{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FVVLO2U22F2Q7STW4W6FM5IM4O","short_pith_number":"pith:FVVLO2U2","canonical_record":{"source":{"id":"1703.01507","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2b1f9793fe9854fb1f6358f56bd73faa737a6648ea3c44aa44dce6595f974a6e","abstract_canon_sha256":"b6bb3c10b581b57ec6e71c4063fe62f58c5bd35d149c274a5daf2b4cfcb7efd6"},"schema_version":"1.0"},"canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","source":{"kind":"arxiv","id":"1703.01507","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01507","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01507v5","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01507","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVLO2U22F2Q","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVVLO2U22F2Q7STW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVVLO2U2","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FVVLO2U22F2Q7STW4W6FM5IM4O","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01507","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2b1f9793fe9854fb1f6358f56bd73faa737a6648ea3c44aa44dce6595f974a6e","abstract_canon_sha256":"b6bb3c10b581b57ec6e71c4063fe62f58c5bd35d149c274a5daf2b4cfcb7efd6"},"schema_version":"1.0"},"canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.095495Z","signature_b64":"5tmVjip1kDas2v+4xL30uLyuhqr57dxWE24W5KeOdnmzfDWVZJTqzdbgzC+BqRgDTcNFjHfjMlH2KlDt7qq6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","last_reissued_at":"2026-05-18T00:31:00.094774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.094774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01507","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kogL+QOnJPx56fMBZ+33QamHm2/3E6j+qzvqiiqHiLTkrnC22hD5z1K2DVFH41pDcY0r7peqtbnlTAIGHlYaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:17:28.463052Z"},"content_sha256":"104bad00ff9a26802b3403d4ff9d3ad9a5beaeaefc3ed460ba89f2ddf2cb8621","schema_version":"1.0","event_id":"sha256:104bad00ff9a26802b3403d4ff9d3ad9a5beaeaefc3ed460ba89f2ddf2cb8621"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FVVLO2U22F2Q7STW4W6FM5IM4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Machine Learning Friendly Set Version of Johnson-Lindenstrauss Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Mieczys{\\l}aw A. K{\\l}opotek","submitted_at":"2017-03-04T19:08:22Z","abstract_excerpt":"In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into predefined error range $\\delta$.\n  We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformation in such a way that with probability $1-\\epsilon$ all of them fall into predefined error range $\\delta$ for any user-predefined failure probability $\\epsilon$.\n  This result is important for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01507","kind":"arxiv","version":5},"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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoSDd1ArIFZgriuXSo/r5lBWbXdVKEJWQgwaNCHRMfInIFSsBXZyjsJwdywkjD7ZCxa2DmFHaznQ8WfIAQCNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:17:28.463408Z"},"content_sha256":"ce3b918b59636106c972cf4e3b9b2b8299aa463d6e13b7039054d5789e4c8e03","schema_version":"1.0","event_id":"sha256:ce3b918b59636106c972cf4e3b9b2b8299aa463d6e13b7039054d5789e4c8e03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/bundle.json","state_url":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/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":"2026-06-23T18:17:28Z","links":{"resolver":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O","bundle":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/bundle.json","state":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FVVLO2U22F2Q7STW4W6FM5IM4O","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":"b6bb3c10b581b57ec6e71c4063fe62f58c5bd35d149c274a5daf2b4cfcb7efd6","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","title_canon_sha256":"2b1f9793fe9854fb1f6358f56bd73faa737a6648ea3c44aa44dce6595f974a6e"},"schema_version":"1.0","source":{"id":"1703.01507","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01507","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01507v5","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01507","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVLO2U22F2Q","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVVLO2U22F2Q7STW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVVLO2U2","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ce3b918b59636106c972cf4e3b9b2b8299aa463d6e13b7039054d5789e4c8e03","target":"graph","created_at":"2026-05-18T00:31:00Z","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":"In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into predefined error range $\\delta$.\n  We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformation in such a way that with probability $1-\\epsilon$ all of them fall into predefined error range $\\delta$ for any user-predefined failure probability $\\epsilon$.\n  This result is important for","authors_text":"Mieczys{\\l}aw A. K{\\l}opotek","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","title":"Machine Learning Friendly Set Version of Johnson-Lindenstrauss Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01507","kind":"arxiv","version":5},"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":"sha256:104bad00ff9a26802b3403d4ff9d3ad9a5beaeaefc3ed460ba89f2ddf2cb8621","target":"record","created_at":"2026-05-18T00:31:00Z","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":"b6bb3c10b581b57ec6e71c4063fe62f58c5bd35d149c274a5daf2b4cfcb7efd6","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","title_canon_sha256":"2b1f9793fe9854fb1f6358f56bd73faa737a6648ea3c44aa44dce6595f974a6e"},"schema_version":"1.0","source":{"id":"1703.01507","kind":"arxiv","version":5}},"canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","first_computed_at":"2026-05-18T00:31:00.094774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:00.094774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5tmVjip1kDas2v+4xL30uLyuhqr57dxWE24W5KeOdnmzfDWVZJTqzdbgzC+BqRgDTcNFjHfjMlH2KlDt7qq6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:00.095495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01507","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:104bad00ff9a26802b3403d4ff9d3ad9a5beaeaefc3ed460ba89f2ddf2cb8621","sha256:ce3b918b59636106c972cf4e3b9b2b8299aa463d6e13b7039054d5789e4c8e03"],"state_sha256":"9e1bc891ba299746bc4139b0645db26659c6cd90c71ec6803c73a1547c6f7235"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QtvOR5Wp0zPkKKEADBof2n8KHUSrg/gXEaNHcZPQIwMXVFC1wYBhl4xfrGdgqkaD7c4mQLiLKjcszYqFOYUAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:17:28.465293Z","bundle_sha256":"0e6f5046a0a8b0fa553bf80111bfebdd5250df6b8103efea4973e08b4466200b"}}