{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6VNXSASYTW775Z5H4SHE5NTL64","short_pith_number":"pith:6VNXSASY","canonical_record":{"source":{"id":"1611.06222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-18T20:56:26Z","cross_cats_sorted":["cs.CG","cs.LG","math.MG"],"title_canon_sha256":"487b274e5e9f333f9a09cbd3435ebefd82a800faae5e8afd4d73271e7e830028","abstract_canon_sha256":"500c3f011c5cf1539712e65140d74622b239ebebb3c92a17595db5d47ebb71cc"},"schema_version":"1.0"},"canonical_sha256":"f55b7902589dbffee7a7e48e4eb66bf727e9cf483f3b0216b49efd642ad9c30e","source":{"kind":"arxiv","id":"1611.06222","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06222","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06222v2","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06222","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"6VNXSASYTW77","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VNXSASYTW775Z5H","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VNXSASY","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6VNXSASYTW775Z5H4SHE5NTL64","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-18T20:56:26Z","cross_cats_sorted":["cs.CG","cs.LG","math.MG"],"title_canon_sha256":"487b274e5e9f333f9a09cbd3435ebefd82a800faae5e8afd4d73271e7e830028","abstract_canon_sha256":"500c3f011c5cf1539712e65140d74622b239ebebb3c92a17595db5d47ebb71cc"},"schema_version":"1.0"},"canonical_sha256":"f55b7902589dbffee7a7e48e4eb66bf727e9cf483f3b0216b49efd642ad9c30e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:47.172631Z","signature_b64":"bePJX2IU54tYRoMlSUnP0PO4SqdwZ+l6ReRBarjM/+XoBwkmiIFdrwci+cmGHWQNU4oGJBz1MB2YKSq9Tjk6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f55b7902589dbffee7a7e48e4eb66bf727e9cf483f3b0216b49efd642ad9c30e","last_reissued_at":"2026-05-18T00:39:47.171946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:47.171946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06222","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":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFH38pA9F693w6uFOxrEykPivEljqygmYMbYahNrM5blfqEmHvm9Ojt+8EN56fV+TRvsjxOkeh0nT7rc+97IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:46:40.910535Z"},"content_sha256":"55fd3f16527f982b609247dd8775ee2bf4cd1e82a0a66ee9df24d4b7dee329d3","schema_version":"1.0","event_id":"sha256:55fd3f16527f982b609247dd8775ee2bf4cd1e82a0a66ee9df24d4b7dee329d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6VNXSASYTW775Z5H4SHE5NTL64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Near Neighbors for General Symmetric Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.LG","math.MG"],"primary_cat":"cs.DS","authors_text":"Aleksandar Nikolov, Alexandr Andoni, Erik Waingarten, Huy L. Nguyen, Ilya Razenshteyn","submitted_at":"2016-11-18T20:56:26Z","abstract_excerpt":"We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\\|\\cdot\\|$, there exists a data structure for $\\mathrm{poly}(\\log \\log n)$-approximate nearest neighbor search over $\\|\\cdot\\|$ for $n$-point datasets achieving $n^{o(1)}$ query time and $n^{1+o(1)}$ space. The main technical ingredient of the algorithm is a low-distortion embedding of a symmetric norm into a low-dimensional iterated product of top-$k$ norms.\n  We also s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06222","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":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36eUJCYAgrxQm8W30G5PMA/VDMYXPNRWDMZwdyEV0TsJRRNuxt5Y54yNHg/GDuIBtMahJW0mVDomqwMP9wZ0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:46:40.911161Z"},"content_sha256":"158b81158f0a056a256d287e3edf81c5cbc1e647397e0e43939b86ed5006fa9f","schema_version":"1.0","event_id":"sha256:158b81158f0a056a256d287e3edf81c5cbc1e647397e0e43939b86ed5006fa9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VNXSASYTW775Z5H4SHE5NTL64/bundle.json","state_url":"https://pith.science/pith/6VNXSASYTW775Z5H4SHE5NTL64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