{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GGYQC7SVF2IR3LIM6GYXKDMP3W","short_pith_number":"pith:GGYQC7SV","canonical_record":{"source":{"id":"1611.08836","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-27T12:58:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"c53485846644da6888603b21a7aa372158a7eab4a33f76259f06bab4b17eadce","abstract_canon_sha256":"e08988550314eaa487158e33688c94f67885f23a180bf0e9fd67e27f9d4e54cf"},"schema_version":"1.0"},"canonical_sha256":"31b1017e552e911dad0cf1b1750d8fddb9459a7db405eee8318f01982a7491d3","source":{"kind":"arxiv","id":"1611.08836","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08836","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08836v4","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08836","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"GGYQC7SVF2IR","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGYQC7SVF2IR3LIM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGYQC7SV","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GGYQC7SVF2IR3LIM6GYXKDMP3W","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08836","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-27T12:58:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"c53485846644da6888603b21a7aa372158a7eab4a33f76259f06bab4b17eadce","abstract_canon_sha256":"e08988550314eaa487158e33688c94f67885f23a180bf0e9fd67e27f9d4e54cf"},"schema_version":"1.0"},"canonical_sha256":"31b1017e552e911dad0cf1b1750d8fddb9459a7db405eee8318f01982a7491d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:18.776891Z","signature_b64":"msfjEZUM1puEt+A/2BLxu2sdujo2vPvfk4Nb385OUN7QXs80/rydeNOdTHEbiGyt0IRMRVq+E5seqxDAlwQmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31b1017e552e911dad0cf1b1750d8fddb9459a7db405eee8318f01982a7491d3","last_reissued_at":"2026-05-18T00:46:18.776363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:18.776363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08836","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPDaIbGEUZ4z9Aq5dL1D850h+FZVnH6Pb++v3VxX2sFijaYDp4m0EQz6jZk3avn3obcc0BnyuUAMBN0A2o/fDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:03.988912Z"},"content_sha256":"22109a9ee689c517dbf9089c8868d2fcb6df634d65857fc9d2e677296750f7f0","schema_version":"1.0","event_id":"sha256:22109a9ee689c517dbf9089c8868d2fcb6df634d65857fc9d2e677296750f7f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GGYQC7SVF2IR3LIM6GYXKDMP3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterating evolutes of spatial polygons and of spatial curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Dmitry Fuchs, Serge Tabachnikov","submitted_at":"2016-11-27T12:58:07Z","abstract_excerpt":"The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose consecutive vertices are the centers of the spheres through the consecutive (m+1)-tuples of vertices of the original polygon. We study the iterations of these evolute transformations. This work continues the recent study of similar problems in dimension two, see arXiv:1510.07742. Here is a sampler of our results. The set of n-gons with fixed directions of the sides, considered up to parallel translation, is an (n-m)-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08836","kind":"arxiv","version":4},"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":"2026-05-18T00:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7VVV3BRsC1jBRQZkgnqVPLWcQpTmZRXK/ww7xyoo8A9xyOjn8X5c3fznI0fRUcfwdm1MNorUd3cGi4uOwQtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:03.989259Z"},"content_sha256":"34befc2947798fca299c7596bc6b7a7fbaf11b563c2d083ac9b67f73453046ed","schema_version":"1.0","event_id":"sha256:34befc2947798fca299c7596bc6b7a7fbaf11b563c2d083ac9b67f73453046ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/bundle.json","state_url":"https://pith.science/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/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":"2026-06-23T00:52:03Z","links":{"resolver":"https://pith.science/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W","bundle":"https://pith.science/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/bundle.json","state":"https://pith.science/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGYQC7SVF2IR3LIM6GYXKDMP3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GGYQC7SVF2IR3LIM6GYXKDMP3W","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":"e08988550314eaa487158e33688c94f67885f23a180bf0e9fd67e27f9d4e54cf","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-27T12:58:07Z","title_canon_sha256":"c53485846644da6888603b21a7aa372158a7eab4a33f76259f06bab4b17eadce"},"schema_version":"1.0","source":{"id":"1611.08836","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08836","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08836v4","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08836","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"GGYQC7SVF2IR","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGYQC7SVF2IR3LIM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGYQC7SV","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:34befc2947798fca299c7596bc6b7a7fbaf11b563c2d083ac9b67f73453046ed","target":"graph","created_at":"2026-05-18T00:46:18Z","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":"The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose consecutive vertices are the centers of the spheres through the consecutive (m+1)-tuples of vertices of the original polygon. We study the iterations of these evolute transformations. This work continues the recent study of similar problems in dimension two, see arXiv:1510.07742. Here is a sampler of our results. The set of n-gons with fixed directions of the sides, considered up to parallel translation, is an (n-m)-dimen","authors_text":"Dmitry Fuchs, Serge Tabachnikov","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-27T12:58:07Z","title":"Iterating evolutes of spatial polygons and of spatial curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08836","kind":"arxiv","version":4},"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":"sha256:22109a9ee689c517dbf9089c8868d2fcb6df634d65857fc9d2e677296750f7f0","target":"record","created_at":"2026-05-18T00:46:18Z","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":"e08988550314eaa487158e33688c94f67885f23a180bf0e9fd67e27f9d4e54cf","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-27T12:58:07Z","title_canon_sha256":"c53485846644da6888603b21a7aa372158a7eab4a33f76259f06bab4b17eadce"},"schema_version":"1.0","source":{"id":"1611.08836","kind":"arxiv","version":4}},"canonical_sha256":"31b1017e552e911dad0cf1b1750d8fddb9459a7db405eee8318f01982a7491d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31b1017e552e911dad0cf1b1750d8fddb9459a7db405eee8318f01982a7491d3","first_computed_at":"2026-05-18T00:46:18.776363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:18.776363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"msfjEZUM1puEt+A/2BLxu2sdujo2vPvfk4Nb385OUN7QXs80/rydeNOdTHEbiGyt0IRMRVq+E5seqxDAlwQmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:18.776891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08836","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22109a9ee689c517dbf9089c8868d2fcb6df634d65857fc9d2e677296750f7f0","sha256:34befc2947798fca299c7596bc6b7a7fbaf11b563c2d083ac9b67f73453046ed"],"state_sha256":"a9d614f311515face5d1cbea03d381e075a8a49798ffb2bd042e79825a2f99ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5nExmgiB43WBUSnSlZh2DYDWHCN9labgfJ1jjJT0ce0MBU9lbaeRs3Ucedn8CzlOOLx/KUT7s3L1BGxAsHLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:52:03.991270Z","bundle_sha256":"f2846f2aa2d9d203eea092190bdd776ae5c87b963a3c80a679fd13ed5ff9b440"}}