{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MASJ5C7NEI6ODQ6SDGZDG637BY","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":"f798b284196c185184e3f25df81ba404d519c7396ba7549ea8bf513745f65eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-30T08:51:35Z","title_canon_sha256":"f25216b2c1e9c7ac23488e37a1686a26514d9052ffdd71f96d710db3138c5ac4"},"schema_version":"1.0","source":{"id":"1701.08514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08514","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08514v1","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08514","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"pith_short_12","alias_value":"MASJ5C7NEI6O","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MASJ5C7NEI6ODQ6S","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MASJ5C7N","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:d816357d3620785be191d365a0ab9d63f62aa894e6e20de17b245924eb65c6ee","target":"graph","created_at":"2026-05-18T00:51:53Z","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":"A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and strictly motivated by the interpretation of the payoff as multi-dimensional loss for one and gain for the other player. The new concept provides coherent worst case estimates, i.e. minimax and maximin strategies, for games with multi-dimensional payoffs. It is shown that-in contrast to games with one-dimensional payoff-minimax and maximin strategies are ind","authors_text":"Andreas H. Hamel, Andreas Loehne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-30T08:51:35Z","title":"A set optimization approach to zero-sum matrix games with multi-dimensional payoffs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08514","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":"sha256:5261199f04b197b725df3a8da961d63e3fcfea05c7904b106d75ac572afaf294","target":"record","created_at":"2026-05-18T00:51:53Z","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":"f798b284196c185184e3f25df81ba404d519c7396ba7549ea8bf513745f65eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-30T08:51:35Z","title_canon_sha256":"f25216b2c1e9c7ac23488e37a1686a26514d9052ffdd71f96d710db3138c5ac4"},"schema_version":"1.0","source":{"id":"1701.08514","kind":"arxiv","version":1}},"canonical_sha256":"60249e8bed223ce1c3d219b2337b7f0e1c92e8ac443b06f5966276680370d631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60249e8bed223ce1c3d219b2337b7f0e1c92e8ac443b06f5966276680370d631","first_computed_at":"2026-05-18T00:51:53.865101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:53.865101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gub/B+dGApC88j4ctSm0ng0/PdsDlme86YS4hnhEO2eVDfK5+0fPtSYg/RL41PGhRNe8IwtMgmPtTZLrb2l/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:53.865890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5261199f04b197b725df3a8da961d63e3fcfea05c7904b106d75ac572afaf294","sha256:d816357d3620785be191d365a0ab9d63f62aa894e6e20de17b245924eb65c6ee"],"state_sha256":"056ac77b0a211593760853def50fe8205407ba48d7fec8ebd9048d67f1ed8ac9"}