{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BNQ2GGTTI7GRBR27AVSG74RW6I","short_pith_number":"pith:BNQ2GGTT","schema_version":"1.0","canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","source":{"kind":"arxiv","id":"2504.09331","version":1},"attestation_state":"computed","paper":{"title":"Adaptive Robustness of Hypergrid Johnson-Lindenstrauss","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"stat.CO","authors_text":"Alon Rosen, Andrej Bogdanov, Neekon Vafa, Vinod Vaikuntanathan","submitted_at":"2025-04-12T20:23:34Z","abstract_excerpt":"Johnson and Lindenstrauss (Contemporary Mathematics, 1984) showed that for $n > m$, a scaled random projection $\\mathbf{A}$ from $\\mathbb{R}^n$ to $\\mathbb{R}^m$ is an approximate isometry on any set $S$ of size at most exponential in $m$. If $S$ is larger, however, its points can contract arbitrarily under $\\mathbf{A}$. In particular, the hypergrid $([-B, B] \\cap \\mathbb{Z})^n$ is expected to contain a point that is contracted by a factor of $\\kappa_{\\mathsf{stat}} = \\Theta(B)^{-1/\\alpha}$, where $\\alpha = m/n$.\n  We give evidence that finding such a point exhibits a statistical-computational"},"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":"2504.09331","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2025-04-12T20:23:34Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"9d329fbddf5296bdb3b933dce4198ad7e82ed9c6192097a477b3d98758ad023f","abstract_canon_sha256":"acc20ed92cc3cedfbe16d52513198454a783a5ecf66fbb5c48a1487fa36739d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:35.584721Z","signature_b64":"d1XDFtPA8EbwnDQBfTLWGblDYiXnMzx9miMQpWS+doLyJ3+3E2M+pUxcAiDpmn+emZx3Nof7asdyV3o6EF3MCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","last_reissued_at":"2026-07-05T10:48:35.584206Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:35.584206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive Robustness of Hypergrid Johnson-Lindenstrauss","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"stat.CO","authors_text":"Alon Rosen, Andrej Bogdanov, Neekon Vafa, Vinod Vaikuntanathan","submitted_at":"2025-04-12T20:23:34Z","abstract_excerpt":"Johnson and Lindenstrauss (Contemporary Mathematics, 1984) showed that for $n > m$, a scaled random projection $\\mathbf{A}$ from $\\mathbb{R}^n$ to $\\mathbb{R}^m$ is an approximate isometry on any set $S$ of size at most exponential in $m$. If $S$ is larger, however, its points can contract arbitrarily under $\\mathbf{A}$. In particular, the hypergrid $([-B, B] \\cap \\mathbb{Z})^n$ is expected to contain a point that is contracted by a factor of $\\kappa_{\\mathsf{stat}} = \\Theta(B)^{-1/\\alpha}$, where $\\alpha = m/n$.\n  We give evidence that finding such a point exhibits a statistical-computational"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09331","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09331/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.09331","created_at":"2026-07-05T10:48:35.584267+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.09331v1","created_at":"2026-07-05T10:48:35.584267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09331","created_at":"2026-07-05T10:48:35.584267+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNQ2GGTTI7GR","created_at":"2026-07-05T10:48:35.584267+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNQ2GGTTI7GRBR27","created_at":"2026-07-05T10:48:35.584267+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNQ2GGTT","created_at":"2026-07-05T10:48:35.584267+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.09532","citing_title":"Statistically Undetectable Backdoors in Deep Neural Networks","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I","json":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I.json","graph_json":"https://pith.science/api/pith-number/BNQ2GGTTI7GRBR27AVSG74RW6I/graph.json","events_json":"https://pith.science/api/pith-number/BNQ2GGTTI7GRBR27AVSG74RW6I/events.json","paper":"https://pith.science/paper/BNQ2GGTT"},"agent_actions":{"view_html":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I","download_json":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I.json","view_paper":"https://pith.science/paper/BNQ2GGTT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.09331&json=true","fetch_graph":"https://pith.science/api/pith-number/BNQ2GGTTI7GRBR27AVSG74RW6I/graph.json","fetch_events":"https://pith.science/api/pith-number/BNQ2GGTTI7GRBR27AVSG74RW6I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/action/storage_attestation","attest_author":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/action/author_attestation","sign_citation":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/action/citation_signature","submit_replication":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/action/replication_record"}},"created_at":"2026-07-05T10:48:35.584267+00:00","updated_at":"2026-07-05T10:48:35.584267+00:00"}