{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6U6BV3KL3QYQMR4NXTDJMVLDLR","short_pith_number":"pith:6U6BV3KL","canonical_record":{"source":{"id":"1706.09998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-30T01:44:48Z","cross_cats_sorted":[],"title_canon_sha256":"fb7c3ac32768af65b718e38ff6c19362ff068738a133c972195d3e7114ffe7d9","abstract_canon_sha256":"04a468cf12a68ed8329e2b6e7744360b95aaf5a97dd9fbe4cfd7c76625928597"},"schema_version":"1.0"},"canonical_sha256":"f53c1aed4bdc3106478dbcc69655635c478642c70af5468e23b865e157bc48aa","source":{"kind":"arxiv","id":"1706.09998","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6U6BV3KL3QYQMR4NXTDJMVLDLR","target":"record","payload":{"canonical_record":{"source":{"id":"1706.09998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-30T01:44:48Z","cross_cats_sorted":[],"title_canon_sha256":"fb7c3ac32768af65b718e38ff6c19362ff068738a133c972195d3e7114ffe7d9","abstract_canon_sha256":"04a468cf12a68ed8329e2b6e7744360b95aaf5a97dd9fbe4cfd7c76625928597"},"schema_version":"1.0"},"canonical_sha256":"f53c1aed4bdc3106478dbcc69655635c478642c70af5468e23b865e157bc48aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:28.226752Z","signature_b64":"XkhP4SGIIiaBbdZhmsbwkWX06923JflTw/YcHsP/WzslA4eNRytXYDdRC6t4ZBadywAK3LOVXOPFu7r2H7yBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f53c1aed4bdc3106478dbcc69655635c478642c70af5468e23b865e157bc48aa","last_reissued_at":"2026-05-18T00:40:28.226241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:28.226241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.09998","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":"2026-05-18T00:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"heC4bcNeC5l7zrGavoBibVJPYkNks9oH76CJ+TUSBGYbtw0Vlksbh3iGDSaIPdFv47lSddV05la5HCyRSDolCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:56.901840Z"},"content_sha256":"c2864a7919c0bc9a4d50a1cd3968c4f86452bc3f5cac4fe458672eaeb719e91d","schema_version":"1.0","event_id":"sha256:c2864a7919c0bc9a4d50a1cd3968c4f86452bc3f5cac4fe458672eaeb719e91d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6U6BV3KL3QYQMR4NXTDJMVLDLR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension of a snowflake of a finite Euclidean subspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Vladimir Zolotov","submitted_at":"2017-06-30T01:44:48Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09998","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":"2026-05-18T00:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+sWO7Q5GkMWcdlKdML850vCGvjvmpcDZE0xqp/pfztQoefM1rrPF0d88icKXMdLndWG/NPUDU3O1IUz7PYDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:56.902183Z"},"content_sha256":"6bbb2d0cbb2a0e98a25ae15417cd27a30c43c17d6a2a4ef0af2a060daefcddc2","schema_version":"1.0","event_id":"sha256:6bbb2d0cbb2a0e98a25ae15417cd27a30c43c17d6a2a4ef0af2a060daefcddc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/bundle.json","state_url":"https://pith.science/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/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":"2026-06-26T12:43:56Z","links":{"resolver":"https://pith.science/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR","bundle":"https://pith.science/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/bundle.json","state":"https://pith.science/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6U6BV3KL3QYQMR4NXTDJMVLDLR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTZM+5nffcUxKGND9DBJH7WU70su5co86tqcMND1yYhHNoqcGyDD4jSeqUnN/sWHnmLl1aYhsieCA8MV2lKFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:43:56.904088Z","bundle_sha256":"4a00dcd848bc3263d55f8ea6ee7fb53c42293560cc58ae9b131a76df085783b9"}}