{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NYAX73FWLHXPLQQ26WPN43PS6O","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":"4c4edf2432f4c9fd04d429ffbe0ecf5d1a9975b1d83b652bf9f5568fc90a0976","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-01-04T17:31:09Z","title_canon_sha256":"16cc6d4a1a148c067a9af295a0b6f30098c5ca62f6e6ed85bff6096bb8c00ef5"},"schema_version":"1.0","source":{"id":"1101.0773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0773","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0773v1","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0773","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"pith_short_12","alias_value":"NYAX73FWLHXP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NYAX73FWLHXPLQQ2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NYAX73FW","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:97bf482c876b6099f16d54e98dd8e841af603ff7dcb54713f3344bda0217e849","target":"graph","created_at":"2026-05-18T04:27:26Z","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":"Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of matrix potentials is obtained which reveals a double degeneracy or equidistant splitting of energy levels (hidden symmetry).","authors_text":"A.A.Andrianov, M.V.Ioffe, Tsu Zhun-Pin","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-01-04T17:31:09Z","title":"Factorization Method in Curvilinear Coordinates and Pairing of Levels for Matrix Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0773","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:ef7ef0c033a134115fad6c07ef89063c59a0d75da4cbece088d572c61bf3081d","target":"record","created_at":"2026-05-18T04:27:26Z","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":"4c4edf2432f4c9fd04d429ffbe0ecf5d1a9975b1d83b652bf9f5568fc90a0976","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-01-04T17:31:09Z","title_canon_sha256":"16cc6d4a1a148c067a9af295a0b6f30098c5ca62f6e6ed85bff6096bb8c00ef5"},"schema_version":"1.0","source":{"id":"1101.0773","kind":"arxiv","version":1}},"canonical_sha256":"6e017fecb659eef5c21af59ede6df2f386796bcb75b9c64e54a122d9bbb94324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e017fecb659eef5c21af59ede6df2f386796bcb75b9c64e54a122d9bbb94324","first_computed_at":"2026-05-18T04:27:26.396155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:26.396155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ulB2++SPysDK6AlOKtolr0YAp1MrAqWj4EsnejmWDealm/AcOTherCX1zioaparSbRXGxSlBXlU0vymsezENBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:26.396709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef7ef0c033a134115fad6c07ef89063c59a0d75da4cbece088d572c61bf3081d","sha256:97bf482c876b6099f16d54e98dd8e841af603ff7dcb54713f3344bda0217e849"],"state_sha256":"40372ac7ff246f069a5ae7d48e0e01473b77a440e1b757cc08634565f8d83406"}