{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:RCS3GSO6CGG3GQMSQ45TI5D4G4","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":"56563c3ea84889641a6171a3e0b78e997bb13a0046c6a5917bba168b7e255c99","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-04-09T14:01:04Z","title_canon_sha256":"4ac75d6ee1168187efa443af90dd7c17d041f50897390699f9540ca8ceb47a67"},"schema_version":"1.0","source":{"id":"math-ph/0104012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0104012","created_at":"2026-07-04T14:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0104012v1","created_at":"2026-07-04T14:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0104012","created_at":"2026-07-04T14:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"RCS3GSO6CGG3","created_at":"2026-07-04T14:33:38Z"},{"alias_kind":"pith_short_16","alias_value":"RCS3GSO6CGG3GQMS","created_at":"2026-07-04T14:33:38Z"},{"alias_kind":"pith_short_8","alias_value":"RCS3GSO6","created_at":"2026-07-04T14:33:38Z"}],"graph_snapshots":[{"event_id":"sha256:2a1ebc3ab14bc13cf44b75c29f5a272ef9ea4fe612afb818773ae5eb744ee4a5","target":"graph","created_at":"2026-07-04T14:33:38Z","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/math-ph/0104012/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An extension of the Stone's theorem to PT symmetric, extended quantum mechanics must employ its pseudo-norm. We show that the evolution of the wave functions is then pseudo-unitary, and emphasize that their pseudo-norm remains time-independent even in the spontaneously broken symmetry regime where the energies themselves cease to be real.","authors_text":"Miloslav Znojil","cross_cats":["math.AP","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-04-09T14:01:04Z","title":"Conservation of pseudo-norm in PT symmetric quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0104012","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":"sha256:08d46c6a65514f63af86d97533b16378e8630b9079f6247c3a32237116363e84","target":"record","created_at":"2026-07-04T14:33:38Z","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":"56563c3ea84889641a6171a3e0b78e997bb13a0046c6a5917bba168b7e255c99","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-04-09T14:01:04Z","title_canon_sha256":"4ac75d6ee1168187efa443af90dd7c17d041f50897390699f9540ca8ceb47a67"},"schema_version":"1.0","source":{"id":"math-ph/0104012","kind":"arxiv","version":1}},"canonical_sha256":"88a5b349de118db34192873b34747c3730a1692776ceafe99f194719ec60cecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88a5b349de118db34192873b34747c3730a1692776ceafe99f194719ec60cecd","first_computed_at":"2026-07-04T14:33:38.704465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:33:38.704465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"voFnYUKp5OUyPt4DBfMCMN3/BvsYj8rQIB2yehYiXES5z1KJsNWPOknyNRKYIfP4eyBgccilVlviRRjv6bmHBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:33:38.704927Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0104012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08d46c6a65514f63af86d97533b16378e8630b9079f6247c3a32237116363e84","sha256:2a1ebc3ab14bc13cf44b75c29f5a272ef9ea4fe612afb818773ae5eb744ee4a5"],"state_sha256":"5a9d3437f2c9c5bd6345250c69bb0b161657e64e15aad0a767764502d69ac962"}