{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FHIEW3TFAU4KT6R6SM3VYVTMK3","short_pith_number":"pith:FHIEW3TF","canonical_record":{"source":{"id":"1605.02701","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-09T19:13:06Z","cross_cats_sorted":["cs.CC","cs.CG","cs.IT","math.IT"],"title_canon_sha256":"5625b62bbdfd4cba65c113735349b127431c233800c2bdcc817026eda86c1832","abstract_canon_sha256":"5ccb17dcab510d501c4cbc7fda441c85b6c836fec5a8650bd1e84878ffc2cfe0"},"schema_version":"1.0"},"canonical_sha256":"29d04b6e650538a9fa3e93375c566c56e87f97e8afd282d5d3badf25b4d88412","source":{"kind":"arxiv","id":"1605.02701","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02701","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02701v3","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02701","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"pith_short_12","alias_value":"FHIEW3TFAU4K","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FHIEW3TFAU4KT6R6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FHIEW3TF","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FHIEW3TFAU4KT6R6SM3VYVTMK3","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02701","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-09T19:13:06Z","cross_cats_sorted":["cs.CC","cs.CG","cs.IT","math.IT"],"title_canon_sha256":"5625b62bbdfd4cba65c113735349b127431c233800c2bdcc817026eda86c1832","abstract_canon_sha256":"5ccb17dcab510d501c4cbc7fda441c85b6c836fec5a8650bd1e84878ffc2cfe0"},"schema_version":"1.0"},"canonical_sha256":"29d04b6e650538a9fa3e93375c566c56e87f97e8afd282d5d3badf25b4d88412","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:30.991245Z","signature_b64":"kC2YgotQK6xN8UO+5yel9HPuFH7FWJL968sZ/N6ncJi0p0FaoQqegzqdPk9YF9R5Tc4HcqMmx/598q2Cfzv6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29d04b6e650538a9fa3e93375c566c56e87f97e8afd282d5d3badf25b4d88412","last_reissued_at":"2026-05-18T01:08:30.990608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:30.990608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02701","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjjFUpxOlCYp61tDrLj/fzH6nLZTQFjzTP1nVGBe3Qfj9Xa5sGozVj+QkPsyRcQRlYkE+cERm7W+OVylBxJRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:30:50.050655Z"},"content_sha256":"b9e04d8ba5527d302f7d949d06ebc4c1a6857af20ba9fc73b52c01e14723785f","schema_version":"1.0","event_id":"sha256:b9e04d8ba5527d302f7d949d06ebc4c1a6857af20ba9fc73b52c01e14723785f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FHIEW3TFAU4KT6R6SM3VYVTMK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower Bounds on Time-Space Trade-Offs for Approximate Near Neighbors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Alexandr Andoni, Erik Waingarten, Ilya Razenshteyn, Thijs Laarhoven","submitted_at":"2016-05-09T19:13:06Z","abstract_excerpt":"We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In articular, our lower bound matches the upper bound recently shown in [Laarhoven 2015] for the random instance on a Euclidean sphere (which we show in fact extends to the entire space $\\mathbb{R}^d$ using the techniques from [Andoni, Razenshteyn 2015]).\n  We also show tight, unconditional cell-probe lower bounds for one and two probes, improving upon the best "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02701","kind":"arxiv","version":3},"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":"2026-05-18T01:08:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pHYbCoitb93UgP0FmYtyY+L2zG11qdCAkpqr9k/7CeANINHuxpw9wldm6Tyy6MkCfOm12S9bLfEhA+IxU2dAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:30:50.051168Z"},"content_sha256":"1ff77e32d2df0055a7a8451f7ad2387865be23bf20d8f8fe5b3d11e904b345b4","schema_version":"1.0","event_id":"sha256:1ff77e32d2df0055a7a8451f7ad2387865be23bf20d8f8fe5b3d11e904b345b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/bundle.json","state_url":"https://pith.science/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/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":"2026-05-25T22:30:50Z","links":{"resolver":"https://pith.science/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3","bundle":"https://pith.science/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/bundle.json","state":"https://pith.science/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHIEW3TFAU4KT6R6SM3VYVTMK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FHIEW3TFAU4KT6R6SM3VYVTMK3","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":"5ccb17dcab510d501c4cbc7fda441c85b6c836fec5a8650bd1e84878ffc2cfe0","cross_cats_sorted":["cs.CC","cs.CG","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-09T19:13:06Z","title_canon_sha256":"5625b62bbdfd4cba65c113735349b127431c233800c2bdcc817026eda86c1832"},"schema_version":"1.0","source":{"id":"1605.02701","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02701","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02701v3","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02701","created_at":"2026-05-18T01:08:30Z"},{"alias_kind":"pith_short_12","alias_value":"FHIEW3TFAU4K","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FHIEW3TFAU4KT6R6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FHIEW3TF","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:1ff77e32d2df0055a7a8451f7ad2387865be23bf20d8f8fe5b3d11e904b345b4","target":"graph","created_at":"2026-05-18T01:08:30Z","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 tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In articular, our lower bound matches the upper bound recently shown in [Laarhoven 2015] for the random instance on a Euclidean sphere (which we show in fact extends to the entire space $\\mathbb{R}^d$ using the techniques from [Andoni, Razenshteyn 2015]).\n  We also show tight, unconditional cell-probe lower bounds for one and two probes, improving upon the best ","authors_text":"Alexandr Andoni, Erik Waingarten, Ilya Razenshteyn, Thijs Laarhoven","cross_cats":["cs.CC","cs.CG","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-09T19:13:06Z","title":"Lower Bounds on Time-Space Trade-Offs for Approximate Near Neighbors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02701","kind":"arxiv","version":3},"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:b9e04d8ba5527d302f7d949d06ebc4c1a6857af20ba9fc73b52c01e14723785f","target":"record","created_at":"2026-05-18T01:08:30Z","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":"5ccb17dcab510d501c4cbc7fda441c85b6c836fec5a8650bd1e84878ffc2cfe0","cross_cats_sorted":["cs.CC","cs.CG","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-09T19:13:06Z","title_canon_sha256":"5625b62bbdfd4cba65c113735349b127431c233800c2bdcc817026eda86c1832"},"schema_version":"1.0","source":{"id":"1605.02701","kind":"arxiv","version":3}},"canonical_sha256":"29d04b6e650538a9fa3e93375c566c56e87f97e8afd282d5d3badf25b4d88412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29d04b6e650538a9fa3e93375c566c56e87f97e8afd282d5d3badf25b4d88412","first_computed_at":"2026-05-18T01:08:30.990608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:30.990608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kC2YgotQK6xN8UO+5yel9HPuFH7FWJL968sZ/N6ncJi0p0FaoQqegzqdPk9YF9R5Tc4HcqMmx/598q2Cfzv6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:30.991245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9e04d8ba5527d302f7d949d06ebc4c1a6857af20ba9fc73b52c01e14723785f","sha256:1ff77e32d2df0055a7a8451f7ad2387865be23bf20d8f8fe5b3d11e904b345b4"],"state_sha256":"0e08295e05b5d673a79154c695e37aa70249b5322da1f83864512aa1d7d1b6ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ynIn9X5wThdAh5mwBvE3gXE7/kTEnML5IAXXgRHDydIwLkVxwKsBkF4ZM7wnNIW9lEqedtJAeUuzOOa4trv0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:30:50.054300Z","bundle_sha256":"ed1016d7996b02c80e6e2a1f039d8357a932d126101e2f8a038c7186d7880602"}}