{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QWYRTMX5ZAK7EERHSD5GMEGFKK","short_pith_number":"pith:QWYRTMX5","canonical_record":{"source":{"id":"1211.3844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-16T10:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"81b1e651903bcc4818ca39db3320ff98c3d55bd04ef8e001675f41a0fc50330f","abstract_canon_sha256":"75eb1279be5ee671c39aec817d10aaad2c4e956b8e50c52013a8e516eb7ee9f2"},"schema_version":"1.0"},"canonical_sha256":"85b119b2fdc815f2122790fa6610c552b8e9f7807578d828e5d34155e705cc3b","source":{"kind":"arxiv","id":"1211.3844","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3844","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3844v1","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3844","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"QWYRTMX5ZAK7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QWYRTMX5ZAK7EERH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QWYRTMX5","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QWYRTMX5ZAK7EERHSD5GMEGFKK","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-16T10:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"81b1e651903bcc4818ca39db3320ff98c3d55bd04ef8e001675f41a0fc50330f","abstract_canon_sha256":"75eb1279be5ee671c39aec817d10aaad2c4e956b8e50c52013a8e516eb7ee9f2"},"schema_version":"1.0"},"canonical_sha256":"85b119b2fdc815f2122790fa6610c552b8e9f7807578d828e5d34155e705cc3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:37.867980Z","signature_b64":"KSPDr4J2pSr9uJpBuGgz5+gr/ZzHFu3RSH/NhClvCFx0ola6Sa1rD7qPL42lZp4ff0P3uQ4nMc9Rxlm0/zvhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b119b2fdc815f2122790fa6610c552b8e9f7807578d828e5d34155e705cc3b","last_reissued_at":"2026-05-18T03:40:37.867190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:37.867190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3844","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":"2026-05-18T03:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTPrBBJPLHLW0tpUPdGv2vnA+7UYbHfO2+W9uBxcVPsCRh/npflT0f+3DUmjY8w3HuPUq1OYXN+MP6xQx69pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:17:25.432260Z"},"content_sha256":"0eb190b347e77da50b801f9db079577807a83e578e32deb6c0a5271ab6af2bf6","schema_version":"1.0","event_id":"sha256:0eb190b347e77da50b801f9db079577807a83e578e32deb6c0a5271ab6af2bf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QWYRTMX5ZAK7EERHSD5GMEGFKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finiteness of the total first curvature of a non-closed curve in $\\mathbb{E}^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C. Y. Kim, H. Matsuda, J. H. Park, S. Yorozu","submitted_at":"2012-11-16T10:04:53Z","abstract_excerpt":"We consider a regular smooth curve in $\\mathbb{E}^n$ such that its coordinates' components are the fundamental solutions of the differential equation $ y^{(n)} (x) - y(x) = 0 ,$ $x \\in \\mathbb{R} $ of order $n$. We show that the total first curvature of this curve is infinite for odd $n$ and is finite for even $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3844","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":"2026-05-18T03:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XkIxS31SHG7x3HVdoLJppIqECQrq09jgpvBaonDZk2lBRZ8FkZQ/ppp6Ox9xRn3wPnGd5PHerpj60dY68pRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:17:25.432915Z"},"content_sha256":"2fc3982cb063b483d776e7bb78683136cb26d1f09a975e3c94cdc49bbb23820e","schema_version":"1.0","event_id":"sha256:2fc3982cb063b483d776e7bb78683136cb26d1f09a975e3c94cdc49bbb23820e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/bundle.json","state_url":"https://pith.science/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/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":"2026-06-03T06:17:25Z","links":{"resolver":"https://pith.science/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK","bundle":"https://pith.science/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/bundle.json","state":"https://pith.science/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWYRTMX5ZAK7EERHSD5GMEGFKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QWYRTMX5ZAK7EERHSD5GMEGFKK","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":"75eb1279be5ee671c39aec817d10aaad2c4e956b8e50c52013a8e516eb7ee9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-16T10:04:53Z","title_canon_sha256":"81b1e651903bcc4818ca39db3320ff98c3d55bd04ef8e001675f41a0fc50330f"},"schema_version":"1.0","source":{"id":"1211.3844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3844","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3844v1","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3844","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"QWYRTMX5ZAK7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QWYRTMX5ZAK7EERH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QWYRTMX5","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:2fc3982cb063b483d776e7bb78683136cb26d1f09a975e3c94cdc49bbb23820e","target":"graph","created_at":"2026-05-18T03:40:37Z","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 consider a regular smooth curve in $\\mathbb{E}^n$ such that its coordinates' components are the fundamental solutions of the differential equation $ y^{(n)} (x) - y(x) = 0 ,$ $x \\in \\mathbb{R} $ of order $n$. We show that the total first curvature of this curve is infinite for odd $n$ and is finite for even $n$.","authors_text":"C. Y. Kim, H. Matsuda, J. H. Park, S. Yorozu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-16T10:04:53Z","title":"Finiteness of the total first curvature of a non-closed curve in $\\mathbb{E}^{n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3844","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":"sha256:0eb190b347e77da50b801f9db079577807a83e578e32deb6c0a5271ab6af2bf6","target":"record","created_at":"2026-05-18T03:40:37Z","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":"75eb1279be5ee671c39aec817d10aaad2c4e956b8e50c52013a8e516eb7ee9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-16T10:04:53Z","title_canon_sha256":"81b1e651903bcc4818ca39db3320ff98c3d55bd04ef8e001675f41a0fc50330f"},"schema_version":"1.0","source":{"id":"1211.3844","kind":"arxiv","version":1}},"canonical_sha256":"85b119b2fdc815f2122790fa6610c552b8e9f7807578d828e5d34155e705cc3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85b119b2fdc815f2122790fa6610c552b8e9f7807578d828e5d34155e705cc3b","first_computed_at":"2026-05-18T03:40:37.867190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:37.867190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KSPDr4J2pSr9uJpBuGgz5+gr/ZzHFu3RSH/NhClvCFx0ola6Sa1rD7qPL42lZp4ff0P3uQ4nMc9Rxlm0/zvhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:37.867980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eb190b347e77da50b801f9db079577807a83e578e32deb6c0a5271ab6af2bf6","sha256:2fc3982cb063b483d776e7bb78683136cb26d1f09a975e3c94cdc49bbb23820e"],"state_sha256":"113fe05a929b32661f032b28972e1a6f5033d0356ecd635d0a275eed52c13ec1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ilww/9xF/Wdt+DHDDQypsZ8Uoe9BqBLMmq6wZ69dKt0UlxgXz8vJ5uJeecNhYVDp71DoOnZ3dOzK5zYN9NMfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:17:25.435694Z","bundle_sha256":"f691fa8c0bcfcbb88406845d290e582432e954694ece81455dfcb450a4134eef"}}