{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4T376IN2R5L46YHKN7Z3KVU7PQ","short_pith_number":"pith:4T376IN2","canonical_record":{"source":{"id":"1002.4458","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-24T02:54:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"17dbdf84512690fbcc0b121b34c5a7938a0836a9fcc52517105cf7834a64fc4d","abstract_canon_sha256":"15021d4efb02fdefe7e87698438522f42d2990b3ba060a34ce807fcfb5bc701b"},"schema_version":"1.0"},"canonical_sha256":"e4f7ff21ba8f57cf60ea6ff3b5569f7c08cb3b4d4ec3878b34e96b6de32a394f","source":{"kind":"arxiv","id":"1002.4458","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4458","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4458v4","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4458","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"4T376IN2R5L4","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4T376IN2R5L46YHK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4T376IN2","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4T376IN2R5L46YHKN7Z3KVU7PQ","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4458","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-24T02:54:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"17dbdf84512690fbcc0b121b34c5a7938a0836a9fcc52517105cf7834a64fc4d","abstract_canon_sha256":"15021d4efb02fdefe7e87698438522f42d2990b3ba060a34ce807fcfb5bc701b"},"schema_version":"1.0"},"canonical_sha256":"e4f7ff21ba8f57cf60ea6ff3b5569f7c08cb3b4d4ec3878b34e96b6de32a394f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:36.064434Z","signature_b64":"vW8JZxn6lBc3936tu0hWDiEPFwxlMcg1N/8u+eQTajHp+Khj3AeCYy2M0SsykmYMLmgOF307Gf22BQi9U1BLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4f7ff21ba8f57cf60ea6ff3b5569f7c08cb3b4d4ec3878b34e96b6de32a394f","last_reissued_at":"2026-05-18T03:34:36.063824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:36.063824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4458","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":"2026-05-18T03:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pnzjH4uPZZHaNkBmdr9D/UXk8b/9E43RUhnuLejsWTdNJnKVVj8t5taQtjs6YhR8QciHmxgfhg4dnfpVrXrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:22:54.650676Z"},"content_sha256":"8682c83b131dec07fc24bc8e0927b60721fc928a4ed91c7781617c02fce63f50","schema_version":"1.0","event_id":"sha256:8682c83b131dec07fc24bc8e0927b60721fc928a4ed91c7781617c02fce63f50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4T376IN2R5L46YHKN7Z3KVU7PQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Galen Reeves, Michael Gastpar","submitted_at":"2010-02-24T02:54:37Z","abstract_excerpt":"Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4458","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":"2026-05-18T03:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/7R3B3e2ogr/wHRIulFuVW1to/ApbaJgiavhFhSn1gtxVW7a4IPuRF24OskwrKttwnyKYKT8fMagZfOzUL1xCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:22:54.651269Z"},"content_sha256":"25c29d5989fd7bf30a0adde3ac51754986fb94e3552775485bdd74d9315b518f","schema_version":"1.0","event_id":"sha256:25c29d5989fd7bf30a0adde3ac51754986fb94e3552775485bdd74d9315b518f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/bundle.json","state_url":"https://pith.science/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/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":"2026-05-27T22:22:54Z","links":{"resolver":"https://pith.science/pith/4T376IN2R5L46YHKN7Z3KVU7PQ","bundle":"https://pith.science/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/bundle.json","state":"https://pith.science/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4T376IN2R5L46YHKN7Z3KVU7PQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4T376IN2R5L46YHKN7Z3KVU7PQ","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":"15021d4efb02fdefe7e87698438522f42d2990b3ba060a34ce807fcfb5bc701b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-24T02:54:37Z","title_canon_sha256":"17dbdf84512690fbcc0b121b34c5a7938a0836a9fcc52517105cf7834a64fc4d"},"schema_version":"1.0","source":{"id":"1002.4458","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4458","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4458v4","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4458","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"4T376IN2R5L4","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4T376IN2R5L46YHK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4T376IN2","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:25c29d5989fd7bf30a0adde3ac51754986fb94e3552775485bdd74d9315b518f","target":"graph","created_at":"2026-05-18T03:34:36Z","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":"Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters o","authors_text":"Galen Reeves, Michael Gastpar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-24T02:54:37Z","title":"Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4458","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":"sha256:8682c83b131dec07fc24bc8e0927b60721fc928a4ed91c7781617c02fce63f50","target":"record","created_at":"2026-05-18T03:34:36Z","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":"15021d4efb02fdefe7e87698438522f42d2990b3ba060a34ce807fcfb5bc701b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-24T02:54:37Z","title_canon_sha256":"17dbdf84512690fbcc0b121b34c5a7938a0836a9fcc52517105cf7834a64fc4d"},"schema_version":"1.0","source":{"id":"1002.4458","kind":"arxiv","version":4}},"canonical_sha256":"e4f7ff21ba8f57cf60ea6ff3b5569f7c08cb3b4d4ec3878b34e96b6de32a394f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4f7ff21ba8f57cf60ea6ff3b5569f7c08cb3b4d4ec3878b34e96b6de32a394f","first_computed_at":"2026-05-18T03:34:36.063824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:36.063824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vW8JZxn6lBc3936tu0hWDiEPFwxlMcg1N/8u+eQTajHp+Khj3AeCYy2M0SsykmYMLmgOF307Gf22BQi9U1BLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:36.064434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4458","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8682c83b131dec07fc24bc8e0927b60721fc928a4ed91c7781617c02fce63f50","sha256:25c29d5989fd7bf30a0adde3ac51754986fb94e3552775485bdd74d9315b518f"],"state_sha256":"21662dd5ce35109c7789c9192eb69b29d5e287c492ff089a214666836921eef8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOq6ClYKNnkdP8RzMO2cjeRzWDvQPgIM/BAVnfeCK4kloloB7VCn01EIgsUjm+T9p8ha5rKfIkdDWNhtx1jWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:22:54.655384Z","bundle_sha256":"feaef62b562263ccab819db7faf18a4e64d0b4b1ed1f9791748c97e2af5c880b"}}