{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z2VY2FZM7JD22EOUSMPCEHNKRH","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":"af8eb9d72ed1290d9be91c01a09eeb697054190bf47fe2b8cf642b7caa789bbf","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-06T05:48:40Z","title_canon_sha256":"da183178debb720da835272da7b7d793e3f896aad8c31a3bb14f3db983b6a1db"},"schema_version":"1.0","source":{"id":"1309.1541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1541","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1541v1","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1541","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z2VY2FZM7JD2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2VY2FZM7JD22EOU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2VY2FZM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:15228203b304b8f6ec6a13d7bc6985fefe62ebac05c82ff6b67748ab98b0d1c2","target":"graph","created_at":"2026-05-18T03:13:59Z","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 provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.","authors_text":"Miguel \\'A. Carreira-Perpi\\~n\\'an, Weiran Wang","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-06T05:48:40Z","title":"Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1541","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:e5728de8be83593437c183b146993047e10a4549b3442e3beb45bab18f1e1ece","target":"record","created_at":"2026-05-18T03:13:59Z","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":"af8eb9d72ed1290d9be91c01a09eeb697054190bf47fe2b8cf642b7caa789bbf","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-06T05:48:40Z","title_canon_sha256":"da183178debb720da835272da7b7d793e3f896aad8c31a3bb14f3db983b6a1db"},"schema_version":"1.0","source":{"id":"1309.1541","kind":"arxiv","version":1}},"canonical_sha256":"ceab8d172cfa47ad11d4931e221daa89fdb7b37d661f232031a3486d85ebfc13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceab8d172cfa47ad11d4931e221daa89fdb7b37d661f232031a3486d85ebfc13","first_computed_at":"2026-05-18T03:13:59.186388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:59.186388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32Lzq6CGCHYbWzFjGe9zglC1EpuMJrnvlYi5krIKDYkaIAYiUpwzs+Qs6QrBFO1AZ5s1puCld5O/aN2WdKdeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:59.187188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5728de8be83593437c183b146993047e10a4549b3442e3beb45bab18f1e1ece","sha256:15228203b304b8f6ec6a13d7bc6985fefe62ebac05c82ff6b67748ab98b0d1c2"],"state_sha256":"22dd7035463b8d8df124e588d38b17428ab9f6112a5928323d4f645125b011a0"}