{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7CRTQ23S2THAAAO2L5SSPSFB6Z","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":"8346ef62fde6f1818c26b7e5f7f13828d459c4efde04a17b7bd2cd462cc04160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-02-22T03:14:05Z","title_canon_sha256":"7ea951c7d9947ffdec55a4a4ceea0fc3510e1912b7216a78c842a5d00c80a9ab"},"schema_version":"1.0","source":{"id":"1702.06662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06662","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06662v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06662","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"7CRTQ23S2THA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7CRTQ23S2THAAAO2","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7CRTQ23S","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:61b16b59978618d0cc5352be18762b65ee90faabc104c91e469d7ba127c989c1","target":"graph","created_at":"2026-05-18T00:50:13Z","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":"Binary Knapsack Problem (BKP) is to select a subset of an element (item) set with the highest value while keeping the total weight within the capacity of the knapsack. This paper presents an integer programming model for a variation of BKP where the value of each element may depend on selecting or ignoring other elements. Strengths of such Value-Related Dependencies are assumed to be imprecise and hard to specify. To capture this imprecision, we have proposed modeling value-related dependencies using fuzzy graphs and their algebraic structure.","authors_text":"Asghar Moeini, David M. W. Powers, Davoud Mougouei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-02-22T03:14:05Z","title":"An Integer Programming Model for Binary Knapsack Problem with Value-Related Dependencies among Elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06662","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":"sha256:2d4a5218d46f353fea19958dc095dd79e36ab20baf4f10364fb422f1fdacbc85","target":"record","created_at":"2026-05-18T00:50:13Z","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":"8346ef62fde6f1818c26b7e5f7f13828d459c4efde04a17b7bd2cd462cc04160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-02-22T03:14:05Z","title_canon_sha256":"7ea951c7d9947ffdec55a4a4ceea0fc3510e1912b7216a78c842a5d00c80a9ab"},"schema_version":"1.0","source":{"id":"1702.06662","kind":"arxiv","version":1}},"canonical_sha256":"f8a3386b72d4ce0001da5f6527c8a1f652f245c097efde1d96d9b769b1641e1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8a3386b72d4ce0001da5f6527c8a1f652f245c097efde1d96d9b769b1641e1b","first_computed_at":"2026-05-18T00:50:13.028459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.028459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zWs+s2omG3iqbVnyNVtWzADOYnYipSLPkwd2jndBBMYo/JBHK4V1APZm0gll/HnRUGVNbaydg/1BjwmX+EkqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.028860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d4a5218d46f353fea19958dc095dd79e36ab20baf4f10364fb422f1fdacbc85","sha256:61b16b59978618d0cc5352be18762b65ee90faabc104c91e469d7ba127c989c1"],"state_sha256":"4b47b6844cad48245ad2ae78b8529a24c2332115f8a786c117bb292d638e78e1"}