{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BAVYFZF7QBKHOCTAXJPRLHUL7V","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":"979b4b5b7e985333a81b6e74626f65b394d497dbd674163241596bc1a2d4db88","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-07T15:10:05Z","title_canon_sha256":"f6b9fdfd0992559ae1faa7072fe762db4313c2f128031218ba25590c7800dbe4"},"schema_version":"1.0","source":{"id":"2506.06827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06827","created_at":"2026-07-05T11:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06827v1","created_at":"2026-07-05T11:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06827","created_at":"2026-07-05T11:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"BAVYFZF7QBKH","created_at":"2026-07-05T11:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"BAVYFZF7QBKHOCTA","created_at":"2026-07-05T11:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"BAVYFZF7","created_at":"2026-07-05T11:17:56Z"}],"graph_snapshots":[{"event_id":"sha256:1e9c128fab307a957ee578028601bc4281aa705e1c62f5a85cc0ead1e78ddc45","target":"graph","created_at":"2026-07-05T11:17:56Z","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/2506.06827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper describes solutions of the Laplace-Beltrami equation on two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-sircular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in the specified coordinate systems through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in three non-subgroup coordinate systems from the hyperboloid to the Euclidean plane is realized.","authors_text":"A. Yakhno, G.S. Pogosyan","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-07T15:10:05Z","title":"Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIB. Non-Subgroup Basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06827","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:e4ea423c63d5de600b49f360ed7abe6b2b79ad14a588cf290ada4a2e31a1825f","target":"record","created_at":"2026-07-05T11:17:56Z","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":"979b4b5b7e985333a81b6e74626f65b394d497dbd674163241596bc1a2d4db88","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-07T15:10:05Z","title_canon_sha256":"f6b9fdfd0992559ae1faa7072fe762db4313c2f128031218ba25590c7800dbe4"},"schema_version":"1.0","source":{"id":"2506.06827","kind":"arxiv","version":1}},"canonical_sha256":"082b82e4bf8054770a60ba5f159e8bfd4731086a484d796cb901e554d806a71e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"082b82e4bf8054770a60ba5f159e8bfd4731086a484d796cb901e554d806a71e","first_computed_at":"2026-07-05T11:17:56.458628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:56.458628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zRGgDyYp3ggsk+Uelk/xX1rWRz54c31w1W0Uhjkpv4xYWYzOWRlqpADn96U7HR9ujnmBRHlvf0hhdZaNElODg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:56.459085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4ea423c63d5de600b49f360ed7abe6b2b79ad14a588cf290ada4a2e31a1825f","sha256:1e9c128fab307a957ee578028601bc4281aa705e1c62f5a85cc0ead1e78ddc45"],"state_sha256":"9d3d16effe61ac401209a035677473cef8a1ffe7148f6d33ab2dc188c91cc132"}