{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:E3MJ77R2SSBGO5IKL7XZ64DY7S","short_pith_number":"pith:E3MJ77R2","schema_version":"1.0","canonical_sha256":"26d89ffe3a948267750a5fef9f7078fc9388ba0895ead3c98bffc81250b9da7d","source":{"kind":"arxiv","id":"1502.05746","version":2},"attestation_state":"computed","paper":{"title":"Binary Embedding: Fundamental Limits and Fast Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Constantine Caramanis, Eric Price, Xinyang Yi","submitted_at":"2015-02-19T23:15:02Z","abstract_excerpt":"Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in $\\mathbb{S}^{p-1}$, our goal is to encode each point using $m$-dimensional binary strings such that we can reconstruct their geodesic distance up to $\\delta$ uniform distortion. Existing binary embedding algorithms either lack theoretical guarantees or suffer from running time $O\\big(mp\\big)$. We make three contributions: (1) we establish a lower bound that shows"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.05746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-19T23:15:02Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"e34600e7465dfb09c1ae06a87bb4ed35040a4831f6204726e4ab9088560eddd6","abstract_canon_sha256":"98c6cb1ad5478375b3d43c582c16bcc140bcdec36b1bbef439f3eab666d0f86b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:43.522208Z","signature_b64":"5S28evVoMcTCOYcpesfABhSF/jEuljcNm7J4tfpwGKYPyWNOgzq2eAKNriVPIZcfLZwuD20VbZM0JphhP3YTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26d89ffe3a948267750a5fef9f7078fc9388ba0895ead3c98bffc81250b9da7d","last_reissued_at":"2026-05-17T23:55:43.521528Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:43.521528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Binary Embedding: Fundamental Limits and Fast Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Constantine Caramanis, Eric Price, Xinyang Yi","submitted_at":"2015-02-19T23:15:02Z","abstract_excerpt":"Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in $\\mathbb{S}^{p-1}$, our goal is to encode each point using $m$-dimensional binary strings such that we can reconstruct their geodesic distance up to $\\delta$ uniform distortion. Existing binary embedding algorithms either lack theoretical guarantees or suffer from running time $O\\big(mp\\big)$. We make three contributions: (1) we establish a lower bound that shows"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05746","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.05746","created_at":"2026-05-17T23:55:43.521640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05746v2","created_at":"2026-05-17T23:55:43.521640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05746","created_at":"2026-05-17T23:55:43.521640+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3MJ77R2SSBG","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3MJ77R2SSBGO5IK","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3MJ77R2","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S","json":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S.json","graph_json":"https://pith.science/api/pith-number/E3MJ77R2SSBGO5IKL7XZ64DY7S/graph.json","events_json":"https://pith.science/api/pith-number/E3MJ77R2SSBGO5IKL7XZ64DY7S/events.json","paper":"https://pith.science/paper/E3MJ77R2"},"agent_actions":{"view_html":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S","download_json":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S.json","view_paper":"https://pith.science/paper/E3MJ77R2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05746&json=true","fetch_graph":"https://pith.science/api/pith-number/E3MJ77R2SSBGO5IKL7XZ64DY7S/graph.json","fetch_events":"https://pith.science/api/pith-number/E3MJ77R2SSBGO5IKL7XZ64DY7S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S/action/storage_attestation","attest_author":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S/action/author_attestation","sign_citation":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S/action/citation_signature","submit_replication":"https://pith.science/pith/E3MJ77R2SSBGO5IKL7XZ64DY7S/action/replication_record"}},"created_at":"2026-05-17T23:55:43.521640+00:00","updated_at":"2026-05-17T23:55:43.521640+00:00"}