{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OVEKRWZFZPFEDY3UUX73HOAS7G","short_pith_number":"pith:OVEKRWZF","canonical_record":{"source":{"id":"1307.7544","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-29T11:23:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"daff159d899470b9bb43d06a5d8b98e7669d1b4a4fec0be3855124de531c24f8","abstract_canon_sha256":"062e35067feaaf18c0cc5178e4fdfeb59661aa0bc498bb919cc57ae7bf5fe05f"},"schema_version":"1.0"},"canonical_sha256":"7548a8db25cbca41e374a5ffb3b812f9845ca4dda1d61bdba6d5a9e0a1775107","source":{"kind":"arxiv","id":"1307.7544","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7544","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7544v4","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7544","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"OVEKRWZFZPFE","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OVEKRWZFZPFEDY3U","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OVEKRWZF","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OVEKRWZFZPFEDY3UUX73HOAS7G","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7544","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-29T11:23:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"daff159d899470b9bb43d06a5d8b98e7669d1b4a4fec0be3855124de531c24f8","abstract_canon_sha256":"062e35067feaaf18c0cc5178e4fdfeb59661aa0bc498bb919cc57ae7bf5fe05f"},"schema_version":"1.0"},"canonical_sha256":"7548a8db25cbca41e374a5ffb3b812f9845ca4dda1d61bdba6d5a9e0a1775107","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:23.465351Z","signature_b64":"45Bbi58Me53uNbCf5OILZoyZI7HDa6xYGl/DKmc5+/Dv/5egSx4EaQxdPJDxyqOfUl/TdHokP7XKRfNZ47vODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7548a8db25cbca41e374a5ffb3b812f9845ca4dda1d61bdba6d5a9e0a1775107","last_reissued_at":"2026-05-18T02:58:23.464899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:23.464899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7544","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlK1SnMTWHddki/Us4z+fLQJd1acbsItadqN2C3Dmv5s42q+Ezk7PqLN1GA0k1LHVIu3PvtnnOBR0rtbHHIKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:55:29.428076Z"},"content_sha256":"2dd8cff0793ddd743f205e5b5bd3b60c6edc4d973f3d5ac73d0385e331e6147a","schema_version":"1.0","event_id":"sha256:2dd8cff0793ddd743f205e5b5bd3b60c6edc4d973f3d5ac73d0385e331e6147a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OVEKRWZFZPFEDY3UUX73HOAS7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On block coherence of frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrew Thompson, Robert Calderbank, Yao Xie","submitted_at":"2013-07-29T11:23:25Z","abstract_excerpt":"Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the matrix is constrained to be a union of orthobases. We then present deterministic matrix constructions based upon Kronecker products which obtain these lower bounds. We also characterize the worst-case block coherence of random subspaces. Fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7544","kind":"arxiv","version":4},"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":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqiMBcTpLotkzBgFg5MeKYd8hwEwDEGtgStkk4SHLxqE6kqBeFbXblUoI6Ui4sANJFoPIWxedv/I+MVw1UwrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:55:29.428433Z"},"content_sha256":"989184d2d8795620930075cee7b70418f859d6dd768a1641bec8856ebaa7c9aa","schema_version":"1.0","event_id":"sha256:989184d2d8795620930075cee7b70418f859d6dd768a1641bec8856ebaa7c9aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/bundle.json","state_url":"https://pith.science/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/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":"2026-06-04T19:55:29Z","links":{"resolver":"https://pith.science/pith/OVEKRWZFZPFEDY3UUX73HOAS7G","bundle":"https://pith.science/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/bundle.json","state":"https://pith.science/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVEKRWZFZPFEDY3UUX73HOAS7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OVEKRWZFZPFEDY3UUX73HOAS7G","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":"062e35067feaaf18c0cc5178e4fdfeb59661aa0bc498bb919cc57ae7bf5fe05f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-29T11:23:25Z","title_canon_sha256":"daff159d899470b9bb43d06a5d8b98e7669d1b4a4fec0be3855124de531c24f8"},"schema_version":"1.0","source":{"id":"1307.7544","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7544","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7544v4","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7544","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"OVEKRWZFZPFE","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OVEKRWZFZPFEDY3U","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OVEKRWZF","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:989184d2d8795620930075cee7b70418f859d6dd768a1641bec8856ebaa7c9aa","target":"graph","created_at":"2026-05-18T02:58:23Z","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":"Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the matrix is constrained to be a union of orthobases. We then present deterministic matrix constructions based upon Kronecker products which obtain these lower bounds. We also characterize the worst-case block coherence of random subspaces. Fin","authors_text":"Andrew Thompson, Robert Calderbank, Yao Xie","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-29T11:23:25Z","title":"On block coherence of frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7544","kind":"arxiv","version":4},"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":"sha256:2dd8cff0793ddd743f205e5b5bd3b60c6edc4d973f3d5ac73d0385e331e6147a","target":"record","created_at":"2026-05-18T02:58:23Z","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":"062e35067feaaf18c0cc5178e4fdfeb59661aa0bc498bb919cc57ae7bf5fe05f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-29T11:23:25Z","title_canon_sha256":"daff159d899470b9bb43d06a5d8b98e7669d1b4a4fec0be3855124de531c24f8"},"schema_version":"1.0","source":{"id":"1307.7544","kind":"arxiv","version":4}},"canonical_sha256":"7548a8db25cbca41e374a5ffb3b812f9845ca4dda1d61bdba6d5a9e0a1775107","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7548a8db25cbca41e374a5ffb3b812f9845ca4dda1d61bdba6d5a9e0a1775107","first_computed_at":"2026-05-18T02:58:23.464899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:23.464899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45Bbi58Me53uNbCf5OILZoyZI7HDa6xYGl/DKmc5+/Dv/5egSx4EaQxdPJDxyqOfUl/TdHokP7XKRfNZ47vODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:23.465351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7544","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd8cff0793ddd743f205e5b5bd3b60c6edc4d973f3d5ac73d0385e331e6147a","sha256:989184d2d8795620930075cee7b70418f859d6dd768a1641bec8856ebaa7c9aa"],"state_sha256":"cea75b74be7128c7bb1faecf03a008970965a9c5a631e720263e12d73043fc1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dT84Crrf5lmaKfofJ9+J+t4YmIvbPWano3Wha23nntT7yuidtt4sFRRrPCEQmWAwMdlg7m2qMcKWdj8a59uEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:55:29.430343Z","bundle_sha256":"cba28e278b7f071a0187fba90a4d140cdeaabce3ef83c2e72c6d2298bdbe24df"}}