{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:RLISZNZTXRLZITBLYTSVIU2ABM","short_pith_number":"pith:RLISZNZT","canonical_record":{"source":{"id":"2203.02607","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-03-04T23:21:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bc82a84f365009d404debd9dcc0785608b4125fc0767c88bac4d8bccae4a20f4","abstract_canon_sha256":"024f5772bee8b612b511a3f0b6f10b99cd11eae82f19ded3128a7dea058c8f97"},"schema_version":"1.0"},"canonical_sha256":"8ad12cb733bc57944c2bc4e55453400b3da6c8877cc0b064d8091b73129cec87","source":{"kind":"arxiv","id":"2203.02607","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.02607","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"2203.02607v3","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.02607","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"RLISZNZTXRLZ","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_16","alias_value":"RLISZNZTXRLZITBL","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_8","alias_value":"RLISZNZT","created_at":"2026-05-20T00:02:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:RLISZNZTXRLZITBLYTSVIU2ABM","target":"record","payload":{"canonical_record":{"source":{"id":"2203.02607","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-03-04T23:21:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bc82a84f365009d404debd9dcc0785608b4125fc0767c88bac4d8bccae4a20f4","abstract_canon_sha256":"024f5772bee8b612b511a3f0b6f10b99cd11eae82f19ded3128a7dea058c8f97"},"schema_version":"1.0"},"canonical_sha256":"8ad12cb733bc57944c2bc4e55453400b3da6c8877cc0b064d8091b73129cec87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:01.025838Z","signature_b64":"49mOaOsypyUyVQ3CJh2DJFCAsyO0qdgAzCzdLpReDru0eTwoHyGvqXIRf6eBFegCrqpGeLMXEq51LsV9yblPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ad12cb733bc57944c2bc4e55453400b3da6c8877cc0b064d8091b73129cec87","last_reissued_at":"2026-05-20T00:02:01.024964Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:01.024964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.02607","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRWIZ9q/weyoWCQ4MAkG8gUrQM7REOB8QYleB1V9noxcfbWxdnQ3FXAQ2BCO/4CysNa5X/l5wVVEM4lZmiGtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:12:02.959494Z"},"content_sha256":"41e5ca520dd2451576cbaa753165acf523a6ded7f7ad100b8f347e72dff36209","schema_version":"1.0","event_id":"sha256:41e5ca520dd2451576cbaa753165acf523a6ded7f7ad100b8f347e72dff36209"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:RLISZNZTXRLZITBLYTSVIU2ABM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An SDP Relaxation for the Sparse Integer Least Squares Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.OC","authors_text":"Alberto Del Pia, Dekun Zhou","submitted_at":"2022-03-04T23:21:38Z","abstract_excerpt":"In this paper, we study the \\emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\\{0, \\pm 1\\}$-vectors. We propose an $\\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which computes feasible solutions with high probability with an asymptotic approximation ratio $1/T^2$ as long as the sparsity constant $\\sigma \\ll T$. Our algorithm handles large-scale problems, delivering high-quality approximate solutions for dimensions up to $d = 10,000$. The proposed randomized algorithm applies broadly to binary quadratic programs with a car"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.02607","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.02607/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T00:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S34wIbhO4QSW3UwPqb43LjVegoP5wLnOid7B+qzE1E5/3ehJ0LyuwsP54YKP5eJcTCufoS2MofhEoV69auzsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:12:02.959894Z"},"content_sha256":"392b674ae0dcdb64521531a271c0c077961b5e0ad6ea4a376dedfdd8a6ef7f43","schema_version":"1.0","event_id":"sha256:392b674ae0dcdb64521531a271c0c077961b5e0ad6ea4a376dedfdd8a6ef7f43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLISZNZTXRLZITBLYTSVIU2ABM/bundle.json","state_url":"https://pith.science/pith/RLISZNZTXRLZITBLYTSVIU2ABM