{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IWWGLE4RZ2KL4MWADXADFIOD7I","short_pith_number":"pith:IWWGLE4R","canonical_record":{"source":{"id":"1308.4996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-22T21:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"70335772079a59e275618b8985a9ed9a1b45287d287c84f0919d7efee2433603","abstract_canon_sha256":"417221d6758d2372bf46eb2d6f5f6e20b1663856fd368b6335f251a970c44f62"},"schema_version":"1.0"},"canonical_sha256":"45ac659391ce94be32c01dc032a1c3fa2d87f385c57c3a68967e7f80d47472d0","source":{"kind":"arxiv","id":"1308.4996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4996","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4996v1","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4996","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"IWWGLE4RZ2KL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWWGLE4RZ2KL4MWA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWWGLE4R","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IWWGLE4RZ2KL4MWADXADFIOD7I","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-22T21:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"70335772079a59e275618b8985a9ed9a1b45287d287c84f0919d7efee2433603","abstract_canon_sha256":"417221d6758d2372bf46eb2d6f5f6e20b1663856fd368b6335f251a970c44f62"},"schema_version":"1.0"},"canonical_sha256":"45ac659391ce94be32c01dc032a1c3fa2d87f385c57c3a68967e7f80d47472d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:17.727516Z","signature_b64":"Y4T32q5B+g31x51nZ6tERWWrYGBB2vP5qeAQ6Tl+cOYkMR7+hnxx/b1xUgt5XlbSmMIP+S1MI9lK+svGawDJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45ac659391ce94be32c01dc032a1c3fa2d87f385c57c3a68967e7f80d47472d0","last_reissued_at":"2026-05-18T03:15:17.726516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:17.726516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4996","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":"2026-05-18T03:15:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dgmVPKx32Mn9NsMxx7wJc+SPum0ovAJPhiwHEBM+zh+nuoog7Au/b/kl7pSxIEjKqUZdX4nv0caCgBqEjKuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:56.816122Z"},"content_sha256":"f5dfbba90cda2ad25b5672a4f194fe8ff8bfe75bc5adf9baad899b522e41bac2","schema_version":"1.0","event_id":"sha256:f5dfbba90cda2ad25b5672a4f194fe8ff8bfe75bc5adf9baad899b522e41bac2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IWWGLE4RZ2KL4MWADXADFIOD7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Impossibility of Dimension Reduction for Doubling Subsets of $\\ell_p$, $p>2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Lee-Ad Gottlieb, Ofer Neiman, Yair Bartal","submitted_at":"2013-08-22T21:34:33Z","abstract_excerpt":"A major open problem in the field of metric embedding is the existence of dimension reduction for $n$-point subsets of Euclidean space, such that both distortion and dimension depend only on the {\\em doubling constant} of the pointset, and not on its cardinality. In this paper, we negate this possibility for $\\ell_p$ spaces with $p>2$. In particular, we introduce an $n$-point subset of $\\ell_p$ with doubling constant O(1), and demonstrate that any embedding of the set into $\\ell_p^d$ with distortion $D$ must have $D\\ge\\Omega\\left(\\left(\\frac{c\\log n}{d}\\right)^{\\frac{1}{2}-\\frac{1}{p}}\\right)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4996","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":"2026-05-18T03:15:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4v8ai3HdiuF6P66Y8i3revoek57KF9PULgEVjDjDRoK9Wfke5O4S3TxhJYwDhj99HS7lEF0/2Qfa7h5RqmlACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:56.816475Z"},"content_sha256":"07efc6412f147dca63785a84a13c762017e981782da2ac41a45757d949e28e15","schema_version":"1.0","event_id":"sha256:07efc6412f147dca63785a84a13c762017e981782da2ac41a45757d949e28e15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/bundle.json","state_url":"https://pith.science/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/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":"2026-06-05T10:19:56Z","links":{"resolver":"https://pith.science/pith/IWWGLE4RZ2KL4MWADXADFIOD7I","bundle":"https://pith.science/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/bundle.json","state":"https://pith.science/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWWGLE4RZ2KL4MWADXADFIOD7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IWWGLE4RZ2KL4MWADXADFIOD7I","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":"417221d6758d2372bf46eb2d6f5f6e20b1663856fd368b6335f251a970c44f62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-22T21:34:33Z","title_canon_sha256":"70335772079a59e275618b8985a9ed9a1b45287d287c84f0919d7efee2433603"},"schema_version":"1.0","source":{"id":"1308.4996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4996","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4996v1","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4996","created_at":"2026-05-18T03:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"IWWGLE4RZ2KL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWWGLE4RZ2KL4MWA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWWGLE4R","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:07efc6412f147dca63785a84a13c762017e981782da2ac41a45757d949e28e15","target":"graph","created_at":"2026-05-18T03:15:17Z","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":"A major open problem in the field of metric embedding is the existence of dimension reduction for $n$-point subsets of Euclidean space, such that both distortion and dimension depend only on the {\\em doubling constant} of the pointset, and not on its cardinality. In this paper, we negate this possibility for $\\ell_p$ spaces with $p>2$. In particular, we introduce an $n$-point subset of $\\ell_p$ with doubling constant O(1), and demonstrate that any embedding of the set into $\\ell_p^d$ with distortion $D$ must have $D\\ge\\Omega\\left(\\left(\\frac{c\\log n}{d}\\right)^{\\frac{1}{2}-\\frac{1}{p}}\\right)$","authors_text":"Lee-Ad Gottlieb, Ofer Neiman, Yair Bartal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-22T21:34:33Z","title":"On the Impossibility of Dimension Reduction for Doubling Subsets of $\\ell_p$, $p>2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4996","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:f5dfbba90cda2ad25b5672a4f194fe8ff8bfe75bc5adf9baad899b522e41bac2","target":"record","created_at":"2026-05-18T03:15:17Z","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":"417221d6758d2372bf46eb2d6f5f6e20b1663856fd368b6335f251a970c44f62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-22T21:34:33Z","title_canon_sha256":"70335772079a59e275618b8985a9ed9a1b45287d287c84f0919d7efee2433603"},"schema_version":"1.0","source":{"id":"1308.4996","kind":"arxiv","version":1}},"canonical_sha256":"45ac659391ce94be32c01dc032a1c3fa2d87f385c57c3a68967e7f80d47472d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45ac659391ce94be32c01dc032a1c3fa2d87f385c57c3a68967e7f80d47472d0","first_computed_at":"2026-05-18T03:15:17.726516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:17.726516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4T32q5B+g31x51nZ6tERWWrYGBB2vP5qeAQ6Tl+cOYkMR7+hnxx/b1xUgt5XlbSmMIP+S1MI9lK+svGawDJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:17.727516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5dfbba90cda2ad25b5672a4f194fe8ff8bfe75bc5adf9baad899b522e41bac2","sha256:07efc6412f147dca63785a84a13c762017e981782da2ac41a45757d949e28e15"],"state_sha256":"cacabd622ddffafa8d5efb9135113f12779b6baac93cfa981be03c70759dc7e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOcHEd82MVvCvMWX32Z5pNDrpTjV4UoekSYy1KM23xg8wbr+AqFDyzGRu65uFqLWPB2iR5Qk5VsazKeTFvF3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:19:56.818340Z","bundle_sha256":"91b9f255867c5e4f9bf10d762c61d3e2ca9864b0afbedf60e8509d20e0aa712f"}}