{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y3X7M2YJ6BYDR6L5URURBT6E5G","short_pith_number":"pith:Y3X7M2YJ","canonical_record":{"source":{"id":"1212.5577","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-21T20:11:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2b394b7f866ea342da880e289f6972e911573cfc01ec2b536bff31b9c027cbc4","abstract_canon_sha256":"a6f858d72f1ac77ae3e78be6a9cd6df305581a28e9b7eaabd680da216b6ddf3a"},"schema_version":"1.0"},"canonical_sha256":"c6eff66b09f07038f97da46910cfc4e9ab30e1f49651cb93386ee32cc7e876f9","source":{"kind":"arxiv","id":"1212.5577","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5577","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5577v5","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5577","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"Y3X7M2YJ6BYD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3X7M2YJ6BYDR6L5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3X7M2YJ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y3X7M2YJ6BYDR6L5URURBT6E5G","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5577","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-21T20:11:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2b394b7f866ea342da880e289f6972e911573cfc01ec2b536bff31b9c027cbc4","abstract_canon_sha256":"a6f858d72f1ac77ae3e78be6a9cd6df305581a28e9b7eaabd680da216b6ddf3a"},"schema_version":"1.0"},"canonical_sha256":"c6eff66b09f07038f97da46910cfc4e9ab30e1f49651cb93386ee32cc7e876f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.749950Z","signature_b64":"vVxrKRFhiJ/oxjRCMKj36+A2FfoA9orcSfMsbS4b14PGff+00TwweLkdn4avkfNgIz2zPKttcKgiTzg1dRUBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6eff66b09f07038f97da46910cfc4e9ab30e1f49651cb93386ee32cc7e876f9","last_reissued_at":"2026-05-18T02:30:32.749312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.749312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5577","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBTzMchueMzHKlsFQQ9u8MkgyrdMibGLn0HU14bsvdVXtx0wJdgOEhCS2a2D6M6kiGqzZoV4pdUY/Hp+fMaKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:06:30.438247Z"},"content_sha256":"ceb7095428b3a920c9e74d9af91fc5b4ca88ca9e4512c03d8b4a59e11148e40f","schema_version":"1.0","event_id":"sha256:ceb7095428b3a920c9e74d9af91fc5b4ca88ca9e4512c03d8b4a59e11148e40f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y3X7M2YJ6BYDR6L5URURBT6E5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Structured Construction of Optimal Measurement Matrix for Noiseless Compressed Sensing via Analog Polarization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hessam Mahdavifar, Inyup Kang, Linbo Li","submitted_at":"2012-12-21T20:11:29Z","abstract_excerpt":"In this paper, we propose a method of structured construction of the optimal measurement matrix for noiseless compressed sensing (CS), which achieves the minimum number of measurements which only needs to be as large as the sparsity of the signal itself to be recovered to guarantee almost error-free recovery, for sufficiently large dimension. To arrive at the results, we employ a duality between noiseless CS and analog coding across sparse additive noisy channel (SANC). Extending Renyi Information Dimension to Mutual Information Dimension (MID), we show the operational meaning of MID to be the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5577","kind":"arxiv","version":5},"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":"2026-05-18T02:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4/0TpY/fR0YC6sXf4GwiP7YxA1lUnmLOaoh1gSOQAeYDr3rcZ/HjpL5OwE99lWLA8bxyM9NeBd3/RJdo38aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:06:30.438621Z"},"content_sha256":"fa115955df9b27124b899548b0a267d47066f3a16d68fad6fad4aaa4c37002b2","schema_version":"1.0","event_id":"sha256:fa115955df9b27124b899548b0a267d47066f3a16d68fad6fad4aaa4c37002b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/bundle.json","state_url":"https://pith.science/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/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":"2026-06-02T15:06:30Z","links":{"resolver":"https://pith.science/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G","bundle":"https://pith.science/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/bundle.json","state":"https://pith.science/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3X7M2YJ6BYDR6L5URURBT6E5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y3X7M2YJ6BYDR6L5URURBT6E5G","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":"a6f858d72f1ac77ae3e78be6a9cd6df305581a28e9b7eaabd680da216b6ddf3a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-21T20:11:29Z","title_canon_sha256":"2b394b7f866ea342da880e289f6972e911573cfc01ec2b536bff31b9c027cbc4"},"schema_version":"1.0","source":{"id":"1212.5577","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5577","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5577v5","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5577","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"Y3X7M2YJ6BYD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3X7M2YJ6BYDR6L5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3X7M2YJ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:fa115955df9b27124b899548b0a267d47066f3a16d68fad6fad4aaa4c37002b2","target":"graph","created_at":"2026-05-18T02:30:32Z","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 propose a method of structured construction of the optimal measurement matrix for noiseless compressed sensing (CS), which achieves the minimum number of measurements which only needs to be as large as the sparsity of the signal itself to be recovered to guarantee almost error-free recovery, for sufficiently large dimension. To arrive at the results, we employ a duality between noiseless CS and analog coding across sparse additive noisy channel (SANC). Extending Renyi Information Dimension to Mutual Information Dimension (MID), we show the operational meaning of MID to be the","authors_text":"Hessam Mahdavifar, Inyup Kang, Linbo Li","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-21T20:11:29Z","title":"A Structured Construction of Optimal Measurement Matrix for Noiseless Compressed Sensing via Analog Polarization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5577","kind":"arxiv","version":5},"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:ceb7095428b3a920c9e74d9af91fc5b4ca88ca9e4512c03d8b4a59e11148e40f","target":"record","created_at":"2026-05-18T02:30:32Z","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":"a6f858d72f1ac77ae3e78be6a9cd6df305581a28e9b7eaabd680da216b6ddf3a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-21T20:11:29Z","title_canon_sha256":"2b394b7f866ea342da880e289f6972e911573cfc01ec2b536bff31b9c027cbc4"},"schema_version":"1.0","source":{"id":"1212.5577","kind":"arxiv","version":5}},"canonical_sha256":"c6eff66b09f07038f97da46910cfc4e9ab30e1f49651cb93386ee32cc7e876f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6eff66b09f07038f97da46910cfc4e9ab30e1f49651cb93386ee32cc7e876f9","first_computed_at":"2026-05-18T02:30:32.749312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:32.749312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vVxrKRFhiJ/oxjRCMKj36+A2FfoA9orcSfMsbS4b14PGff+00TwweLkdn4avkfNgIz2zPKttcKgiTzg1dRUBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:32.749950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5577","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceb7095428b3a920c9e74d9af91fc5b4ca88ca9e4512c03d8b4a59e11148e40f","sha256:fa115955df9b27124b899548b0a267d47066f3a16d68fad6fad4aaa4c37002b2"],"state_sha256":"7435cd6974beaf9d69137b484b1d3b63f12d2c0dd9f3b165d3c9f3086f758472"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WZFcXrWA+mS5KfB/aDM/fiihu4QdFHD7adOGG6rOo0D9vZunzdh7HCHuVZhA4NykpAsfUYJ4SNBriMgyJ958Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:06:30.440940Z","bundle_sha256":"c62f47860eeb7f418f7b04b5383e4207ed48b2276a89c10a981fa252cc961646"}}