{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:XFXHHQ75U5KYPQINUACSFJSC65","short_pith_number":"pith:XFXHHQ75","canonical_record":{"source":{"id":"nlin/0506063","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2005-06-29T20:05:34Z","cross_cats_sorted":[],"title_canon_sha256":"4ecbef89e83a2c538c6fc6b11f72ac762078a652c4c8a1f40e5f851805307e2a","abstract_canon_sha256":"15029e3b95a1ae2662c5e3f565aa50d8831c27370b8795f473f997810a43816d"},"schema_version":"1.0"},"canonical_sha256":"b96e73c3fda75587c10da00522a642f763cf13c10141c3a66ea82ac8c6ff394c","source":{"kind":"arxiv","id":"nlin/0506063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0506063","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0506063v2","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0506063","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"XFXHHQ75U5KY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"XFXHHQ75U5KYPQIN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"XFXHHQ75","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:XFXHHQ75U5KYPQINUACSFJSC65","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0506063","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2005-06-29T20:05:34Z","cross_cats_sorted":[],"title_canon_sha256":"4ecbef89e83a2c538c6fc6b11f72ac762078a652c4c8a1f40e5f851805307e2a","abstract_canon_sha256":"15029e3b95a1ae2662c5e3f565aa50d8831c27370b8795f473f997810a43816d"},"schema_version":"1.0"},"canonical_sha256":"b96e73c3fda75587c10da00522a642f763cf13c10141c3a66ea82ac8c6ff394c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:18.626873Z","signature_b64":"pweJEJ1l+E2L17UM4IjLpvhzp0NMgfQjIKTAmLgr+ApQuhHYerJpojANkaO4jkHJafd843BhT5VE5dIkdRPtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b96e73c3fda75587c10da00522a642f763cf13c10141c3a66ea82ac8c6ff394c","last_reissued_at":"2026-05-18T01:38:18.626223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:18.626223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0506063","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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TUqKbAygM17aO4rg3lQtYtHqIjHr37kBaxHUXbp2e7EC9K/WWSH6thwWDZZ+LR7c0oUr8XjVz8HSI9ak6YBnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:59.482698Z"},"content_sha256":"a4839e5c4b6b707e9acd341b2b60156213e01f837582a5c839570b423c0033cb","schema_version":"1.0","event_id":"sha256:a4839e5c4b6b707e9acd341b2b60156213e01f837582a5c839570b423c0033cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:XFXHHQ75U5KYPQINUACSFJSC65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Closed Geodesics on a Triaxial Ellipsoid","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Yuri Fedorov","submitted_at":"2005-06-29T20:05:34Z","abstract_excerpt":"We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational curves.\n  Our approach is based on elements of the Weierstrass--Poncar\\'e reduction theory for hyperelliptic tangential covers of elliptic curves and the addition law for elliptic functions.\n  For the case of 3-fold and 4-fold coverings, explicit formulas for the cutting algebraic surfaces are provided and some properties of the corresponding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0506063","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":""},"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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fiDyOkhQWx+2Beg0pGoe9v9N7ViMaGiT57o+3LC5hToZNgAwZK3cET0gj2aELBjTrKPCTv/VkmQQ7am8/pe7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:59.483050Z"},"content_sha256":"49a007d1a7b776cdff79c3026835a2940257ba9aca46b150f0b7480d7bafacb0","schema_version":"1.0","event_id":"sha256:49a007d1a7b776cdff79c3026835a2940257ba9aca46b150f0b7480d7bafacb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFXHHQ75U5KYPQINUACSFJSC65/bundle.json","state_url":"https://pith.science/pith/XFXHHQ75U5KYPQINUACSFJSC65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFXHHQ75U5KYPQINUACSFJSC65/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":"2026-06-02T15:39:59Z","links":{"resolver":"https://pith.science/pith/XFXHHQ75U5KYPQINUACSFJSC65","bundle":"https://pith.science/pith/XFXHHQ75U5KYPQINUACSFJSC65/bundle.json","state":"https://pith.science/pith/XFXHHQ75U5KYPQINUACSFJSC65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFXHHQ75U5KYPQINUACSFJSC65/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:XFXHHQ75U5KYPQINUACSFJSC65","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":"15029e3b95a1ae2662c5e3f565aa50d8831c27370b8795f473f997810a43816d","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2005-06-29T20:05:34Z","title_canon_sha256":"4ecbef89e83a2c538c6fc6b11f72ac762078a652c4c8a1f40e5f851805307e2a"},"schema_version":"1.0","source":{"id":"nlin/0506063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0506063","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0506063v2","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0506063","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"XFXHHQ75U5KY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"XFXHHQ75U5KYPQIN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"XFXHHQ75","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:49a007d1a7b776cdff79c3026835a2940257ba9aca46b150f0b7480d7bafacb0","target":"graph","created_at":"2026-05-18T01:38:18Z","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":"We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational curves.\n  Our approach is based on elements of the Weierstrass--Poncar\\'e reduction theory for hyperelliptic tangential covers of elliptic curves and the addition law for elliptic functions.\n  For the case of 3-fold and 4-fold coverings, explicit formulas for the cutting algebraic surfaces are provided and some properties of the corresponding","authors_text":"Yuri Fedorov","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2005-06-29T20:05:34Z","title":"Algebraic Closed Geodesics on a Triaxial Ellipsoid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0506063","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:a4839e5c4b6b707e9acd341b2b60156213e01f837582a5c839570b423c0033cb","target":"record","created_at":"2026-05-18T01:38:18Z","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":"15029e3b95a1ae2662c5e3f565aa50d8831c27370b8795f473f997810a43816d","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2005-06-29T20:05:34Z","title_canon_sha256":"4ecbef89e83a2c538c6fc6b11f72ac762078a652c4c8a1f40e5f851805307e2a"},"schema_version":"1.0","source":{"id":"nlin/0506063","kind":"arxiv","version":2}},"canonical_sha256":"b96e73c3fda75587c10da00522a642f763cf13c10141c3a66ea82ac8c6ff394c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b96e73c3fda75587c10da00522a642f763cf13c10141c3a66ea82ac8c6ff394c","first_computed_at":"2026-05-18T01:38:18.626223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:18.626223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pweJEJ1l+E2L17UM4IjLpvhzp0NMgfQjIKTAmLgr+ApQuhHYerJpojANkaO4jkHJafd843BhT5VE5dIkdRPtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:18.626873Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0506063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4839e5c4b6b707e9acd341b2b60156213e01f837582a5c839570b423c0033cb","sha256:49a007d1a7b776cdff79c3026835a2940257ba9aca46b150f0b7480d7bafacb0"],"state_sha256":"65d731e06e5ab55ca26d685338de2a1de0b62d6165713b8b177f997ae94673d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rbALJ+li+my7hhKCuWmhMyUKEk0UpytLTkCVIxgPXGjpZbEXvolBVaf2Q0dJ0FPEoSe3h5JjiScG2GgvAlsHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:39:59.485038Z","bundle_sha256":"38e057ae7df934f46b72cb7d01ca339192011dac1cae7f528e1cfd624096f5df"}}