{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LE5MO6QFZVAI6AB37YO4LWA5JJ","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":"a4fd7b064cbc79f600a6ed0dff07a6f38148a2f96b19c13f0f072ae0902250c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2013-08-29T08:00:20Z","title_canon_sha256":"6a6892be95647f650408dba34c724102d0e823d3a54f9a7ae6703e8a97228167"},"schema_version":"1.0","source":{"id":"1308.6388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6388","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6388v1","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6388","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"LE5MO6QFZVAI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LE5MO6QFZVAI6AB3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LE5MO6QF","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:f7fac6ca586f6a4950c5fb8e5e67c32d9be3a52ea43c09528756f8d8230fa3cb","target":"graph","created_at":"2026-05-18T03:14:40Z","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":"In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices. GNCGCP comprises two sub-procedures, graduated nonconvexity (GNC) which realizes a convex relaxation and graduated concavity (GC) which realizes a concave relaxation. It is proved that GNCGCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way","authors_text":"Hong Qiao, Zhi-yong Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2013-08-29T08:00:20Z","title":"GNCGCP - Graduated NonConvexity and Graduated Concavity Procedure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6388","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:f5aefc740f2eb1f1bfc70977416a32fe03936cd6a88d4d3298aa6a4f24824f87","target":"record","created_at":"2026-05-18T03:14:40Z","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":"a4fd7b064cbc79f600a6ed0dff07a6f38148a2f96b19c13f0f072ae0902250c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2013-08-29T08:00:20Z","title_canon_sha256":"6a6892be95647f650408dba34c724102d0e823d3a54f9a7ae6703e8a97228167"},"schema_version":"1.0","source":{"id":"1308.6388","kind":"arxiv","version":1}},"canonical_sha256":"593ac77a05cd408f003bfe1dc5d81d4a74ae43c74927a939114229499b604b08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"593ac77a05cd408f003bfe1dc5d81d4a74ae43c74927a939114229499b604b08","first_computed_at":"2026-05-18T03:14:40.086016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:40.086016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hiTQAF/eMtsJgpogDVr/mlz+q3zF4mP/+o7ONNushc3TjQkcsSo8Nf6rXbS3PuqUZUtPp1t85n5Kiym3SQNCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:40.086692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5aefc740f2eb1f1bfc70977416a32fe03936cd6a88d4d3298aa6a4f24824f87","sha256:f7fac6ca586f6a4950c5fb8e5e67c32d9be3a52ea43c09528756f8d8230fa3cb"],"state_sha256":"91bd238442079df488e7d188940dc26eb8a78579b51eb11ee480c05e336a4b16"}