{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:I3XFOFFEDHJYBZP5UL4ODJGDVS","short_pith_number":"pith:I3XFOFFE","canonical_record":{"source":{"id":"1302.0490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-03T13:40:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bd21c5140dd9a52d56ca59ae84930f1ffe783b4219adc7223a963b8095727879","abstract_canon_sha256":"7e2cfd8d0c14803a1c3055dcbdc26b1197ef0d5233457add57ca5c90eedde2a4"},"schema_version":"1.0"},"canonical_sha256":"46ee5714a419d380e5fda2f8e1a4c3aca6ede3d77fdf97ad62d9e6a863c6a99b","source":{"kind":"arxiv","id":"1302.0490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0490","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0490v1","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0490","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"I3XFOFFEDHJY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I3XFOFFEDHJYBZP5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I3XFOFFE","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:I3XFOFFEDHJYBZP5UL4ODJGDVS","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-03T13:40:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bd21c5140dd9a52d56ca59ae84930f1ffe783b4219adc7223a963b8095727879","abstract_canon_sha256":"7e2cfd8d0c14803a1c3055dcbdc26b1197ef0d5233457add57ca5c90eedde2a4"},"schema_version":"1.0"},"canonical_sha256":"46ee5714a419d380e5fda2f8e1a4c3aca6ede3d77fdf97ad62d9e6a863c6a99b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:51.042909Z","signature_b64":"3mitkt1/fY+Ln9RwH2BCuU6aheAKXOmG/US6pqYE1bYzMlL3nNGAfYQk8oZasslaVgVFlv/TnmuBrsMpxSULCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ee5714a419d380e5fda2f8e1a4c3aca6ede3d77fdf97ad62d9e6a863c6a99b","last_reissued_at":"2026-05-18T01:51:51.042526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:51.042526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0490","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":"2026-05-18T01:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYYGfjrQdFOx0hW4buqmVn1n4VqDOkCmEBiU1ZLszy/MEmUeApWm9FKCeh7ld/V6gd6nkQx2jM/qf8tgl6rLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:14.561163Z"},"content_sha256":"71905819135017d0c0f549ee90ed3167e5ae84e940ce9b11b7d115ccd9320acc","schema_version":"1.0","event_id":"sha256:71905819135017d0c0f549ee90ed3167e5ae84e940ce9b11b7d115ccd9320acc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:I3XFOFFEDHJYBZP5UL4ODJGDVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mrityunjoy Chakraborty, Rajib Lochan Das, Siddhartha Satpathi","submitted_at":"2013-02-03T13:40:49Z","abstract_excerpt":"Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select $N (\\geq1)$ atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a $K$-sparse signal from a compressed measurement $ {\\bf y}={\\bf \\Phi x}$ by $K^{th}$ iteration if the sensing matrix ${\\bf \\Phi}$ satisfies restricted isometry property (RIP) of order $NK$ where $\\delta_{NK} < \\frac {\\sqrt{N}}{\\sqrt{K}+2\\sqrt{N}}$. Our bound offers an improvement over the very recent result shown in \\cite{wang_2012b}. Moreover, we present another bound fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0490","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":"2026-05-18T01:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3S3LJDZlYK1bnbFJXgsXF/HcuSb7PscEzieDhpiowgKrRxvMf988X1GNzLn9HP5dnfFF2XvMLj/FILaF53VDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:14.562174Z"},"content_sha256":"a9c91a2d0394371ba6ad8971f04b74ab0a1bc695fc642e7b165784899bf1fee6","schema_version":"1.0","event_id":"sha256:a9c91a2d0394371ba6ad8971f04b74ab0a1bc695fc642e7b165784899bf1fee6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/bundle.json","state_url":"https://pith.science/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/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":"2026-05-31T08:38:14Z","links":{"resolver":"https://pith.science/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS","bundle":"https://pith.science/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/bundle.json","state":"https://pith.science/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3XFOFFEDHJYBZP5UL4ODJGDVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:I3XFOFFEDHJYBZP5UL4ODJGDVS","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":"7e2cfd8d0c14803a1c3055dcbdc26b1197ef0d5233457add57ca5c90eedde2a4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-03T13:40:49Z","title_canon_sha256":"bd21c5140dd9a52d56ca59ae84930f1ffe783b4219adc7223a963b8095727879"},"schema_version":"1.0","source":{"id":"1302.0490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0490","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0490v1","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0490","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"I3XFOFFEDHJY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I3XFOFFEDHJYBZP5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I3XFOFFE","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:a9c91a2d0394371ba6ad8971f04b74ab0a1bc695fc642e7b165784899bf1fee6","target":"graph","created_at":"2026-05-18T01:51:51Z","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":"Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select $N (\\geq1)$ atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a $K$-sparse signal from a compressed measurement $ {\\bf y}={\\bf \\Phi x}$ by $K^{th}$ iteration if the sensing matrix ${\\bf \\Phi}$ satisfies restricted isometry property (RIP) of order $NK$ where $\\delta_{NK} < \\frac {\\sqrt{N}}{\\sqrt{K}+2\\sqrt{N}}$. Our bound offers an improvement over the very recent result shown in \\cite{wang_2012b}. Moreover, we present another bound fo","authors_text":"Mrityunjoy Chakraborty, Rajib Lochan Das, Siddhartha Satpathi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-03T13:40:49Z","title":"Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0490","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":"sha256:71905819135017d0c0f549ee90ed3167e5ae84e940ce9b11b7d115ccd9320acc","target":"record","created_at":"2026-05-18T01:51:51Z","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":"7e2cfd8d0c14803a1c3055dcbdc26b1197ef0d5233457add57ca5c90eedde2a4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-03T13:40:49Z","title_canon_sha256":"bd21c5140dd9a52d56ca59ae84930f1ffe783b4219adc7223a963b8095727879"},"schema_version":"1.0","source":{"id":"1302.0490","kind":"arxiv","version":1}},"canonical_sha256":"46ee5714a419d380e5fda2f8e1a4c3aca6ede3d77fdf97ad62d9e6a863c6a99b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46ee5714a419d380e5fda2f8e1a4c3aca6ede3d77fdf97ad62d9e6a863c6a99b","first_computed_at":"2026-05-18T01:51:51.042526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:51.042526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3mitkt1/fY+Ln9RwH2BCuU6aheAKXOmG/US6pqYE1bYzMlL3nNGAfYQk8oZasslaVgVFlv/TnmuBrsMpxSULCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:51.042909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71905819135017d0c0f549ee90ed3167e5ae84e940ce9b11b7d115ccd9320acc","sha256:a9c91a2d0394371ba6ad8971f04b74ab0a1bc695fc642e7b165784899bf1fee6"],"state_sha256":"fe2c5549667fc93b36ca5de6c385010770bc91f127235170f0324636bb9b01df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zm+5yvvd5g7P6Fh98o7iebVoGiKwsR09x2qMRjoRWBxV8Z2AvN0g5kBUH18HwjVSTl0tGZNblyWsWS15m1/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:14.568201Z","bundle_sha256":"d36049006b0012b6eb43feef51bfbb42a28042500702ce2c03f7fc9b42a4709b"}}