{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:S4SH6NNXZH5XDD6WMJLX4DVYYS","short_pith_number":"pith:S4SH6NNX","canonical_record":{"source":{"id":"1504.06170","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-23T13:16:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fbe8dcdebff66eac1df965bcc73322b5f960816370d17ba4f3777775fb8e26ae","abstract_canon_sha256":"a20b6e94046767ad5aa6b41e76fb2d26529b98617b43b7ff86fc84a948911313"},"schema_version":"1.0"},"canonical_sha256":"97247f35b7c9fb718fd662577e0eb8c496831959ee9d178a68041eba76172427","source":{"kind":"arxiv","id":"1504.06170","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06170","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06170v3","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06170","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"S4SH6NNXZH5X","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S4SH6NNXZH5XDD6W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S4SH6NNX","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:S4SH6NNXZH5XDD6WMJLX4DVYYS","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06170","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-23T13:16:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fbe8dcdebff66eac1df965bcc73322b5f960816370d17ba4f3777775fb8e26ae","abstract_canon_sha256":"a20b6e94046767ad5aa6b41e76fb2d26529b98617b43b7ff86fc84a948911313"},"schema_version":"1.0"},"canonical_sha256":"97247f35b7c9fb718fd662577e0eb8c496831959ee9d178a68041eba76172427","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:27.790732Z","signature_b64":"YJMpYXlAdE7k6MLCCElnPWze73BjL2LFm3Mt2QBZ6Clahewf/jPtpxhL6jUKJibUqkDZemVGhXxlagMfS5FgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97247f35b7c9fb718fd662577e0eb8c496831959ee9d178a68041eba76172427","last_reissued_at":"2026-05-18T00:59:27.790218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:27.790218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06170","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qS7gi2YFoWoiW6wVLT0G4xtxDgwZIO2vlryaPmZd+9cDsuepXQuIxNK0gR3Enihs8bOkl71rGwO2Lr3O5OUJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:33:56.899821Z"},"content_sha256":"7d4861a6bbac3c6ef0c50c84c4f0aa6ce74d65e608250bb95cfc342e49f5e89f","schema_version":"1.0","event_id":"sha256:7d4861a6bbac3c6ef0c50c84c4f0aa6ce74d65e608250bb95cfc342e49f5e89f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:S4SH6NNXZH5XDD6WMJLX4DVYYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Laurent Jacques","submitted_at":"2015-04-23T13:16:30Z","abstract_excerpt":"Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors? This work addresses this general question through the specific use of a quantized and dithered random linear mapping which combines, in the following order, a sub-Gaussian random projection in $\\mathbb R^M$ of vectors in $\\mathbb R^N$, a random translation, or \"dither\", of the projected vectors and a uniform scalar quantizer of resolution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06170","kind":"arxiv","version":3},"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":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jcOKzSl3CaAzrwj+tveY29WwBWxYhmi2x+0pGfByImTA3dff9l99CTsTDVoELN7qwlEaly/jQwfvqPdK+tMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:33:56.900467Z"},"content_sha256":"9b2fbb6eb984b6f075cdf02f1e09b9f3fe14c684849379c79de84ca6ecff4a2a","schema_version":"1.0","event_id":"sha256:9b2fbb6eb984b6f075cdf02f1e09b9f3fe14c684849379c79de84ca6ecff4a2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/bundle.json","state_url":"https://pith.science/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/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":"2026-05-31T22:33:56Z","links":{"resolver":"https://pith.science/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS","bundle":"https://pith.science/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/bundle.json","state":"https://pith.science/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4SH6NNXZH5XDD6WMJLX4DVYYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S4SH6NNXZH5XDD6WMJLX4DVYYS","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":"a20b6e94046767ad5aa6b41e76fb2d26529b98617b43b7ff86fc84a948911313","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-23T13:16:30Z","title_canon_sha256":"fbe8dcdebff66eac1df965bcc73322b5f960816370d17ba4f3777775fb8e26ae"},"schema_version":"1.0","source":{"id":"1504.06170","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06170","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06170v3","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06170","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"S4SH6NNXZH5X","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S4SH6NNXZH5XDD6W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S4SH6NNX","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:9b2fbb6eb984b6f075cdf02f1e09b9f3fe14c684849379c79de84ca6ecff4a2a","target":"graph","created_at":"2026-05-18T00:59:27Z","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":"Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors? This work addresses this general question through the specific use of a quantized and dithered random linear mapping which combines, in the following order, a sub-Gaussian random projection in $\\mathbb R^M$ of vectors in $\\mathbb R^N$, a random translation, or \"dither\", of the projected vectors and a uniform scalar quantizer of resolution ","authors_text":"Laurent Jacques","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-23T13:16:30Z","title":"Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06170","kind":"arxiv","version":3},"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":"sha256:7d4861a6bbac3c6ef0c50c84c4f0aa6ce74d65e608250bb95cfc342e49f5e89f","target":"record","created_at":"2026-05-18T00:59:27Z","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":"a20b6e94046767ad5aa6b41e76fb2d26529b98617b43b7ff86fc84a948911313","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-23T13:16:30Z","title_canon_sha256":"fbe8dcdebff66eac1df965bcc73322b5f960816370d17ba4f3777775fb8e26ae"},"schema_version":"1.0","source":{"id":"1504.06170","kind":"arxiv","version":3}},"canonical_sha256":"97247f35b7c9fb718fd662577e0eb8c496831959ee9d178a68041eba76172427","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97247f35b7c9fb718fd662577e0eb8c496831959ee9d178a68041eba76172427","first_computed_at":"2026-05-18T00:59:27.790218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:27.790218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJMpYXlAdE7k6MLCCElnPWze73BjL2LFm3Mt2QBZ6Clahewf/jPtpxhL6jUKJibUqkDZemVGhXxlagMfS5FgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:27.790732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06170","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d4861a6bbac3c6ef0c50c84c4f0aa6ce74d65e608250bb95cfc342e49f5e89f","sha256:9b2fbb6eb984b6f075cdf02f1e09b9f3fe14c684849379c79de84ca6ecff4a2a"],"state_sha256":"c370ecf5dea2e905ef647ba1c0b63e9777f57dc8e4ec0f501fe443a53dd43559"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZrPUVu/rTXnwBR4h5hr7wORh1LGvcQKjQb7MWxMJJnwnRHv1nbD6OIrzR03jyiDtQtH9twVyjnVWrjLPNqkBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:33:56.903974Z","bundle_sha256":"0468acc39e5d41d61a5129c6012436595573434530576d10e588872211f8ecc1"}}