{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:O5GTDRP2QK3COEHG76QT6ZTTXB","short_pith_number":"pith:O5GTDRP2","canonical_record":{"source":{"id":"1108.0276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-01T10:38:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7683e1d9022f8fed45da376910a67bdb8c1b97c6b0d88c735160e788a811753c","abstract_canon_sha256":"7ad1af47ed03530c9ebe5744f15b66b54ae6d5f817aa03b5e28e0c7a0b9520c9"},"schema_version":"1.0"},"canonical_sha256":"774d31c5fa82b62710e6ffa13f6673b866aa1de58487eb0f1fea2f80b1bdfab6","source":{"kind":"arxiv","id":"1108.0276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0276","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0276v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0276","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"O5GTDRP2QK3C","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O5GTDRP2QK3COEHG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O5GTDRP2","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:O5GTDRP2QK3COEHG76QT6ZTTXB","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-01T10:38:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7683e1d9022f8fed45da376910a67bdb8c1b97c6b0d88c735160e788a811753c","abstract_canon_sha256":"7ad1af47ed03530c9ebe5744f15b66b54ae6d5f817aa03b5e28e0c7a0b9520c9"},"schema_version":"1.0"},"canonical_sha256":"774d31c5fa82b62710e6ffa13f6673b866aa1de58487eb0f1fea2f80b1bdfab6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:31.350850Z","signature_b64":"B1F4QioxNnOPKK8E1RWMBk11rFPaG1ngHP1EPrPEeuXzR7ksmRcDyRdAw34atvQ2ltf8N3wf5gjzf0vRhUfWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"774d31c5fa82b62710e6ffa13f6673b866aa1de58487eb0f1fea2f80b1bdfab6","last_reissued_at":"2026-05-18T04:16:31.350381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:31.350381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0276","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":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"an54+VhgN/eUW2hl3botqZgkf0svqSJNBZmYVgGeVakFY2662OoNNdMzcgEmXsxfk8rUW+5du68kvfnsXl0xDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:06:08.588734Z"},"content_sha256":"9e54be205dca67edf616e363d120a87f67c9132aec9ccb8aeb89234e24836c1d","schema_version":"1.0","event_id":"sha256:9e54be205dca67edf616e363d120a87f67c9132aec9ccb8aeb89234e24836c1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:O5GTDRP2QK3COEHG76QT6ZTTXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric embeddings of pretangent spaces in E^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"O. Dovgoshey, V. Bilet","submitted_at":"2011-08-01T10:38:03Z","abstract_excerpt":"We prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0276","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":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsEvcR8MxQKWG96hzqaXaA6ls7hpw8+mdikRFhLCo/lIFtrmqCJ9FqKl/y+IinZWlVJC9VaNVkqsrpPCWkAcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:06:08.589079Z"},"content_sha256":"2084bba574e832327219e115848fa77fc41af99e2923285cf49ca0dcce20039e","schema_version":"1.0","event_id":"sha256:2084bba574e832327219e115848fa77fc41af99e2923285cf49ca0dcce20039e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/bundle.json","state_url":"https://pith.science/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/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":"2026-06-24T20:06:08Z","links":{"resolver":"https://pith.science/pith/O5GTDRP2QK3COEHG76QT6ZTTXB","bundle":"https://pith.science/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/bundle.json","state":"https://pith.science/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5GTDRP2QK3COEHG76QT6ZTTXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O5GTDRP2QK3COEHG76QT6ZTTXB","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":"7ad1af47ed03530c9ebe5744f15b66b54ae6d5f817aa03b5e28e0c7a0b9520c9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-01T10:38:03Z","title_canon_sha256":"7683e1d9022f8fed45da376910a67bdb8c1b97c6b0d88c735160e788a811753c"},"schema_version":"1.0","source":{"id":"1108.0276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0276","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0276v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0276","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"O5GTDRP2QK3C","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O5GTDRP2QK3COEHG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O5GTDRP2","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:2084bba574e832327219e115848fa77fc41af99e2923285cf49ca0dcce20039e","target":"graph","created_at":"2026-05-18T04:16:31Z","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 prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces.","authors_text":"O. Dovgoshey, V. Bilet","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-01T10:38:03Z","title":"Isometric embeddings of pretangent spaces in E^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0276","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":"sha256:9e54be205dca67edf616e363d120a87f67c9132aec9ccb8aeb89234e24836c1d","target":"record","created_at":"2026-05-18T04:16:31Z","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":"7ad1af47ed03530c9ebe5744f15b66b54ae6d5f817aa03b5e28e0c7a0b9520c9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-01T10:38:03Z","title_canon_sha256":"7683e1d9022f8fed45da376910a67bdb8c1b97c6b0d88c735160e788a811753c"},"schema_version":"1.0","source":{"id":"1108.0276","kind":"arxiv","version":1}},"canonical_sha256":"774d31c5fa82b62710e6ffa13f6673b866aa1de58487eb0f1fea2f80b1bdfab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774d31c5fa82b62710e6ffa13f6673b866aa1de58487eb0f1fea2f80b1bdfab6","first_computed_at":"2026-05-18T04:16:31.350381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.350381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B1F4QioxNnOPKK8E1RWMBk11rFPaG1ngHP1EPrPEeuXzR7ksmRcDyRdAw34atvQ2ltf8N3wf5gjzf0vRhUfWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.350850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e54be205dca67edf616e363d120a87f67c9132aec9ccb8aeb89234e24836c1d","sha256:2084bba574e832327219e115848fa77fc41af99e2923285cf49ca0dcce20039e"],"state_sha256":"4b14d682d754ba3e0a837f8cc472c0246132d033f37b984440a80f7b812497a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3+GoeY2xXe6jGGaTbwzihwrEkPjnSzoZ/6GRO0LJ+qwJEOKmsnIaVgGAt+Q8Pvw1qkq83WiX8sfZTpsZzbJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:06:08.591022Z","bundle_sha256":"1f0d615770fa6e92ba1ab8c281440d84f94011661e473483100e6c7398d331f5"}}