{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WYFGF3JA6CXSMEEFIJD4KGEUZS","short_pith_number":"pith:WYFGF3JA","schema_version":"1.0","canonical_sha256":"b60a62ed20f0af2610854247c51894cc908fdb17e059bd1b260d2887702f9dc2","source":{"kind":"arxiv","id":"2501.05169","version":1},"attestation_state":"computed","paper":{"title":"A New Value for Cooperative Games on Intersection-Closed Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Martin \\v{C}ern\\'y","submitted_at":"2025-01-09T11:43:40Z","abstract_excerpt":"We introduce a new allocation rule, the uniform-dividend value (UD-value), for cooperative games whose characteristic function is incomplete. The UD-value assigns payoffs by distributing the total surplus of each family of indistinguishable coalitions uniformly among them. Our primary focus is on set systems that are intersection-closed, for which we show the UD-value is uniquely determined and can be interpreted as the expected Shapley value over all positive (i.e., nonnegative-surplus) extensions of the incomplete game.\n  We compare the UD-value to two existing allocation rules for intersect"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.05169","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2025-01-09T11:43:40Z","cross_cats_sorted":[],"title_canon_sha256":"c059909eee875a960f1e70586986927a91f552882da863f32f206b03b70602a3","abstract_canon_sha256":"7bc7160bfe5f7065906a5d8c958442cb1986302c00854d01d95fc9503cfed907"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:05.536367Z","signature_b64":"dDo9pkx3kY9fAoMHMttQfJ6NR2uK8vL5OiOfpjF9DW5v1sWDR2kTB0wflRPzCD7lgdXOFxzXjvl5Wb+ap/KdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b60a62ed20f0af2610854247c51894cc908fdb17e059bd1b260d2887702f9dc2","last_reissued_at":"2026-07-05T09:59:05.535918Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:05.535918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Value for Cooperative Games on Intersection-Closed Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Martin \\v{C}ern\\'y","submitted_at":"2025-01-09T11:43:40Z","abstract_excerpt":"We introduce a new allocation rule, the uniform-dividend value (UD-value), for cooperative games whose characteristic function is incomplete. The UD-value assigns payoffs by distributing the total surplus of each family of indistinguishable coalitions uniformly among them. Our primary focus is on set systems that are intersection-closed, for which we show the UD-value is uniquely determined and can be interpreted as the expected Shapley value over all positive (i.e., nonnegative-surplus) extensions of the incomplete game.\n  We compare the UD-value to two existing allocation rules for intersect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05169","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.05169/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.05169","created_at":"2026-07-05T09:59:05.535989+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.05169v1","created_at":"2026-07-05T09:59:05.535989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05169","created_at":"2026-07-05T09:59:05.535989+00:00"},{"alias_kind":"pith_short_12","alias_value":"WYFGF3JA6CXS","created_at":"2026-07-05T09:59:05.535989+00:00"},{"alias_kind":"pith_short_16","alias_value":"WYFGF3JA6CXSMEEF","created_at":"2026-07-05T09:59:05.535989+00:00"},{"alias_kind":"pith_short_8","alias_value":"WYFGF3JA","created_at":"2026-07-05T09:59:05.535989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS","json":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS.json","graph_json":"https://pith.science/api/pith-number/WYFGF3JA6CXSMEEFIJD4KGEUZS/graph.json","events_json":"https://pith.science/api/pith-number/WYFGF3JA6CXSMEEFIJD4KGEUZS/events.json","paper":"https://pith.science/paper/WYFGF3JA"},"agent_actions":{"view_html":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS","download_json":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS.json","view_paper":"https://pith.science/paper/WYFGF3JA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.05169&json=true","fetch_graph":"https://pith.science/api/pith-number/WYFGF3JA6CXSMEEFIJD4KGEUZS/graph.json","fetch_events":"https://pith.science/api/pith-number/WYFGF3JA6CXSMEEFIJD4KGEUZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS/action/storage_attestation","attest_author":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS/action/author_attestation","sign_citation":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS/action/citation_signature","submit_replication":"https://pith.science/pith/WYFGF3JA6CXSMEEFIJD4KGEUZS/action/replication_record"}},"created_at":"2026-07-05T09:59:05.535989+00:00","updated_at":"2026-07-05T09:59:05.535989+00:00"}