{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:WS3GQF24Q5NGG5XVX35ZGLOH2H","short_pith_number":"pith:WS3GQF24","canonical_record":{"source":{"id":"2211.13983","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-25T09:47:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"45b36467bde9a5934185fedad6c1b09f23041ede0fc68b40b0e49022395e3dbc","abstract_canon_sha256":"d0b492afc55cb4c832f5451e25e4045e85dd23db17d2dbe4c90f9887f4cddd2f"},"schema_version":"1.0"},"canonical_sha256":"b4b668175c875a6376f5befb932dc7d1f46253c7a3fd96fda55faffdefcb96af","source":{"kind":"arxiv","id":"2211.13983","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.13983","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2211.13983v2","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.13983","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"WS3GQF24Q5NG","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"WS3GQF24Q5NGG5XV","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"WS3GQF24","created_at":"2026-06-09T01:05:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:WS3GQF24Q5NGG5XVX35ZGLOH2H","target":"record","payload":{"canonical_record":{"source":{"id":"2211.13983","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-25T09:47:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"45b36467bde9a5934185fedad6c1b09f23041ede0fc68b40b0e49022395e3dbc","abstract_canon_sha256":"d0b492afc55cb4c832f5451e25e4045e85dd23db17d2dbe4c90f9887f4cddd2f"},"schema_version":"1.0"},"canonical_sha256":"b4b668175c875a6376f5befb932dc7d1f46253c7a3fd96fda55faffdefcb96af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:02.431409Z","signature_b64":"tf77HMm/5H7/XmFUSUnqD99ZMJUGkgml0nyQKUk/hmO6c07IsI5UIGiD6vn2bBUOg8k15a8AxPbw+RyE6bHJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4b668175c875a6376f5befb932dc7d1f46253c7a3fd96fda55faffdefcb96af","last_reissued_at":"2026-06-09T01:05:02.430918Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:02.430918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.13983","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUs5TyDH18pFggv8om2ruPkJodkGtqVfEHMHQE12d9qJOpChJ0WI+QXW+l2TXOalUMMGGeVhXAeTC0I+4xPeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:30:02.661799Z"},"content_sha256":"dec626845fbea4b22cd98a47ccb78c1e6c6c15744e4417dbc41ef63f3ce4e0c6","schema_version":"1.0","event_id":"sha256:dec626845fbea4b22cd98a47ccb78c1e6c6c15744e4417dbc41ef63f3ce4e0c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:WS3GQF24Q5NGG5XVX35ZGLOH2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperspherical Trigonometry and Corresponding Elliptic Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Nijhoff, Paul Jennings","submitted_at":"2022-11-25T09:47:18Z","abstract_excerpt":"We develop the basic formulae of hyperspherical trigonometry in multidimensional Euclidean space, using multidimensional vector products, and their conversion to identities for elliptic functions. We show that the basic addition formulae for functions on the 3-sphere embedded in 4-dimensional space lead to addition formulae for elliptic functions, associated with algebraic curves, which have two distinct moduli. We give an application of these formulae to the cases of a multidimensional Euler top, using them to provide a link to the Double Elliptic model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13983","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.13983/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5ZepKwwup77H8YDEvJZVFEEbis/2mEWnTUc3mGIgtTg1GgyGI1KYjuWcre3DXlAtBekRsNgEXr508cyUHCbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:30:02.662193Z"},"content_sha256":"b0f08922215b69a3dc13804f328fbca41e1cbddbc5230ed62f4f27df8d575391","schema_version":"1.0","event_id":"sha256:b0f08922215b69a3dc13804f328fbca41e1cbddbc5230ed62f4f27df8d575391"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/bundle.json","state_url":"https://pith.science/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T03:30:02Z","links":{"resolver":"https://pith.science/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H","bundle":"https://pith.science/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/bundle.json","state":"https://pith.science/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WS3GQF24Q5NGG5XVX35ZGLOH2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WS3GQF24Q5NGG5XVX35ZGLOH2H","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":"d0b492afc55cb4c832f5451e25e4045e85dd23db17d2dbe4c90f9887f4cddd2f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-25T09:47:18Z","title_canon_sha256":"45b36467bde9a5934185fedad6c1b09f23041ede0fc68b40b0e49022395e3dbc"},"schema_version":"1.0","source":{"id":"2211.13983","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.13983","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2211.13983v2","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.13983","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"WS3GQF24Q5NG","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"WS3GQF24Q5NGG5XV","created_at":"2026-06-09T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"WS3GQF24","created_at":"2026-06-09T01:05:02Z"}],"graph_snapshots":[{"event_id":"sha256:b0f08922215b69a3dc13804f328fbca41e1cbddbc5230ed62f4f27df8d575391","target":"graph","created_at":"2026-06-09T01:05:02Z","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/2211.13983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the basic formulae of hyperspherical trigonometry in multidimensional Euclidean space, using multidimensional vector products, and their conversion to identities for elliptic functions. We show that the basic addition formulae for functions on the 3-sphere embedded in 4-dimensional space lead to addition formulae for elliptic functions, associated with algebraic curves, which have two distinct moduli. We give an application of these formulae to the cases of a multidimensional Euler top, using them to provide a link to the Double Elliptic model.","authors_text":"Frank Nijhoff, Paul Jennings","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-25T09:47:18Z","title":"Hyperspherical Trigonometry and Corresponding Elliptic Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13983","kind":"arxiv","version":2},"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:dec626845fbea4b22cd98a47ccb78c1e6c6c15744e4417dbc41ef63f3ce4e0c6","target":"record","created_at":"2026-06-09T01:05:02Z","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":"d0b492afc55cb4c832f5451e25e4045e85dd23db17d2dbe4c90f9887f4cddd2f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-25T09:47:18Z","title_canon_sha256":"45b36467bde9a5934185fedad6c1b09f23041ede0fc68b40b0e49022395e3dbc"},"schema_version":"1.0","source":{"id":"2211.13983","kind":"arxiv","version":2}},"canonical_sha256":"b4b668175c875a6376f5befb932dc7d1f46253c7a3fd96fda55faffdefcb96af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4b668175c875a6376f5befb932dc7d1f46253c7a3fd96fda55faffdefcb96af","first_computed_at":"2026-06-09T01:05:02.430918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:02.430918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tf77HMm/5H7/XmFUSUnqD99ZMJUGkgml0nyQKUk/hmO6c07IsI5UIGiD6vn2bBUOg8k15a8AxPbw+RyE6bHJBA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:02.431409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.13983","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dec626845fbea4b22cd98a47ccb78c1e6c6c15744e4417dbc41ef63f3ce4e0c6","sha256:b0f08922215b69a3dc13804f328fbca41e1cbddbc5230ed62f4f27df8d575391"],"state_sha256":"219d8b10070f40303c41af67779faea8fc8ce43469d13b41eb3e63714f269231"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZINjXmJa2JkKoyEPmGRlngXmtRDbb9aPRrxGZzZEa/4ooUFPjAKtXpnN2oUCSJrQwwdJ/oprRThvKAVCcwnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:30:02.664108Z","bundle_sha256":"ddad590b3b353ffd51e1c8c4400275c4934e626fada5a45a79ae57c86eefaacc"}}