{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7LQ2PKWWU3RLDDPX4XKCXBMFKB","short_pith_number":"pith:7LQ2PKWW","canonical_record":{"source":{"id":"1205.5892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-26T16:25:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b9d1509fd855700e2934ec45eae2c5f469ffc8355aecb324607ce778a5df34c","abstract_canon_sha256":"bbacb28e0c7242a4f5dbdccd1541351c5d277ea5e69d2931fa45eaa06c36758c"},"schema_version":"1.0"},"canonical_sha256":"fae1a7aad6a6e2b18df7e5d42b8585507f1896eb39568c373c675076f4f48b81","source":{"kind":"arxiv","id":"1205.5892","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5892","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5892v1","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5892","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"7LQ2PKWWU3RL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LQ2PKWWU3RLDDPX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LQ2PKWW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7LQ2PKWWU3RLDDPX4XKCXBMFKB","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-26T16:25:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b9d1509fd855700e2934ec45eae2c5f469ffc8355aecb324607ce778a5df34c","abstract_canon_sha256":"bbacb28e0c7242a4f5dbdccd1541351c5d277ea5e69d2931fa45eaa06c36758c"},"schema_version":"1.0"},"canonical_sha256":"fae1a7aad6a6e2b18df7e5d42b8585507f1896eb39568c373c675076f4f48b81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:09.385266Z","signature_b64":"9abh52NjCS7dfbYpfbVgzpXzzXoQGSAzFheYK00+Ap7YIjMLxyBfeXszEqFU6rS3ngq8HAaV8qs0P6+dyfdsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fae1a7aad6a6e2b18df7e5d42b8585507f1896eb39568c373c675076f4f48b81","last_reissued_at":"2026-05-18T02:21:09.384875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:09.384875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5892","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":"2026-05-18T02:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4eyNZnpEj1iQqUdhjnVEllia3G6N6RzRReT8Y+TKWb5IwGpSjCzAJiACL2zkhTufzxjadkKBPfQMldbWgCw1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:49:02.711448Z"},"content_sha256":"3e6e0fe25b3824778d926a02d1d67419408b93c65305440c02b4bd39246e7aea","schema_version":"1.0","event_id":"sha256:3e6e0fe25b3824778d926a02d1d67419408b93c65305440c02b4bd39246e7aea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7LQ2PKWWU3RLDDPX4XKCXBMFKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximations of periodic functions to R^n by curvatures of closed curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jacob Mostovoy, Rustam Sadykov","submitted_at":"2012-05-26T16:25:39Z","abstract_excerpt":"We show that for any n real periodic functions f_1,..., f_n with the same period, such that f_i>0 for i<n, and a real number e >0, there is a closed curve in R^{n+1} with curvatures k_1, ..., k_n such that |k_i(t)-f_i(t)| < e for all i and t. This neither holds for closed curves in the hyperbolic space H^{n+1}, nor for parametric families of closed curves in R^{n+1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5892","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":"2026-05-18T02:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2CLsxgRP8imDsxuHGmmq/R2+H4FQB6lQtttax+ovlNDcq4gX9yAgE/qgvAVMNLoE6DfEVZitGSvOK2eVItxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:49:02.711785Z"},"content_sha256":"c06b58d9538376ce5827d8c416e84c735292129b427cd86e56b73a35110a43e2","schema_version":"1.0","event_id":"sha256:c06b58d9538376ce5827d8c416e84c735292129b427cd86e56b73a35110a43e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/bundle.json","state_url":"https://pith.science/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/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":"2026-06-23T07:49:02Z","links":{"resolver":"https://pith.science/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB","bundle":"https://pith.science/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/bundle.json","state":"https://pith.science/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LQ2PKWWU3RLDDPX4XKCXBMFKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7LQ2PKWWU3RLDDPX4XKCXBMFKB","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":"bbacb28e0c7242a4f5dbdccd1541351c5d277ea5e69d2931fa45eaa06c36758c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-26T16:25:39Z","title_canon_sha256":"2b9d1509fd855700e2934ec45eae2c5f469ffc8355aecb324607ce778a5df34c"},"schema_version":"1.0","source":{"id":"1205.5892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5892","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5892v1","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5892","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"7LQ2PKWWU3RL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LQ2PKWWU3RLDDPX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LQ2PKWW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c06b58d9538376ce5827d8c416e84c735292129b427cd86e56b73a35110a43e2","target":"graph","created_at":"2026-05-18T02:21:09Z","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 show that for any n real periodic functions f_1,..., f_n with the same period, such that f_i>0 for i<n, and a real number e >0, there is a closed curve in R^{n+1} with curvatures k_1, ..., k_n such that |k_i(t)-f_i(t)| < e for all i and t. This neither holds for closed curves in the hyperbolic space H^{n+1}, nor for parametric families of closed curves in R^{n+1}.","authors_text":"Jacob Mostovoy, Rustam Sadykov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-26T16:25:39Z","title":"Approximations of periodic functions to R^n by curvatures of closed curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5892","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":"sha256:3e6e0fe25b3824778d926a02d1d67419408b93c65305440c02b4bd39246e7aea","target":"record","created_at":"2026-05-18T02:21:09Z","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":"bbacb28e0c7242a4f5dbdccd1541351c5d277ea5e69d2931fa45eaa06c36758c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-26T16:25:39Z","title_canon_sha256":"2b9d1509fd855700e2934ec45eae2c5f469ffc8355aecb324607ce778a5df34c"},"schema_version":"1.0","source":{"id":"1205.5892","kind":"arxiv","version":1}},"canonical_sha256":"fae1a7aad6a6e2b18df7e5d42b8585507f1896eb39568c373c675076f4f48b81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae1a7aad6a6e2b18df7e5d42b8585507f1896eb39568c373c675076f4f48b81","first_computed_at":"2026-05-18T02:21:09.384875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:09.384875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9abh52NjCS7dfbYpfbVgzpXzzXoQGSAzFheYK00+Ap7YIjMLxyBfeXszEqFU6rS3ngq8HAaV8qs0P6+dyfdsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:09.385266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e6e0fe25b3824778d926a02d1d67419408b93c65305440c02b4bd39246e7aea","sha256:c06b58d9538376ce5827d8c416e84c735292129b427cd86e56b73a35110a43e2"],"state_sha256":"64fa5e4d69fce105c525e36570fb54a67cbc003870d38aaa0d1fd8d7061c4367"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5TzEyAL4xJWWTmUtFhK4xDQH7vAoJMOMuIBylgqmK01N68hpklbJvF7iJQGvfdc9tnwLAvcy7IjP7MHTXOVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:49:02.713741Z","bundle_sha256":"5cc71c0240e605d2c290b21ff4093417d4e8aec09c2a36a3542036b1bdc316ae"}}