{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CM4MFMXPC5BUY5HODWYOM5PCM3","short_pith_number":"pith:CM4MFMXP","canonical_record":{"source":{"id":"1509.04375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"381b0f1d2c96bd1c5c78ef11f4579966b3401ca398e8ff0581f2796c2b55c4a9","abstract_canon_sha256":"c17a05e38d1a769f81e7524dc66ae5ed0bffc896b5278c1a9f2bcada74a5ac04"},"schema_version":"1.0"},"canonical_sha256":"1338c2b2ef17434c74ee1db0e675e266d383cdf231ab17c842d4f2bc0fa35c3c","source":{"kind":"arxiv","id":"1509.04375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04375","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04375v1","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04375","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"CM4MFMXPC5BU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CM4MFMXPC5BUY5HO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CM4MFMXP","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CM4MFMXPC5BUY5HODWYOM5PCM3","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"381b0f1d2c96bd1c5c78ef11f4579966b3401ca398e8ff0581f2796c2b55c4a9","abstract_canon_sha256":"c17a05e38d1a769f81e7524dc66ae5ed0bffc896b5278c1a9f2bcada74a5ac04"},"schema_version":"1.0"},"canonical_sha256":"1338c2b2ef17434c74ee1db0e675e266d383cdf231ab17c842d4f2bc0fa35c3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:07.335670Z","signature_b64":"8FslFKxxNhkmVsZsGxz0RxHs3NnIRdiXh5KMNkuIS7Jc3dU9Jsu3/Mgk29P6I9rBcywTePMRmUd60o+/E01kBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1338c2b2ef17434c74ee1db0e675e266d383cdf231ab17c842d4f2bc0fa35c3c","last_reissued_at":"2026-05-18T01:33:07.335106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:07.335106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04375","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":"2026-05-18T01:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJlKd29OdlrodnVDzaOn0HVS+XrVN+xbWKYChIScJv6fdF2ofquBvgnstbCgH0MYBzE9KO6Kd+NxWEBJilqxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:41:31.207781Z"},"content_sha256":"2fd9bd226cda2b73290e248e1cc95d447171ba983f3e4260f588727222f05395","schema_version":"1.0","event_id":"sha256:2fd9bd226cda2b73290e248e1cc95d447171ba983f3e4260f588727222f05395"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CM4MFMXPC5BUY5HODWYOM5PCM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comment on \"Asymptotic Achievability of the Cram\\'{e}r-Rao Bound for Noisy Compressive Sampling\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behtash Babadi, Nicholas Kalouptsidis, Vahid Tarokh","submitted_at":"2015-09-15T02:18:04Z","abstract_excerpt":"In [1], we proved the asymptotic achievability of the Cram\\'{e}r-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of $\\alpha \\sigma^2$ for the genie-aided Cram\\'{e}r-Rao bound $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ from Lemma 3.5, which appears in Eqs. (20) and (29). The proof, however, holds if one avoids replacing $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ by the expression of Lemma 3.5, and hence the claim of the Main Theorem stands t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04375","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":"2026-05-18T01:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vG8pF6o4tQOpHzXZTi0z/x1zCMdF0YgHW3gVuitCtUe2vJsgIF8dvOf2BbT62VHiVPmuduo++HAtlVtCpi6KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:41:31.208148Z"},"content_sha256":"6ce84f7a1d359be0a04794c0f2a951fb79fa783894ec8d9b58c65a76b8315bc5","schema_version":"1.0","event_id":"sha256:6ce84f7a1d359be0a04794c0f2a951fb79fa783894ec8d9b58c65a76b8315bc5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/bundle.json","state_url":"https://pith.science/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/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":"2026-05-22T05:41:31Z","links":{"resolver":"https://pith.science/pith/CM4MFMXPC5BUY5HODWYOM5PCM3","bundle":"https://pith.science/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/bundle.json","state":"https://pith.science/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CM4MFMXPC5BUY5HODWYOM5PCM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CM4MFMXPC5BUY5HODWYOM5PCM3","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":"c17a05e38d1a769f81e7524dc66ae5ed0bffc896b5278c1a9f2bcada74a5ac04","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:04Z","title_canon_sha256":"381b0f1d2c96bd1c5c78ef11f4579966b3401ca398e8ff0581f2796c2b55c4a9"},"schema_version":"1.0","source":{"id":"1509.04375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04375","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04375v1","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04375","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"CM4MFMXPC5BU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CM4MFMXPC5BUY5HO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CM4MFMXP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:6ce84f7a1d359be0a04794c0f2a951fb79fa783894ec8d9b58c65a76b8315bc5","target":"graph","created_at":"2026-05-18T01:33:07Z","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 [1], we proved the asymptotic achievability of the Cram\\'{e}r-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of $\\alpha \\sigma^2$ for the genie-aided Cram\\'{e}r-Rao bound $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ from Lemma 3.5, which appears in Eqs. (20) and (29). The proof, however, holds if one avoids replacing $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ by the expression of Lemma 3.5, and hence the claim of the Main Theorem stands t","authors_text":"Behtash Babadi, Nicholas Kalouptsidis, Vahid Tarokh","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:04Z","title":"Comment on \"Asymptotic Achievability of the Cram\\'{e}r-Rao Bound for Noisy Compressive Sampling\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04375","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":"sha256:2fd9bd226cda2b73290e248e1cc95d447171ba983f3e4260f588727222f05395","target":"record","created_at":"2026-05-18T01:33:07Z","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":"c17a05e38d1a769f81e7524dc66ae5ed0bffc896b5278c1a9f2bcada74a5ac04","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:04Z","title_canon_sha256":"381b0f1d2c96bd1c5c78ef11f4579966b3401ca398e8ff0581f2796c2b55c4a9"},"schema_version":"1.0","source":{"id":"1509.04375","kind":"arxiv","version":1}},"canonical_sha256":"1338c2b2ef17434c74ee1db0e675e266d383cdf231ab17c842d4f2bc0fa35c3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1338c2b2ef17434c74ee1db0e675e266d383cdf231ab17c842d4f2bc0fa35c3c","first_computed_at":"2026-05-18T01:33:07.335106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:07.335106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8FslFKxxNhkmVsZsGxz0RxHs3NnIRdiXh5KMNkuIS7Jc3dU9Jsu3/Mgk29P6I9rBcywTePMRmUd60o+/E01kBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:07.335670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fd9bd226cda2b73290e248e1cc95d447171ba983f3e4260f588727222f05395","sha256:6ce84f7a1d359be0a04794c0f2a951fb79fa783894ec8d9b58c65a76b8315bc5"],"state_sha256":"91c978d9fe0f55134849b463832a12c4a34906979a97b5fc70aedc059cef0443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VjNpKROFCRPxttKTSEhjoAVbIlwULeAsbUNtZump0pIaw6fMzqIU3/TWD0T8HCbZFUht/n15XplLQtc7B1bBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T05:41:31.211103Z","bundle_sha256":"63a2f13b13cdab7530c77d1576b8fd4e1d21ac8c889102124cfba372fdb04592"}}