{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U4NEAJDLBJA7U2P42VPZKJIN2R","short_pith_number":"pith:U4NEAJDL","canonical_record":{"source":{"id":"1112.1968","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T21:39:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7f1ccd5f316eb91fd3e85e3168696f4dd2efdf8828fe8f66f18ab73639c808cd","abstract_canon_sha256":"c960cf92932a5229e14e3bc740a6909e54303ee9a52d46869c7ddd8b09e0ef73"},"schema_version":"1.0"},"canonical_sha256":"a71a40246b0a41fa69fcd55f95250dd4769317b36b71da2d051dca5bae62bb90","source":{"kind":"arxiv","id":"1112.1968","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1968","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1968v2","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1968","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"U4NEAJDLBJA7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4NEAJDLBJA7U2P4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4NEAJDL","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U4NEAJDLBJA7U2P42VPZKJIN2R","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1968","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T21:39:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7f1ccd5f316eb91fd3e85e3168696f4dd2efdf8828fe8f66f18ab73639c808cd","abstract_canon_sha256":"c960cf92932a5229e14e3bc740a6909e54303ee9a52d46869c7ddd8b09e0ef73"},"schema_version":"1.0"},"canonical_sha256":"a71a40246b0a41fa69fcd55f95250dd4769317b36b71da2d051dca5bae62bb90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:18.564075Z","signature_b64":"k0qJHg6hGdQMCFykGgD1m/xUOaH2fhdas4n3TkoZUbv5nR8cyIIo8SCPMmvyXVSCA3FEHkEwDBGLZffoNJm8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a71a40246b0a41fa69fcd55f95250dd4769317b36b71da2d051dca5bae62bb90","last_reissued_at":"2026-05-18T00:58:18.563383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:18.563383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1968","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8semVysu7d+IJjtd/mcvhhNUgGJhAjEHVcUQQfC4F1xk4RDnbvRBGpusmWyn1z/N/NKHOibbOBP1tracqrACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:02:39.322140Z"},"content_sha256":"792448bf1b5c0ef4e0a3d879e121ad1d0944065e0fa70aab1885a90a98c7e5b1","schema_version":"1.0","event_id":"sha256:792448bf1b5c0ef4e0a3d879e121ad1d0944065e0fa70aab1885a90a98c7e5b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U4NEAJDLBJA7U2P42VPZKJIN2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concentration of Measure Inequalities for Toeplitz Matrices with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Borhan M. Sanandaji, Michael B. Wakin, Tyrone L. Vincent","submitted_at":"2011-12-08T21:39:50Z","abstract_excerpt":"We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a quantity which is a function of the signal. For the class of sparse signals, the introduced quantity is bounded by the sparsity level of the signal. However, we observe that this bound is highly pessimistic for most sparse signals and we show that if a ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1968","kind":"arxiv","version":2},"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":"2026-05-18T00:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lVbDtk7CUL7X7poQ260nWeKps0jXr+HxRXGdPhy7VCDTowEin2K2uhJkfcuMtgm+Pws+LLzVUbzAKBVBN6giDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:02:39.322519Z"},"content_sha256":"63671873b13bf1fc7c10259416e3de3891f1d1fa08a4abcf334a2027725f5a36","schema_version":"1.0","event_id":"sha256:63671873b13bf1fc7c10259416e3de3891f1d1fa08a4abcf334a2027725f5a36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/bundle.json","state_url":"https://pith.science/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/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":"2026-06-01T13:02:39Z","links":{"resolver":"https://pith.science/pith/U4NEAJDLBJA7U2P42VPZKJIN2R","bundle":"https://pith.science/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/bundle.json","state":"https://pith.science/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4NEAJDLBJA7U2P42VPZKJIN2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U4NEAJDLBJA7U2P42VPZKJIN2R","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":"c960cf92932a5229e14e3bc740a6909e54303ee9a52d46869c7ddd8b09e0ef73","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T21:39:50Z","title_canon_sha256":"7f1ccd5f316eb91fd3e85e3168696f4dd2efdf8828fe8f66f18ab73639c808cd"},"schema_version":"1.0","source":{"id":"1112.1968","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1968","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1968v2","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1968","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"U4NEAJDLBJA7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4NEAJDLBJA7U2P4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4NEAJDL","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:63671873b13bf1fc7c10259416e3de3891f1d1fa08a4abcf334a2027725f5a36","target":"graph","created_at":"2026-05-18T00:58:18Z","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":"We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a quantity which is a function of the signal. For the class of sparse signals, the introduced quantity is bounded by the sparsity level of the signal. However, we observe that this bound is highly pessimistic for most sparse signals and we show that if a ran","authors_text":"Borhan M. Sanandaji, Michael B. Wakin, Tyrone L. Vincent","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T21:39:50Z","title":"Concentration of Measure Inequalities for Toeplitz Matrices with Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1968","kind":"arxiv","version":2},"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":"sha256:792448bf1b5c0ef4e0a3d879e121ad1d0944065e0fa70aab1885a90a98c7e5b1","target":"record","created_at":"2026-05-18T00:58:18Z","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":"c960cf92932a5229e14e3bc740a6909e54303ee9a52d46869c7ddd8b09e0ef73","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T21:39:50Z","title_canon_sha256":"7f1ccd5f316eb91fd3e85e3168696f4dd2efdf8828fe8f66f18ab73639c808cd"},"schema_version":"1.0","source":{"id":"1112.1968","kind":"arxiv","version":2}},"canonical_sha256":"a71a40246b0a41fa69fcd55f95250dd4769317b36b71da2d051dca5bae62bb90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a71a40246b0a41fa69fcd55f95250dd4769317b36b71da2d051dca5bae62bb90","first_computed_at":"2026-05-18T00:58:18.563383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:18.563383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k0qJHg6hGdQMCFykGgD1m/xUOaH2fhdas4n3TkoZUbv5nR8cyIIo8SCPMmvyXVSCA3FEHkEwDBGLZffoNJm8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:18.564075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1968","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792448bf1b5c0ef4e0a3d879e121ad1d0944065e0fa70aab1885a90a98c7e5b1","sha256:63671873b13bf1fc7c10259416e3de3891f1d1fa08a4abcf334a2027725f5a36"],"state_sha256":"a0aaa6fb53b039d8982244eb87f5e6b30e5a3c9f7a14a59c904c8972b72336ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAYGUxnQDFbfwr21dTIy+B0XrhZBYRQJGhWYYy9m8dH2w4J0j1HmxbwuTYuVv59ueIw95tikk3oqZnzJSrzDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:02:39.324703Z","bundle_sha256":"d1e51b6ce152bfed92b458e99d499f07c2ea9d23f15bfd6860f10d53a542afda"}}