{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RD3YJEDIWSBPSBOSC423JQEXAQ","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":"c174c6b083d14a5eb8ee1dc16adaf284cc88db0f3f48c5eca049af6037e83afe","cross_cats_sorted":["cs.CC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-09T12:33:36Z","title_canon_sha256":"42bb5476bb75cace73fb8fb045cba271c5f5f003e46e77aabf351f33040ab2be"},"schema_version":"1.0","source":{"id":"1807.03074","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03074","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03074v2","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03074","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"RD3YJEDIWSBP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RD3YJEDIWSBPSBOS","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RD3YJEDI","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:180d8b2e7cc5e45b9d5c57574c46e7e47b14f808ed810ae2a8c012fab164c9c0","target":"graph","created_at":"2026-05-18T00:04:29Z","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 study sparse generalized inverses $H$ of a rank-$r$ real matrix $A$. We give a construction for reflexive generalized inverses having at most $r^2$ nonzeros. For $r=1$ and for $r=2$ with $A$ nonnegative, we demonstrate how to minimize the (vector) 1-norm over reflexive generalized inverses. For general $r$, we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of $r^2$ of the minimum 1-norm generalized inverse.","authors_text":"Jon Lee, Marcia Fampa","cross_cats":["cs.CC","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-09T12:33:36Z","title":"On Sparse Reflexive Generalized Inverses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03074","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":"sha256:2b7b20aed243f47e649aa48cf89a6ea4f06dfaf342bcf85fbaeb189a6af8ed79","target":"record","created_at":"2026-05-18T00:04:29Z","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":"c174c6b083d14a5eb8ee1dc16adaf284cc88db0f3f48c5eca049af6037e83afe","cross_cats_sorted":["cs.CC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-09T12:33:36Z","title_canon_sha256":"42bb5476bb75cace73fb8fb045cba271c5f5f003e46e77aabf351f33040ab2be"},"schema_version":"1.0","source":{"id":"1807.03074","kind":"arxiv","version":2}},"canonical_sha256":"88f7849068b482f905d21735b4c097041b65314b39d77f84ab82b0d19ad08a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88f7849068b482f905d21735b4c097041b65314b39d77f84ab82b0d19ad08a43","first_computed_at":"2026-05-18T00:04:29.614602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:29.614602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"03fW5btoUXH+T2df3lBD3pLGNDfpn9pV0c5hhd46Qer3GA4UnCTBwJlTisJEfIORTV1vWm2DaxEMADvZYRHYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:29.615046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03074","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b7b20aed243f47e649aa48cf89a6ea4f06dfaf342bcf85fbaeb189a6af8ed79","sha256:180d8b2e7cc5e45b9d5c57574c46e7e47b14f808ed810ae2a8c012fab164c9c0"],"state_sha256":"92ce03d75a0e41ccb335dbd33c707b99dbf37dfdad9792ef147f1ed68702ea5f"}