{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DSH7ZZ2E2KBHAFPXU3YHC3WE6T","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":"5f7edb30f6ac770145132c09ab3003881eb05718c80868c810fbc3720364c373","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-10T09:04:51Z","title_canon_sha256":"0bc54941a4e41d4749aac7db68dfa03823b8a3c1dc90028dbde866d12206abc8"},"schema_version":"1.0","source":{"id":"1707.02757","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02757","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02757v2","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02757","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"DSH7ZZ2E2KBH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DSH7ZZ2E2KBHAFPX","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DSH7ZZ2E","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:312b51ab94628b50adefa20f9cc23301fd0e3e7712939da0634ae7b68a7c510c","target":"graph","created_at":"2026-05-18T00:10:13Z","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":"Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\\ldots,v_m \\in \\mathbb{R}^d$ and a constraint family ${\\cal B}\\subseteq 2^{[m]}$, find a set $S \\in \\cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are ","authors_text":"Damian Straszak, Javad B. Ebrahimi, Nisheeth K. Vishnoi","cross_cats":["cs.LG","math.OC","math.PR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-10T09:04:51Z","title":"Subdeterminant Maximization via Nonconvex Relaxations and Anti-concentration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02757","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:aa957e8bad11c521d03c3e14a7df923d9c30c7fb1d7fe47f3fe9d0b64207ebe0","target":"record","created_at":"2026-05-18T00:10:13Z","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":"5f7edb30f6ac770145132c09ab3003881eb05718c80868c810fbc3720364c373","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-10T09:04:51Z","title_canon_sha256":"0bc54941a4e41d4749aac7db68dfa03823b8a3c1dc90028dbde866d12206abc8"},"schema_version":"1.0","source":{"id":"1707.02757","kind":"arxiv","version":2}},"canonical_sha256":"1c8ffce744d2827015f7a6f0716ec4f4e9c256d0ed206a3972406fb12e4c0d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c8ffce744d2827015f7a6f0716ec4f4e9c256d0ed206a3972406fb12e4c0d84","first_computed_at":"2026-05-18T00:10:13.588950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:13.588950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HHR4FmqKU8BJNiqXZZi/gLkoOARUuI/O9HglNlYaeBw+BNYgRGr3vX4PSu80Ku2dq0FBiPd8xe2G0dznUJkhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:13.589616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02757","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa957e8bad11c521d03c3e14a7df923d9c30c7fb1d7fe47f3fe9d0b64207ebe0","sha256:312b51ab94628b50adefa20f9cc23301fd0e3e7712939da0634ae7b68a7c510c"],"state_sha256":"2ee0fb834d388eae97875ba296e5839227336e9d63c17938426d4cbbb1a7b87a"}