{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X366YIGV5L7X7UGE2KKLW6RVUA","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":"80612b723aa72305c731f04ef9b767184f5f0a33f506a503c173b899f9501d0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-18T21:19:54Z","title_canon_sha256":"5691c348609eafd3e623d462bdb68797d07d665ff118e38fd523e44c28905121"},"schema_version":"1.0","source":{"id":"1210.5921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5921","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5921v1","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5921","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"X366YIGV5L7X","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X366YIGV5L7X7UGE","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X366YIGV","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:eb0ac9a7063e8979ce33403a05b402da1eb6c9ef42f31e1708b03da5a35de5ef","target":"graph","created_at":"2026-05-18T03:42:34Z","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":"GAP functions are useful for solving optimization problems, but the literature contains a variety of different concepts of GAP functions. It is interesting to point out that these concepts have many similarities. Here we introduce G-coupling functions, thus presenting a way to take advantage of these common properties.","authors_text":"Alexander M. Rubinov, Daniel Morales-Silva, Wilfredo Sosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-18T21:19:54Z","title":"G-coupling functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5921","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:dc27f315e93702949022ff7bf8aa44a62a64210d7bdc8ce3d5e04f0041ca528e","target":"record","created_at":"2026-05-18T03:42:34Z","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":"80612b723aa72305c731f04ef9b767184f5f0a33f506a503c173b899f9501d0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-18T21:19:54Z","title_canon_sha256":"5691c348609eafd3e623d462bdb68797d07d665ff118e38fd523e44c28905121"},"schema_version":"1.0","source":{"id":"1210.5921","kind":"arxiv","version":1}},"canonical_sha256":"befdec20d5eaff7fd0c4d294bb7a35a0095e6aee21359f3741657245a9ab079b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"befdec20d5eaff7fd0c4d294bb7a35a0095e6aee21359f3741657245a9ab079b","first_computed_at":"2026-05-18T03:42:34.678487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.678487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X8G1BrtSC3R7j9OAjRhBSyrHYSzOE17ayk+oE1BEbEjZUvtp2DqACvdwRytKXHouZxQmbPurAfcURqWfoQEGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.679156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc27f315e93702949022ff7bf8aa44a62a64210d7bdc8ce3d5e04f0041ca528e","sha256:eb0ac9a7063e8979ce33403a05b402da1eb6c9ef42f31e1708b03da5a35de5ef"],"state_sha256":"ce3b75c07f5ab04db2e9d078449810523a01779471734858532b67f2a2900f56"}