{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PARNEBVWA3FXLQQO7YDS63ZGSO","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":"1914e49a157cfed81d604ce1b05e9c2af1d058504e186b41c9965fc8213d58a0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-06T00:15:49Z","title_canon_sha256":"8286398a7c6d971018ab1ccf72a53cbcfd3c10b1386f63abcd3f371e049f4209"},"schema_version":"1.0","source":{"id":"1903.02123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02123","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02123v1","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02123","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"PARNEBVWA3FX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PARNEBVWA3FXLQQO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PARNEBVW","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:d8a5b6f4c53de8e76cbc96d1dd7b1244cc3105cd004d45d835eb276bc3b83699","target":"graph","created_at":"2026-05-17T23:51:56Z","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":"The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \\mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite set $ \\mathbf{X} \\subset \\mathbb{S}^{N-1}$ into the Hamming cube $\\mathbb{H}_m = \\{0,1\\}^m$, with normalized Hamming metric. We find that for $ 0< \\delta <1$, and $m>\\frac{\\ln n}{2\\delta^2}$ there is a $\\delta$-RIP from $\\mathbf{X}$ into $\\mathbb{H}_m$. This is surprising as the value of $ m$ is virtually identical to best known bound linear J-L Lemma. In both","authors_text":"Amadou Bah, Bryson Kagy, Emily Smith","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-06T00:15:49Z","title":"Phase Transition in the One-bit Johnson-Lindenstrauss Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02123","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":"sha256:68d57e965b3499cd7f2e6507de851819a923d25b2b69bbcd44f200152932ad91","target":"record","created_at":"2026-05-17T23:51:56Z","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":"1914e49a157cfed81d604ce1b05e9c2af1d058504e186b41c9965fc8213d58a0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-06T00:15:49Z","title_canon_sha256":"8286398a7c6d971018ab1ccf72a53cbcfd3c10b1386f63abcd3f371e049f4209"},"schema_version":"1.0","source":{"id":"1903.02123","kind":"arxiv","version":1}},"canonical_sha256":"7822d206b606cb75c20efe072f6f2693bc168cf3a8231ee61ff2d30cbbae8e29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7822d206b606cb75c20efe072f6f2693bc168cf3a8231ee61ff2d30cbbae8e29","first_computed_at":"2026-05-17T23:51:56.663086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:56.663086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMFVQyC5VVgwCPVZ1ktGZROiVJB+wPtS/m7iQB1hXhfk6V994eUrNrYqAYHNcVUyTqRvndLgvpFl8+j6TtKUBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:56.663532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68d57e965b3499cd7f2e6507de851819a923d25b2b69bbcd44f200152932ad91","sha256:d8a5b6f4c53de8e76cbc96d1dd7b1244cc3105cd004d45d835eb276bc3b83699"],"state_sha256":"da1f3399e05a4771cb0f7cc94832bbc670e5bf30d48c18dfdcb49c2d8ef24be1"}