{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P7TJFHSNAILO4MUITSBYASUQKW","short_pith_number":"pith:P7TJFHSN","canonical_record":{"source":{"id":"1808.07333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-22T12:37:34Z","cross_cats_sorted":["math.IT","math.NA"],"title_canon_sha256":"0dd8c3e61d53ae887711988188f4bf6a61c975eaae1a12babff72faf7adfd867","abstract_canon_sha256":"38cf59511f59eb5896b5471fa37824f8ed065a96bb90ddf8c9f90bd034d95869"},"schema_version":"1.0"},"canonical_sha256":"7fe6929e4d0216ee32889c83804a9055a8679d454bdb5afea7b187b57a069411","source":{"kind":"arxiv","id":"1808.07333","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07333","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07333v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07333","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"P7TJFHSNAILO","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P7TJFHSNAILO4MUI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P7TJFHSN","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P7TJFHSNAILO4MUITSBYASUQKW","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-22T12:37:34Z","cross_cats_sorted":["math.IT","math.NA"],"title_canon_sha256":"0dd8c3e61d53ae887711988188f4bf6a61c975eaae1a12babff72faf7adfd867","abstract_canon_sha256":"38cf59511f59eb5896b5471fa37824f8ed065a96bb90ddf8c9f90bd034d95869"},"schema_version":"1.0"},"canonical_sha256":"7fe6929e4d0216ee32889c83804a9055a8679d454bdb5afea7b187b57a069411","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:29.148626Z","signature_b64":"tizmMwARhod0v4Jc7WpYaNVPCYjevefaRq4CM2RcreMFu24h3tZtIUabGDh+SDl4bJ4jq4Co79Es/Bcs8MBaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fe6929e4d0216ee32889c83804a9055a8679d454bdb5afea7b187b57a069411","last_reissued_at":"2026-05-18T00:07:29.147935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:29.147935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07333","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":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UjOCOgIZw/PqH49MyKYSb4qu7gs3bSKaSEFnLcchOIe+GFYfRFIOF10LORw8hiCV/Wg3qLObmUwy+Ku4h3HlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:41:27.321015Z"},"content_sha256":"c5dff2dbea4a8cfded8fdcaf11b3d22d1fafbb0dcb3232a9e063dcfc35e40823","schema_version":"1.0","event_id":"sha256:c5dff2dbea4a8cfded8fdcaf11b3d22d1fafbb0dcb3232a9e063dcfc35e40823"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P7TJFHSNAILO4MUITSBYASUQKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved bounds for the RIP of Subsampled Circulant matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Meng Huang, Yuxuan Pang, Zhiqiang Xu","submitted_at":"2018-08-22T12:37:34Z","abstract_excerpt":"In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high probability if one chooses $m\\gtrsim s \\log^2(s)\\log (n)$ rows randomly where $n$ is the vector length. This improves the previously known bound $m \\gtrsim s \\log^2 s\\log^2 n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07333","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":""},"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":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KqpduKthlYsgjlk3ZRlXD4x1CsevnqQb2wSjpE8Gp/Y8+SvAlBR7keC4sqXz/iEQbwzbJSk8lPUBauSVT8rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:41:27.321361Z"},"content_sha256":"f2da5f903bd8e4d84f9e1f2de0b07f1145d363df9826d261b898547de7719be9","schema_version":"1.0","event_id":"sha256:f2da5f903bd8e4d84f9e1f2de0b07f1145d363df9826d261b898547de7719be9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7TJFHSNAILO4MUITSBYASUQKW/bundle.json","state_url":"https://pith.science/pith/P7TJFHSNAILO4MUITSBYASUQKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7TJFHSNAILO4MUITSBYASUQKW/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":"2026-05-30T08:41:27Z","links":{"resolver":"https://pith.science/pith/P7TJFHSNAILO4MUITSBYASUQKW","bundle":"https://pith.science/pith/P7TJFHSNAILO4MUITSBYASUQKW/bundle.json","state":"https://pith.science/pith/P7TJFHSNAILO4MUITSBYASUQKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7TJFHSNAILO4MUITSBYASUQKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P7TJFHSNAILO4MUITSBYASUQKW","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":"38cf59511f59eb5896b5471fa37824f8ed065a96bb90ddf8c9f90bd034d95869","cross_cats_sorted":["math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-22T12:37:34Z","title_canon_sha256":"0dd8c3e61d53ae887711988188f4bf6a61c975eaae1a12babff72faf7adfd867"},"schema_version":"1.0","source":{"id":"1808.07333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07333","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07333v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07333","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"P7TJFHSNAILO","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P7TJFHSNAILO4MUI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P7TJFHSN","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:f2da5f903bd8e4d84f9e1f2de0b07f1145d363df9826d261b898547de7719be9","target":"graph","created_at":"2026-05-18T00:07:29Z","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 study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high probability if one chooses $m\\gtrsim s \\log^2(s)\\log (n)$ rows randomly where $n$ is the vector length. This improves the previously known bound $m \\gtrsim s \\log^2 s\\log^2 n$.","authors_text":"Meng Huang, Yuxuan Pang, Zhiqiang Xu","cross_cats":["math.IT","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-22T12:37:34Z","title":"Improved bounds for the RIP of Subsampled Circulant matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07333","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:c5dff2dbea4a8cfded8fdcaf11b3d22d1fafbb0dcb3232a9e063dcfc35e40823","target":"record","created_at":"2026-05-18T00:07:29Z","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":"38cf59511f59eb5896b5471fa37824f8ed065a96bb90ddf8c9f90bd034d95869","cross_cats_sorted":["math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-22T12:37:34Z","title_canon_sha256":"0dd8c3e61d53ae887711988188f4bf6a61c975eaae1a12babff72faf7adfd867"},"schema_version":"1.0","source":{"id":"1808.07333","kind":"arxiv","version":1}},"canonical_sha256":"7fe6929e4d0216ee32889c83804a9055a8679d454bdb5afea7b187b57a069411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe6929e4d0216ee32889c83804a9055a8679d454bdb5afea7b187b57a069411","first_computed_at":"2026-05-18T00:07:29.147935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.147935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tizmMwARhod0v4Jc7WpYaNVPCYjevefaRq4CM2RcreMFu24h3tZtIUabGDh+SDl4bJ4jq4Co79Es/Bcs8MBaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.148626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5dff2dbea4a8cfded8fdcaf11b3d22d1fafbb0dcb3232a9e063dcfc35e40823","sha256:f2da5f903bd8e4d84f9e1f2de0b07f1145d363df9826d261b898547de7719be9"],"state_sha256":"8d20935ebe23f4c71441ca3f8d6ce26f9cf04795a52744e8a4ccb454ae165af2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CjVswcHkjy/+PucpXkeGoiTnLnkfDzIwoYnm1xE7wVWTgATBQidgzdLLRCmV2r+OokTVI907Oa8/2e9LStXSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:41:27.323279Z","bundle_sha256":"3170462b74b52de6d988312006f732383f7a02f178a9d141ba614cc83418fcc2"}}