{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A37SVTCME2UKVC2AYOAFAWOEFL","short_pith_number":"pith:A37SVTCM","canonical_record":{"source":{"id":"1307.4213","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2013-07-16T09:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"8e939ed026a7307c2fbd07037701529d1678c9663768bb3b70079311addf4323","abstract_canon_sha256":"c556bddaf05d588eb8078103418d8e439df67cd96b7c05cb44be9256f4cb9c0e"},"schema_version":"1.0"},"canonical_sha256":"06ff2acc4c26a8aa8b40c3805059c42aec2fc140c2a29e4691e0f37490290244","source":{"kind":"arxiv","id":"1307.4213","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4213","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4213v2","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4213","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"A37SVTCME2UK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A37SVTCME2UKVC2A","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A37SVTCM","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A37SVTCME2UKVC2AYOAFAWOEFL","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4213","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2013-07-16T09:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"8e939ed026a7307c2fbd07037701529d1678c9663768bb3b70079311addf4323","abstract_canon_sha256":"c556bddaf05d588eb8078103418d8e439df67cd96b7c05cb44be9256f4cb9c0e"},"schema_version":"1.0"},"canonical_sha256":"06ff2acc4c26a8aa8b40c3805059c42aec2fc140c2a29e4691e0f37490290244","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:04.903852Z","signature_b64":"l9qDhNIEgqlgOOfvA3bs8aO0TVTNeETmXc21eEmv5HF39f2UdWCW4STzZ8gLywLhxJTqthL0WiR+CUw+r0bqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06ff2acc4c26a8aa8b40c3805059c42aec2fc140c2a29e4691e0f37490290244","last_reissued_at":"2026-05-18T02:25:04.903476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:04.903476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4213","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":"2026-05-18T02:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdWQCmJPI45iUTutzPcKe3I9YKtnyxC+p6T/H5qJipSh9lthJVzbdcob5yiojXLj/PrEo0My0FjCrl/pt2JqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:31:10.638156Z"},"content_sha256":"ca5cfc62c30e9bdaf27b0fde4f0c7d1dc748e2b846bd8c1689cdc3b82ba53620","schema_version":"1.0","event_id":"sha256:ca5cfc62c30e9bdaf27b0fde4f0c7d1dc748e2b846bd8c1689cdc3b82ba53620"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A37SVTCME2UKVC2AYOAFAWOEFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locus of the centers of Meusnier spheres in Euclidean 3-space","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beyhan Uzunoglu","submitted_at":"2013-07-16T09:25:46Z","abstract_excerpt":"In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the centers of the Meusnier spheres of the curve is an evolute curve. Then, we give the relations between this evolute curve and the focal curve. Also, we give some relations between helices, slant helices and the locus of the centers of the Meusnier spheres of the curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4213","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":"2026-05-18T02:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfYtgydR8S6b97jv14JwBF8BF+xLoC0uHYnxkZrTHt56NZi416ptYgYNdO4dICcSs7Xw245EFvdsIhZLq11KDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:31:10.638515Z"},"content_sha256":"bf54cb94024dc3fd3ccda122b5a70cc97c3754d7e945a99de3817c3453c0ac26","schema_version":"1.0","event_id":"sha256:bf54cb94024dc3fd3ccda122b5a70cc97c3754d7e945a99de3817c3453c0ac26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A37SVTCME2UKVC2AYOAFAWOEFL/bundle.json","state_url":"https://pith.science/pith/A37SVTCME2UKVC2AYOAFAWOEFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A37SVTCME2UKVC2AYOAFAWOEFL/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":"2026-06-09T12:31:10Z","links":{"resolver":"https://pith.science/pith/A37SVTCME2UKVC2AYOAFAWOEFL","bundle":"https://pith.science/pith/A37SVTCME2UKVC2AYOAFAWOEFL/bundle.json","state":"https://pith.science/pith/A37SVTCME2UKVC2AYOAFAWOEFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A37SVTCME2UKVC2AYOAFAWOEFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A37SVTCME2UKVC2AYOAFAWOEFL","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":"c556bddaf05d588eb8078103418d8e439df67cd96b7c05cb44be9256f4cb9c0e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2013-07-16T09:25:46Z","title_canon_sha256":"8e939ed026a7307c2fbd07037701529d1678c9663768bb3b70079311addf4323"},"schema_version":"1.0","source":{"id":"1307.4213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4213","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4213v2","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4213","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"A37SVTCME2UK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A37SVTCME2UKVC2A","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A37SVTCM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:bf54cb94024dc3fd3ccda122b5a70cc97c3754d7e945a99de3817c3453c0ac26","target":"graph","created_at":"2026-05-18T02:25:04Z","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":"In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the centers of the Meusnier spheres of the curve is an evolute curve. Then, we give the relations between this evolute curve and the focal curve. Also, we give some relations between helices, slant helices and the locus of the centers of the Meusnier spheres of the curve.","authors_text":"Beyhan Uzunoglu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2013-07-16T09:25:46Z","title":"Locus of the centers of Meusnier spheres in Euclidean 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4213","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:ca5cfc62c30e9bdaf27b0fde4f0c7d1dc748e2b846bd8c1689cdc3b82ba53620","target":"record","created_at":"2026-05-18T02:25:04Z","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":"c556bddaf05d588eb8078103418d8e439df67cd96b7c05cb44be9256f4cb9c0e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2013-07-16T09:25:46Z","title_canon_sha256":"8e939ed026a7307c2fbd07037701529d1678c9663768bb3b70079311addf4323"},"schema_version":"1.0","source":{"id":"1307.4213","kind":"arxiv","version":2}},"canonical_sha256":"06ff2acc4c26a8aa8b40c3805059c42aec2fc140c2a29e4691e0f37490290244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06ff2acc4c26a8aa8b40c3805059c42aec2fc140c2a29e4691e0f37490290244","first_computed_at":"2026-05-18T02:25:04.903476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:04.903476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l9qDhNIEgqlgOOfvA3bs8aO0TVTNeETmXc21eEmv5HF39f2UdWCW4STzZ8gLywLhxJTqthL0WiR+CUw+r0bqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:04.903852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca5cfc62c30e9bdaf27b0fde4f0c7d1dc748e2b846bd8c1689cdc3b82ba53620","sha256:bf54cb94024dc3fd3ccda122b5a70cc97c3754d7e945a99de3817c3453c0ac26"],"state_sha256":"2c01259558caeb7840bf16dd409459083d9e3dc00537ddf7218c6fe4bbdf0941"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6aArxFaJyeHTfUskborIbkMjYjzOxDdrAB8Q3MypTFXnavNNt2Tt+JKuiTIayy2aylPHodW3TVNi/crnKGTXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:31:10.640425Z","bundle_sha256":"6efc05292b6eb2373e33c67c7be65e51c76bcca96e919e45a06a52c31bfe6c56"}}