{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A3Z356RTJWUAFWTT7BPSRIFCVG","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":"2518af6653458df477abaa4ef3a9432eb50854a7a45f5a74584a2ec9c7ee78ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-04T15:02:59Z","title_canon_sha256":"14522221f0c9382b0a16de220364950295175581956d44a88a5da98ac814cd74"},"schema_version":"1.0","source":{"id":"1811.01383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01383","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01383v1","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01383","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"A3Z356RTJWUA","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A3Z356RTJWUAFWTT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A3Z356RT","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:7b9214ce0a725b67b8c3a026ff90958522c32d796a8c46c0e38112ce6d7f44e5","target":"graph","created_at":"2026-05-18T00:01:34Z","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 work, we deal with rank-constrained integer least-squares optimization problems arising in low-rank matrix factorization related applications. We propose a solution for constrained integer least-squares problem subject to equality, sparsity, and rank constraints. The algorithm combines the Fincke-Pohst enumeration (or sphere decoding algorithm) with rank constraints and sparse solutions of Diophantine equations to arrive at an optimal solution. The proposed approach consists of two steps as follows: (i) find the solution set for Diophantine equations arising from the linear and sparsit","authors_text":"Arun Ayyar, Nirav Bhatt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-04T15:02:59Z","title":"An Algorithm for Integer Least-squares with Equality, Sparsity and Rank Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01383","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:da34c59c12a954060428d9c114f98f18c7251753a65f4b052a5e46a8f7dfe4fb","target":"record","created_at":"2026-05-18T00:01:34Z","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":"2518af6653458df477abaa4ef3a9432eb50854a7a45f5a74584a2ec9c7ee78ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-04T15:02:59Z","title_canon_sha256":"14522221f0c9382b0a16de220364950295175581956d44a88a5da98ac814cd74"},"schema_version":"1.0","source":{"id":"1811.01383","kind":"arxiv","version":1}},"canonical_sha256":"06f3befa334da802da73f85f28a0a2a99feadf28694678f408271154b3393bee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06f3befa334da802da73f85f28a0a2a99feadf28694678f408271154b3393bee","first_computed_at":"2026-05-18T00:01:34.467688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:34.467688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQsF991a6qe+h8V1XbCZR1YLuyoZYqsWFRNorA5teVejIoSpZ9M1ewpRhmL0mQETRg4dq/zbViZyvJtNjZEpDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:34.468249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da34c59c12a954060428d9c114f98f18c7251753a65f4b052a5e46a8f7dfe4fb","sha256:7b9214ce0a725b67b8c3a026ff90958522c32d796a8c46c0e38112ce6d7f44e5"],"state_sha256":"beefc2666640748f26e0c89912f483addf5b484fa4eeff1478f7f0951c74d68a"}