{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Q4LEROXBIBF5ES574JOIBT4VYM","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":"a1188cc2eb9fcb62c141be7433324a56d3b753ef62eb022e4ed70ea3a65f4a68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-10-07T01:51:27Z","title_canon_sha256":"360672fe38522e74641d474a9a2e466d100dd4c4f6b670b12471101739c614c1"},"schema_version":"1.0","source":{"id":"1910.02573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.02573","created_at":"2026-07-05T03:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1910.02573v2","created_at":"2026-07-05T03:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02573","created_at":"2026-07-05T03:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"Q4LEROXBIBF5","created_at":"2026-07-05T03:03:48Z"},{"alias_kind":"pith_short_16","alias_value":"Q4LEROXBIBF5ES57","created_at":"2026-07-05T03:03:48Z"},{"alias_kind":"pith_short_8","alias_value":"Q4LEROXB","created_at":"2026-07-05T03:03:48Z"}],"graph_snapshots":[{"event_id":"sha256:a459d27a2e7ad9d744f2b1bfdac9e931d19c8d20cfdd299e937507dd67c95971","target":"graph","created_at":"2026-07-05T03:03:48Z","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/1910.02573/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and sign-invariant norm with a cardinality constraint. This gives a nonlinear formulation for the feasible set of sparse principal component analysis (sparse PCA) and an alternative proof of the $K$-support norm. Second, we characterize the convex hull of sets of matrices defined by constraining their singular values. As a consequence, we generalize an earlier result that","authors_text":"Jean-Philippe P. Richard, Jinhak Kim, Mohit Tawarmalani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-10-07T01:51:27Z","title":"Convexification of Permutation-Invariant Sets and an Application to Sparse PCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02573","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:c4c189f917b61ef831e9c4c70ef322d4c2f903b97a308624670b5a0036e1b188","target":"record","created_at":"2026-07-05T03:03:48Z","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":"a1188cc2eb9fcb62c141be7433324a56d3b753ef62eb022e4ed70ea3a65f4a68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-10-07T01:51:27Z","title_canon_sha256":"360672fe38522e74641d474a9a2e466d100dd4c4f6b670b12471101739c614c1"},"schema_version":"1.0","source":{"id":"1910.02573","kind":"arxiv","version":2}},"canonical_sha256":"871648bae1404bd24bbfe25c80cf95c31ffa1ffbaa8d3f2bae7ef43fb077a565","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"871648bae1404bd24bbfe25c80cf95c31ffa1ffbaa8d3f2bae7ef43fb077a565","first_computed_at":"2026-07-05T03:03:48.109632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:48.109632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YPzDDdsm9ZHJuBMy7HnCqgZmXBoUsKU7iC9+kD9H1W+nJgA9E8+1SlocLvJKM//jiDkMReWLOo56x/R1MUsHDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:48.110053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.02573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4c189f917b61ef831e9c4c70ef322d4c2f903b97a308624670b5a0036e1b188","sha256:a459d27a2e7ad9d744f2b1bfdac9e931d19c8d20cfdd299e937507dd67c95971"],"state_sha256":"06bc2e5dc78457d5663a3be2b4a62345038aa588648372a5342fc23a47158243"}