{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TFVAV7AXRBQ5P7MLKS3MUVVGLV","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":"a0771871fdb718807756bf09eb3d5bec39e2a61a0967ed24f46e56b0f49ca9c4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-13T17:20:36Z","title_canon_sha256":"98c565fff3057920fe6d343edca68469feecb90d8765998698216f9ba7e777f6"},"schema_version":"1.0","source":{"id":"1510.03785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03785","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03785v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03785","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"TFVAV7AXRBQ5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TFVAV7AXRBQ5P7ML","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TFVAV7AX","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:e2402e644c3c4a6ac4b5a253a3a62f950afb02cb5efe5e6d2f907d1dfa287468","target":"graph","created_at":"2026-05-18T01:30:16Z","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":"In this work the detailed geometrical description of all possible orthogonal and nonorthogonal systems of coordinates, which allow separation of variables of two-dimensional Helmholtz equation is given as for two-sheeted (upper sheet) $H_2$, either for one-sheeted ${\\tilde H}_2$ hyperboloids. It was proven that only five types of orthogonal systems of coordinates, namely: pseudo-spherical, equidistant, horiciclic, elliptic-parabolic and elliptic system cover one-sheeted ${\\tilde H}_2$ hyperboloid completely. For other systems on ${\\tilde H}_2$ hyperboloid, well defined In\\\"on\\\"u--Wigner contra","authors_text":"A. Yakhno, G.S. Pogosyan","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-13T17:20:36Z","title":"Lie Algebra Contractions and Separation of Variables on Two-Dimensional Hyperboloids. Coordinate Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03785","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":"sha256:52b2e8c33a9ed0ba7345158a2fd7b0e74ec91cfe05d81f6bb6a3128b4a4c05da","target":"record","created_at":"2026-05-18T01:30:16Z","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":"a0771871fdb718807756bf09eb3d5bec39e2a61a0967ed24f46e56b0f49ca9c4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-13T17:20:36Z","title_canon_sha256":"98c565fff3057920fe6d343edca68469feecb90d8765998698216f9ba7e777f6"},"schema_version":"1.0","source":{"id":"1510.03785","kind":"arxiv","version":1}},"canonical_sha256":"996a0afc178861d7fd8b54b6ca56a65d6258a0b50b5fae2197feaf981e5861a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"996a0afc178861d7fd8b54b6ca56a65d6258a0b50b5fae2197feaf981e5861a5","first_computed_at":"2026-05-18T01:30:16.159777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.159777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z290yPpRQHyiXBJAs0rGX7YNQCahJD1p4DRawydCks226a6m81gRXyXWrSCGl0jHYQek6kDiUXlAXiN989seDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.160464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52b2e8c33a9ed0ba7345158a2fd7b0e74ec91cfe05d81f6bb6a3128b4a4c05da","sha256:e2402e644c3c4a6ac4b5a253a3a62f950afb02cb5efe5e6d2f907d1dfa287468"],"state_sha256":"ce556c69f9624f41e980fd0388a82c979df967af4b3cdb9c503cec5f7acb51da"}