{"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"}