{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NJ7OQNLGQLZZX7YHQP2T2CZ7UM","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":"010af1f5e3f3d84f1c11199fe04ec726f7bda141b8297b1041be62a08f32ed95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-15T12:07:23Z","title_canon_sha256":"060f107dd5bf332579583cf4e45d0b37d0accb0317f67a38c9493e8c25a2ba86"},"schema_version":"1.0","source":{"id":"0904.2293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2293","created_at":"2026-05-18T02:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2293v1","created_at":"2026-05-18T02:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2293","created_at":"2026-05-18T02:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"NJ7OQNLGQLZZ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NJ7OQNLGQLZZX7YH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NJ7OQNLG","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:5d6cf486048a10e2e66b8a9ddc811575b9e93ab3c0118625dfb5e655b21ec295","target":"graph","created_at":"2026-05-18T02:14:00Z","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":"Sturm-Schroedinger equations $H\\psi=E W\\psi$ with $H\\neq H^\\dagger$ and $W\\neq W^\\dagger \\neq I$ are considered, with a weak point of the theory lying in the purely numerical matrix-inversion form of the double-series definition of the necessary metric operator $\\Theta$ in the physical Hilbert space of states [M. Znojil, J. Phys. A: Math. Theor. 41 (2008) 215304]. This shortcoming is removed here via an amended, single-series definition of $\\Theta$.","authors_text":"Hendrik B. Geyer, Miloslav Znojil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-15T12:07:23Z","title":"Sturm-Schroedinger equations: formula for metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2293","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":"sha256:5c721d2965f09cf2df26bc559fe9bad288404dc8e1c7cae9163288808f46d978","target":"record","created_at":"2026-05-18T02:14:00Z","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":"010af1f5e3f3d84f1c11199fe04ec726f7bda141b8297b1041be62a08f32ed95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-15T12:07:23Z","title_canon_sha256":"060f107dd5bf332579583cf4e45d0b37d0accb0317f67a38c9493e8c25a2ba86"},"schema_version":"1.0","source":{"id":"0904.2293","kind":"arxiv","version":1}},"canonical_sha256":"6a7ee8356682f39bff0783f53d0b3fa3058c26e5103d67a5de93e2019b84b50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7ee8356682f39bff0783f53d0b3fa3058c26e5103d67a5de93e2019b84b50f","first_computed_at":"2026-05-18T02:14:00.264241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:00.264241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQ+Wj/LF3ldxq3kkp4YZrxmabX2wiYE+kX6B4kF05HeUAo3C4gZSDUSpYMD9/wY8tohD+N/7geryZ5d4EkaXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:00.264938Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c721d2965f09cf2df26bc559fe9bad288404dc8e1c7cae9163288808f46d978","sha256:5d6cf486048a10e2e66b8a9ddc811575b9e93ab3c0118625dfb5e655b21ec295"],"state_sha256":"ef2364ee2d2a2fc633d32fa37cc8a883511a95a8eb2c4f88a47be90eeb941c73"}