{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BNQ2GGTTI7GRBR27AVSG74RW6I","short_pith_number":"pith:BNQ2GGTT","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"},"canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","source":{"kind":"arxiv","id":"2504.09331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09331","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09331v1","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09331","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"BNQ2GGTTI7GR","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"BNQ2GGTTI7GRBR27","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"BNQ2GGTT","created_at":"2026-07-05T10:48:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BNQ2GGTTI7GRBR27AVSG74RW6I","target":"record","payload":{"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"},"canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","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"},"source_kind":"arxiv","source_id":"2504.09331","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":"2026-07-05T10:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"go90l06vtGrN9cxFdXikIdNKzEAYoVGCqUkASIRCJF8OK4ndWvgN9C1CbJmOy+4qWGRgoDlk5h9PefMg1s45DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T05:34:31.017008Z"},"content_sha256":"f9070388a7ffc4810db6dc4c3f66c02a0e522a3343e2f8ddaed667427c6452fd","schema_version":"1.0","event_id":"sha256:f9070388a7ffc4810db6dc4c3f66c02a0e522a3343e2f8ddaed667427c6452fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BNQ2GGTTI7GRBR27AVSG74RW6I","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cpJD0gg1vfJ/kj/ck2Lvu+MookJK2bT/x+q2VWAACJ4H639j26c+liFDQ9TSEmX11pH0zk5Pza30lduwRCf3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T05:34:31.017618Z"},"content_sha256":"63bc67bf871f24d1bb10eae5b94a8ef5b209a17287c186b6c395a4435841fab7","schema_version":"1.0","event_id":"sha256:63bc67bf871f24d1bb10eae5b94a8ef5b209a17287c186b6c395a4435841fab7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/bundle.json","state_url":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/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":"2026-08-03T05:34:31Z","links":{"resolver":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I","bundle":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/bundle.json","state":"https://pith.science/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNQ2GGTTI7GRBR27AVSG74RW6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BNQ2GGTTI7GRBR27AVSG74RW6I","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":"acc20ed92cc3cedfbe16d52513198454a783a5ecf66fbb5c48a1487fa36739d3","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2025-04-12T20:23:34Z","title_canon_sha256":"9d329fbddf5296bdb3b933dce4198ad7e82ed9c6192097a477b3d98758ad023f"},"schema_version":"1.0","source":{"id":"2504.09331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09331","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09331v1","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09331","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"BNQ2GGTTI7GR","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"BNQ2GGTTI7GRBR27","created_at":"2026-07-05T10:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"BNQ2GGTT","created_at":"2026-07-05T10:48:35Z"}],"graph_snapshots":[{"event_id":"sha256:63bc67bf871f24d1bb10eae5b94a8ef5b209a17287c186b6c395a4435841fab7","target":"graph","created_at":"2026-07-05T10:48:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.09331/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Alon Rosen, Andrej Bogdanov, Neekon Vafa, Vinod Vaikuntanathan","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2025-04-12T20:23:34Z","title":"Adaptive Robustness of Hypergrid Johnson-Lindenstrauss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09331","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:f9070388a7ffc4810db6dc4c3f66c02a0e522a3343e2f8ddaed667427c6452fd","target":"record","created_at":"2026-07-05T10:48:35Z","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":"acc20ed92cc3cedfbe16d52513198454a783a5ecf66fbb5c48a1487fa36739d3","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2025-04-12T20:23:34Z","title_canon_sha256":"9d329fbddf5296bdb3b933dce4198ad7e82ed9c6192097a477b3d98758ad023f"},"schema_version":"1.0","source":{"id":"2504.09331","kind":"arxiv","version":1}},"canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b61a31a7347cd10c75f05646ff236f21ad7105f63186f9f4691a56d264e9c50","first_computed_at":"2026-07-05T10:48:35.584206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:35.584206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d1XDFtPA8EbwnDQBfTLWGblDYiXnMzx9miMQpWS+doLyJ3+3E2M+pUxcAiDpmn+emZx3Nof7asdyV3o6EF3MCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:35.584721Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9070388a7ffc4810db6dc4c3f66c02a0e522a3343e2f8ddaed667427c6452fd","sha256:63bc67bf871f24d1bb10eae5b94a8ef5b209a17287c186b6c395a4435841fab7"],"state_sha256":"ce6d3849019064cf6ad7c6ceb845fd509b4bdaad3c106f9a0433562f586527d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99Tj/PakjSOVwIiydfk0ols2BijCugG7wlCH/YTkbGYTdgBw/UbCXACzWVHm0QrWFuSv/65JAiqLXavlKrZkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T05:34:31.022377Z","bundle_sha256":"788fb578e89a2e39d6045f3ee51806b5d77c751987ada402439095952f357ed2"}}