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLISZNZTXRLZITBLYTSVIU2ABM/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":"2026-05-24T16:12:02Z","links":{"resolver":"https://pith.science/pith/RLISZNZTXRLZITBLYTSVIU2ABM","bundle":"https://pith.science/pith/RLISZNZTXRLZITBLYTSVIU2ABM/bundle.json","state":"https://pith.science/pith/RLISZNZTXRLZITBLYTSVIU2ABM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLISZNZTXRLZITBLYTSVIU2ABM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RLISZNZTXRLZITBLYTSVIU2ABM","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":"024f5772bee8b612b511a3f0b6f10b99cd11eae82f19ded3128a7dea058c8f97","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-03-04T23:21:38Z","title_canon_sha256":"bc82a84f365009d404debd9dcc0785608b4125fc0767c88bac4d8bccae4a20f4"},"schema_version":"1.0","source":{"id":"2203.02607","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.02607","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"2203.02607v3","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.02607","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"RLISZNZTXRLZ","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_16","alias_value":"RLISZNZTXRLZITBL","created_at":"2026-05-20T00:02:01Z"},{"alias_kind":"pith_short_8","alias_value":"RLISZNZT","created_at":"2026-05-20T00:02:01Z"}],"graph_snapshots":[{"event_id":"sha256:392b674ae0dcdb64521531a271c0c077961b5e0ad6ea4a376dedfdd8a6ef7f43","target":"graph","created_at":"2026-05-20T00:02:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.02607/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the \\emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\\{0, \\pm 1\\}$-vectors. We propose an $\\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which computes feasible solutions with high probability with an asymptotic approximation ratio $1/T^2$ as long as the sparsity constant $\\sigma \\ll T$. Our algorithm handles large-scale problems, delivering high-quality approximate solutions for dimensions up to $d = 10,000$. The proposed randomized algorithm applies broadly to binary quadratic programs with a car","authors_text":"Alberto Del Pia, Dekun Zhou","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-03-04T23:21:38Z","title":"An SDP Relaxation for the Sparse Integer Least Squares Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.02607","kind":"arxiv","version":3},"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":"sha256:41e5ca520dd2451576cbaa753165acf523a6ded7f7ad100b8f347e72dff36209","target":"record","created_at":"2026-05-20T00:02:01Z","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":"024f5772bee8b612b511a3f0b6f10b99cd11eae82f19ded3128a7dea058c8f97","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-03-04T23:21:38Z","title_canon_sha256":"bc82a84f365009d404debd9dcc0785608b4125fc0767c88bac4d8bccae4a20f4"},"schema_version":"1.0","source":{"id":"2203.02607","kind":"arxiv","version":3}},"canonical_sha256":"8ad12cb733bc57944c2bc4e55453400b3da6c8877cc0b064d8091b73129cec87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ad12cb733bc57944c2bc4e55453400b3da6c8877cc0b064d8091b73129cec87","first_computed_at":"2026-05-20T00:02:01.024964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:01.024964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49mOaOsypyUyVQ3CJh2DJFCAsyO0qdgAzCzdLpReDru0eTwoHyGvqXIRf6eBFegCrqpGeLMXEq51LsV9yblPBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:01.025838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.02607","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41e5ca520dd2451576cbaa753165acf523a6ded7f7ad100b8f347e72dff36209","sha256:392b674ae0dcdb64521531a271c0c077961b5e0ad6ea4a376dedfdd8a6ef7f43"],"state_sha256":"57d0bd38577e74e198c0773d9df8b99ff7a7c6588adff1cde6de98bc34f63df3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCqpTkMHbMA/Q96mDvP2pECgKgkhlDyeBQWg/nZdSDn93ID+5C1OfB/4y8bOu7mz/1Fyalo5eGdifu0Iu0NnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T16:12:02.962342Z","bundle_sha256":"ed4e9788ae8db8df61113fbe365f5af5d5d927f1a5d0cb4462843339d87972e3"}}