{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZRGFHA3KPE3KULHFXEWJ2ASMPZ","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":"ceb264996be8612c490343310755fb4037efceaf819a1e63ed2d86cf7326de49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2024-12-17T19:43:33Z","title_canon_sha256":"2e94d6753de7b3a9c036b4e751603950892babc8ff68c3702119ad775bfeff44"},"schema_version":"1.0","source":{"id":"2412.13290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.13290","created_at":"2026-07-05T09:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"2412.13290v1","created_at":"2026-07-05T09:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13290","created_at":"2026-07-05T09:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZRGFHA3KPE3K","created_at":"2026-07-05T09:50:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZRGFHA3KPE3KULHF","created_at":"2026-07-05T09:50:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZRGFHA3K","created_at":"2026-07-05T09:50:59Z"}],"graph_snapshots":[{"event_id":"sha256:7c071ecc6bbc3c03f86c43466c3d52642a52c05fd9e6b5c85320333e3ca0a712","target":"graph","created_at":"2026-07-05T09:50:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.13290/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study linear contracts for combinatorial problems in multi-agent settings. In this problem, a principal designs a linear contract with several agents, each of whom can decide to take a costly action or not. The principal observes only the outcome of the agents' collective actions, not the actions themselves, and obtains a reward from this outcome. Agents that take an action incur a cost, and so naturally agents require a fraction of the principal's reward as an incentive for taking their action. The principal needs to decide what fraction of their reward to give to each agent so that the pr","authors_text":"Jacob Skitsko, Kanstantsin Pashkovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2024-12-17T19:43:33Z","title":"Linear Contracts for Supermodular Functions Based on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13290","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:de08e008b30c232c48418c3e13df53e09d840bd44f3bd9af77e3094293bdeb49","target":"record","created_at":"2026-07-05T09:50:59Z","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":"ceb264996be8612c490343310755fb4037efceaf819a1e63ed2d86cf7326de49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2024-12-17T19:43:33Z","title_canon_sha256":"2e94d6753de7b3a9c036b4e751603950892babc8ff68c3702119ad775bfeff44"},"schema_version":"1.0","source":{"id":"2412.13290","kind":"arxiv","version":1}},"canonical_sha256":"cc4c53836a7936aa2ce5b92c9d024c7e6a2c92a302eeb140e6f81a667b78a177","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc4c53836a7936aa2ce5b92c9d024c7e6a2c92a302eeb140e6f81a667b78a177","first_computed_at":"2026-07-05T09:50:59.265775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:59.265775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VwncJ169i+zIxEocIj/BEL+Db1/pqUpa1qYVgDbSy5yjMi+LHVNrEnd6Ko/rFnQHGlxpv3P3wI0ajtebON9QDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:59.266292Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.13290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de08e008b30c232c48418c3e13df53e09d840bd44f3bd9af77e3094293bdeb49","sha256:7c071ecc6bbc3c03f86c43466c3d52642a52c05fd9e6b5c85320333e3ca0a712"],"state_sha256":"f3af9f6f3ce8d6e2b76b9ac17675359659fcfa123dd247821e5dd3826c3bc092"}