{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CDEPONKZ3XPGJDAWPSCG6OYPET","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":"f6f0dfb395e63be5d54c9f3303b7eb4558c0a3c38b1916b89c0c91f5f94d6739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-27T22:54:47Z","title_canon_sha256":"b7a57397afaa278e53931d77420dd96143e0137d2f3041d48b66e27674831516"},"schema_version":"1.0","source":{"id":"2006.16781","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16781","created_at":"2026-07-05T02:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16781v6","created_at":"2026-07-05T02:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16781","created_at":"2026-07-05T02:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"CDEPONKZ3XPG","created_at":"2026-07-05T02:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"CDEPONKZ3XPGJDAW","created_at":"2026-07-05T02:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"CDEPONKZ","created_at":"2026-07-05T02:36:44Z"}],"graph_snapshots":[{"event_id":"sha256:06a204afd9b5d79ff7484859401c82d8568ef8957d9f894b0fa3f6f418716bdb","target":"graph","created_at":"2026-07-05T02:36:44Z","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/2006.16781/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened to convexity and that the assumption that the gradients of all constraints at the optimal solution are linearly independent cannot be further weakened. Finally, we illustrate our results with several examples.","authors_text":"Vincent Guigues","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-27T22:54:47Z","title":"On the strong concavity of the dual function of an optimization problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16781","kind":"arxiv","version":6},"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":"sha256:538531eb811b6b40e768d83bbc567394f9d3003f3b840864b0c0501a7b7682f8","target":"record","created_at":"2026-07-05T02:36:44Z","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":"f6f0dfb395e63be5d54c9f3303b7eb4558c0a3c38b1916b89c0c91f5f94d6739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-27T22:54:47Z","title_canon_sha256":"b7a57397afaa278e53931d77420dd96143e0137d2f3041d48b66e27674831516"},"schema_version":"1.0","source":{"id":"2006.16781","kind":"arxiv","version":6}},"canonical_sha256":"10c8f73559ddde648c167c846f3b0f24da5267f8a488731dc38a1e989b65e7ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10c8f73559ddde648c167c846f3b0f24da5267f8a488731dc38a1e989b65e7ab","first_computed_at":"2026-07-05T02:36:44.310267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:36:44.310267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"13Mq7KdxyPbbV2ldwJ9E2+KeQAS8RaFMsMAOsBu6F2OqEdgAosLsgzTznK5IDfan1iMNOg3LkIW9rWBGd88UBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:36:44.310715Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.16781","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:538531eb811b6b40e768d83bbc567394f9d3003f3b840864b0c0501a7b7682f8","sha256:06a204afd9b5d79ff7484859401c82d8568ef8957d9f894b0fa3f6f418716bdb"],"state_sha256":"e4f9f2f3a067a9db219dd3f14f3017b41a50031617960145c9fe26cecc086b5f"}