VNXSASYTW775Z5H4SHE5NTL64/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":"2026-05-28T21:46:40Z","links":{"resolver":"https://pith.science/pith/6VNXSASYTW775Z5H4SHE5NTL64","bundle":"https://pith.science/pith/6VNXSASYTW775Z5H4SHE5NTL64/bundle.json","state":"https://pith.science/pith/6VNXSASYTW775Z5H4SHE5NTL64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VNXSASYTW775Z5H4SHE5NTL64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6VNXSASYTW775Z5H4SHE5NTL64","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":"500c3f011c5cf1539712e65140d74622b239ebebb3c92a17595db5d47ebb71cc","cross_cats_sorted":["cs.CG","cs.LG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-18T20:56:26Z","title_canon_sha256":"487b274e5e9f333f9a09cbd3435ebefd82a800faae5e8afd4d73271e7e830028"},"schema_version":"1.0","source":{"id":"1611.06222","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06222","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06222v2","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06222","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"6VNXSASYTW77","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VNXSASYTW775Z5H","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VNXSASY","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:158b81158f0a056a256d287e3edf81c5cbc1e647397e0e43939b86ed5006fa9f","target":"graph","created_at":"2026-05-18T00:39:47Z","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 show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\\|\\cdot\\|$, there exists a data structure for $\\mathrm{poly}(\\log \\log n)$-approximate nearest neighbor search over $\\|\\cdot\\|$ for $n$-point datasets achieving $n^{o(1)}$ query time and $n^{1+o(1)}$ space. The main technical ingredient of the algorithm is a low-distortion embedding of a symmetric norm into a low-dimensional iterated product of top-$k$ norms.\n  We also s","authors_text":"Aleksandar Nikolov, Alexandr Andoni, Erik Waingarten, Huy L. Nguyen, Ilya Razenshteyn","cross_cats":["cs.CG","cs.LG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-18T20:56:26Z","title":"Approximate Near Neighbors for General Symmetric Norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06222","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":"sha256:55fd3f16527f982b609247dd8775ee2bf4cd1e82a0a66ee9df24d4b7dee329d3","target":"record","created_at":"2026-05-18T00:39:47Z","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":"500c3f011c5cf1539712e65140d74622b239ebebb3c92a17595db5d47ebb71cc","cross_cats_sorted":["cs.CG","cs.LG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-18T20:56:26Z","title_canon_sha256":"487b274e5e9f333f9a09cbd3435ebefd82a800faae5e8afd4d73271e7e830028"},"schema_version":"1.0","source":{"id":"1611.06222","kind":"arxiv","version":2}},"canonical_sha256":"f55b7902589dbffee7a7e48e4eb66bf727e9cf483f3b0216b49efd642ad9c30e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f55b7902589dbffee7a7e48e4eb66bf727e9cf483f3b0216b49efd642ad9c30e","first_computed_at":"2026-05-18T00:39:47.171946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:47.171946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bePJX2IU54tYRoMlSUnP0PO4SqdwZ+l6ReRBarjM/+XoBwkmiIFdrwci+cmGHWQNU4oGJBz1MB2YKSq9Tjk6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:47.172631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06222","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55fd3f16527f982b609247dd8775ee2bf4cd1e82a0a66ee9df24d4b7dee329d3","sha256:158b81158f0a056a256d287e3edf81c5cbc1e647397e0e43939b86ed5006fa9f"],"state_sha256":"bec65eb9d00762e9564932fb2cae83dabf6beecf65beffd7923fd152cfb22c7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aagV3xH9eRuXFpFblaJ6/hk/QcC2toQAr+657wCx70M5ce5N3ZCCjWC3L/hs80LiXlf5BaqPHh0WFM9TwCF0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:46:40.914945Z","bundle_sha256":"b3b7a572c1378515f5b3985f56c684759b1783b6665668dffcf0d3428fbe9c72"}}