cal H}^{\\rm (auxiliary)}$. As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the sa","authors_text":"Miloslav Znojil","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2009-01-06T19:42:37Z","title":"Three-Hilbert-Space Formulation of Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0700","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":"sha256:9d4811305b7098cf6e0f5dad5b8502a2990f49623a9c02e7984d851cc42a0312","target":"record","created_at":"2026-07-04T15:35:31Z","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":"7a44a7524e176f140f4c579d102117d28a07f84a9328a4f0c813fc84b97c757f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2009-01-06T19:42:37Z","title_canon_sha256":"1a1e27209f78672246841fd7e34ab6ff29c3f8119c35df99a04df61a5168fb9c"},"schema_version":"1.0","source":{"id":"0901.0700","kind":"arxiv","version":1}},"canonical_sha256":"05adc96116c7dfdbb9d644eba1deeed5f4b7cf0b56a47815f497a4b7a8060eda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05adc96116c7dfdbb9d644eba1deeed5f4b7cf0b56a47815f497a4b7a8060eda","first_computed_at":"2026-07-04T15:35:31.692309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:35:31.692309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2mrlGrULAYEeKUD5QFTwGZih+YXeVCBYfbHPM2knhVdSS9h40nJMaV24EeJtKnJN8CkSZsSyhJhOf+oMIoJ8Bw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:35:31.692698Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0700","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d4811305b7098cf6e0f5dad5b8502a2990f49623a9c02e7984d851cc42a0312","sha256:342003cee8498940f6c234da38b77af6622883987b50b6f390d45fa29a547bab"],"state_sha256":"cfce3962571dffea41e05fd9a00f459e61ff5263a2c36024268ed7f4c6131b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMUgjkyr1kLKcDYCbYuOO6IDetJcIpGSV9C070c7CrPQ/2P4zMZUZm/7NRg1EWNpnWj+Iy0MkUVvkl9TSMskAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T03:12:24.554725Z","bundle_sha256":"fc54fafb81a3a3346635623d279a875eb5e1ea6a465fdd44683fcc63daeea797"}}