{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TWJI4NMNBZFYZAF7GXMIEAL5Z3","short_pith_number":"pith:TWJI4NMN","canonical_record":{"source":{"id":"1312.0140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-30T18:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"92651e8bbea1b1196c4f52a057efa6160588607644519ae89ab7801275050dd1","abstract_canon_sha256":"7c147e832f95bc9aeeecad361ae879669e8e578bc842356c58d1ea3e88a9b114"},"schema_version":"1.0"},"canonical_sha256":"9d928e358d0e4b8c80bf35d882017dced97282d5fb9c6a41ad86b7a5c0478bb6","source":{"kind":"arxiv","id":"1312.0140","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0140","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0140v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0140","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"TWJI4NMNBZFY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TWJI4NMNBZFYZAF7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TWJI4NMN","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TWJI4NMNBZFYZAF7GXMIEAL5Z3","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-30T18:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"92651e8bbea1b1196c4f52a057efa6160588607644519ae89ab7801275050dd1","abstract_canon_sha256":"7c147e832f95bc9aeeecad361ae879669e8e578bc842356c58d1ea3e88a9b114"},"schema_version":"1.0"},"canonical_sha256":"9d928e358d0e4b8c80bf35d882017dced97282d5fb9c6a41ad86b7a5c0478bb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.645536Z","signature_b64":"RRNpxean6ofyHBz5IK+O5ZpDAaKVMx1qpXAiTJ2H6JLz09i1rdSa/YSV4I392NSI0qm4oZ1dvYnwokFnevSfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d928e358d0e4b8c80bf35d882017dced97282d5fb9c6a41ad86b7a5c0478bb6","last_reissued_at":"2026-05-18T03:05:46.644783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.644783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0140","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1UHQVCiFFZ6QIxImBgYuPUQMP4qemfVsVPFRE+/RvkdocJai185tXGknQPTtOkBeresT2o3Me8ORUkv5ZTdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:43:03.340086Z"},"content_sha256":"3e964d96316a6641ebebb06b69eb919f862e7bd645170897468e806ec0cc08bc","schema_version":"1.0","event_id":"sha256:3e964d96316a6641ebebb06b69eb919f862e7bd645170897468e806ec0cc08bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TWJI4NMNBZFYZAF7GXMIEAL5Z3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Explicit Formula for the Spherical Curves with Constant Torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Demetre Kazaras, Ivan Sterling","submitted_at":"2013-11-30T18:46:19Z","abstract_excerpt":"The purpose of this article is to give an explicit formula for all curves of constant torsion $\\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are discussed in the Appendix. Some example curves, computed with a standard ODE package, with $\\tau=.1,.5,1,2$ are shown in Figure \\ref{peter}. Though their existence and some of their general properties were known, our explicit formulas for them, in terms of hypergeometric functions, are new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0140","kind":"arxiv","version":1},"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":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRUhY2fTiFldMF2sWTwEfVuI4YmrtTgLtnDA0XeIUS1kPihEd36kPg5G/Rwwu5WK2S+o2lF7OHBWv1AWvxLlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:43:03.340788Z"},"content_sha256":"d1a488d7ff6c84f51adc465ff0d84cdbb93fcf26ff1ffad3e2bfbedb16fe3a23","schema_version":"1.0","event_id":"sha256:d1a488d7ff6c84f51adc465ff0d84cdbb93fcf26ff1ffad3e2bfbedb16fe3a23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/bundle.json","state_url":"https://pith.science/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/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":"2026-05-31T23:43:03Z","links":{"resolver":"https://pith.science/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3","bundle":"https://pith.science/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/bundle.json","state":"https://pith.science/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWJI4NMNBZFYZAF7GXMIEAL5Z3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TWJI4NMNBZFYZAF7GXMIEAL5Z3","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":"7c147e832f95bc9aeeecad361ae879669e8e578bc842356c58d1ea3e88a9b114","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-30T18:46:19Z","title_canon_sha256":"92651e8bbea1b1196c4f52a057efa6160588607644519ae89ab7801275050dd1"},"schema_version":"1.0","source":{"id":"1312.0140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0140","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0140v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0140","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"TWJI4NMNBZFY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TWJI4NMNBZFYZAF7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TWJI4NMN","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:d1a488d7ff6c84f51adc465ff0d84cdbb93fcf26ff1ffad3e2bfbedb16fe3a23","target":"graph","created_at":"2026-05-18T03:05:46Z","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":"The purpose of this article is to give an explicit formula for all curves of constant torsion $\\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are discussed in the Appendix. Some example curves, computed with a standard ODE package, with $\\tau=.1,.5,1,2$ are shown in Figure \\ref{peter}. Though their existence and some of their general properties were known, our explicit formulas for them, in terms of hypergeometric functions, are new.","authors_text":"Demetre Kazaras, Ivan Sterling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-30T18:46:19Z","title":"An Explicit Formula for the Spherical Curves with Constant Torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0140","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":"sha256:3e964d96316a6641ebebb06b69eb919f862e7bd645170897468e806ec0cc08bc","target":"record","created_at":"2026-05-18T03:05:46Z","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":"7c147e832f95bc9aeeecad361ae879669e8e578bc842356c58d1ea3e88a9b114","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-30T18:46:19Z","title_canon_sha256":"92651e8bbea1b1196c4f52a057efa6160588607644519ae89ab7801275050dd1"},"schema_version":"1.0","source":{"id":"1312.0140","kind":"arxiv","version":1}},"canonical_sha256":"9d928e358d0e4b8c80bf35d882017dced97282d5fb9c6a41ad86b7a5c0478bb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d928e358d0e4b8c80bf35d882017dced97282d5fb9c6a41ad86b7a5c0478bb6","first_computed_at":"2026-05-18T03:05:46.644783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:46.644783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRNpxean6ofyHBz5IK+O5ZpDAaKVMx1qpXAiTJ2H6JLz09i1rdSa/YSV4I392NSI0qm4oZ1dvYnwokFnevSfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:46.645536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e964d96316a6641ebebb06b69eb919f862e7bd645170897468e806ec0cc08bc","sha256:d1a488d7ff6c84f51adc465ff0d84cdbb93fcf26ff1ffad3e2bfbedb16fe3a23"],"state_sha256":"9af483ce312729f8132866e703372e2499f11c4da83f71ea8e8fa49e1b48490a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikzOtjeyFIj8mqTbP0FEMVusuhnf9Ls70xjhFea/BcHBLRci5wjwOy0IwfUGcv/0GWfAqdcu1r2JAA7f6CZNCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:43:03.344740Z","bundle_sha256":"ae316f1afad0e3fcde60966bce89cef8ae12ee31f89ba8618fe6f599142eb9cb"}}