{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6U6BV3KL3QYQMR4NXTDJMVLDLR","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":"04a468cf12a68ed8329e2b6e7744360b95aaf5a97dd9fbe4cfd7c76625928597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-30T01:44:48Z","title_canon_sha256":"fb7c3ac32768af65b718e38ff6c19362ff068738a133c972195d3e7114ffe7d9"},"schema_version":"1.0","source":{"id":"1706.09998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09998","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09998v2","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09998","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"6U6BV3KL3QYQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6U6BV3KL3QYQMR4N","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6U6BV3KL","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6bbb2d0cbb2a0e98a25ae15417cd27a30c43c17d6a2a4ef0af2a060daefcddc2","target":"graph","created_at":"2026-05-18T00:40:28Z","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":"Let $X$ be an $n$-point subset of a Euclidean space and $0 < a < 1$. The classical theorem of Schoenberg implies that the snowflake space $X^a$ can be isometrically embedded into Euclidean space. In the paper we show that points in the image of such an embedding always are in general position. As application we prove the analogue of Schoenberg's result for quotients of Euclidean spaces by finite groups.","authors_text":"Vladimir Zolotov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-30T01:44:48Z","title":"Dimension of a snowflake of a finite Euclidean subspace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09998","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:c2864a7919c0bc9a4d50a1cd3968c4f86452bc3f5cac4fe458672eaeb719e91d","target":"record","created_at":"2026-05-18T00:40:28Z","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":"04a468cf12a68ed8329e2b6e7744360b95aaf5a97dd9fbe4cfd7c76625928597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-30T01:44:48Z","title_canon_sha256":"fb7c3ac32768af65b718e38ff6c19362ff068738a133c972195d3e7114ffe7d9"},"schema_version":"1.0","source":{"id":"1706.09998","kind":"arxiv","version":2}},"canonical_sha256":"f53c1aed4bdc3106478dbcc69655635c478642c70af5468e23b865e157bc48aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f53c1aed4bdc3106478dbcc69655635c478642c70af5468e23b865e157bc48aa","first_computed_at":"2026-05-18T00:40:28.226241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:28.226241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XkhP4SGIIiaBbdZhmsbwkWX06923JflTw/YcHsP/WzslA4eNRytXYDdRC6t4ZBadywAK3LOVXOPFu7r2H7yBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:28.226752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2864a7919c0bc9a4d50a1cd3968c4f86452bc3f5cac4fe458672eaeb719e91d","sha256:6bbb2d0cbb2a0e98a25ae15417cd27a30c43c17d6a2a4ef0af2a060daefcddc2"],"state_sha256":"b1ae10f0e70e8af504b865d30a65d2257d70b96f9b156450b029dc1e2c17b163"}