{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N42YCQYBWMGBBN326M54ECLZBI","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":"ba2fda0fe3e4048fe8b5b5803e5d3663a47b0d841f613882a240de70e5ffde34","cross_cats_sorted":["cs.DM","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T03:32:39Z","title_canon_sha256":"8042c7f067271f3c735a355c7c41a776cdb67f171259230244f0cf5298130669"},"schema_version":"1.0","source":{"id":"1112.1757","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1757","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1757v2","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1757","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"N42YCQYBWMGB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N42YCQYBWMGBBN32","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N42YCQYB","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:d6b9536e40e9635a9ee4cd9aefcdd20fe415567d169b7660d488bd56bee04383","target":"graph","created_at":"2026-05-18T02:21:27Z","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":"We consider a system of m linear equations in n variables Ax=b where A is a given m x n matrix and b is a given m-vector known to be equal to Ax' for some unknown solution x' that is integer and k-sparse: x' in {0,1}^n and exactly k entries of x' are 1. We give necessary and sufficient conditions for recovering the solution x exactly using an LP relaxation that minimizes l1 norm of x. When A is drawn from a distribution that has exchangeable columns, we show an interesting connection between the recovery probability and a well known problem in geometry, namely the k-set problem. To the best of","authors_text":"Soumitra Pal, T. S. Jayram, Vijay Arya","cross_cats":["cs.DM","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T03:32:39Z","title":"Recovery of a Sparse Integer Solution to an Underdetermined System of Linear Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1757","kind":"arxiv","version":2},"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":"sha256:66063451f92955eae7b836dfec14f08f8947fe58c4baa5b9ad0bebbe78077167","target":"record","created_at":"2026-05-18T02:21:27Z","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":"ba2fda0fe3e4048fe8b5b5803e5d3663a47b0d841f613882a240de70e5ffde34","cross_cats_sorted":["cs.DM","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-08T03:32:39Z","title_canon_sha256":"8042c7f067271f3c735a355c7c41a776cdb67f171259230244f0cf5298130669"},"schema_version":"1.0","source":{"id":"1112.1757","kind":"arxiv","version":2}},"canonical_sha256":"6f35814301b30c10b77af33bc209790a3260d01a106ad35c1878909f7a861802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f35814301b30c10b77af33bc209790a3260d01a106ad35c1878909f7a861802","first_computed_at":"2026-05-18T02:21:27.382517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:27.382517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQlwndoM9DygxfAhaX+qhE+5PejyM2o4x/ktCp+3SfzKmGAggtkYKTIZeDG1oMuGh5M0yLKIw5MHLq1JsmXYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:27.383221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1757","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66063451f92955eae7b836dfec14f08f8947fe58c4baa5b9ad0bebbe78077167","sha256:d6b9536e40e9635a9ee4cd9aefcdd20fe415567d169b7660d488bd56bee04383"],"state_sha256":"256374074a2c2007dc3a4760016b76e4ec38ddea150ad0a3487cd9f9454700bc"}