{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NTMKJIHM7PAMMSR4D6R2BO555P","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":"5a014876e3b569cb4edb4005e9754a59d44ad65d680b2c2e680b4a1ec1565d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-04-23T08:13:13Z","title_canon_sha256":"7b48322d92ced3e57940b7ddf8f70aabe8a8fb88fc6be4bf25cb78787bdbdd82"},"schema_version":"1.0","source":{"id":"2605.20212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20212","created_at":"2026-05-21T00:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20212v1","created_at":"2026-05-21T00:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20212","created_at":"2026-05-21T00:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"NTMKJIHM7PAM","created_at":"2026-05-21T00:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"NTMKJIHM7PAMMSR4","created_at":"2026-05-21T00:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"NTMKJIHM","created_at":"2026-05-21T00:04:21Z"}],"graph_snapshots":[{"event_id":"sha256:029cebb276398a73c4def57ffbff963671655df81f31d029ef163318d668514c","target":"graph","created_at":"2026-05-21T00:04:21Z","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/2605.20212/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key results from real-valued convex analysis to the complex domain, establishing the validity of the minimax theorem and the preservation of saddle-point structure. Building on this foundation, we formulate a complex zero-sum game model that enables mixed strategies to interact with the real and imaginary components of the payoff matrix, and we characterize its sa","authors_text":"Abdel Lisser (L2S), Raneem Madani (L2S), Zeno Toffano (L2S)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-04-23T08:13:13Z","title":"Robust Chance Constrained Complex Zero-Sum Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20212","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":"sha256:5a3fdde4454fce1caf8b2e540d0f9935deb5e6cb7b9e6f238f35781e921d0805","target":"record","created_at":"2026-05-21T00:04:21Z","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":"5a014876e3b569cb4edb4005e9754a59d44ad65d680b2c2e680b4a1ec1565d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-04-23T08:13:13Z","title_canon_sha256":"7b48322d92ced3e57940b7ddf8f70aabe8a8fb88fc6be4bf25cb78787bdbdd82"},"schema_version":"1.0","source":{"id":"2605.20212","kind":"arxiv","version":1}},"canonical_sha256":"6cd8a4a0ecfbc0c64a3c1fa3a0bbbdebdf5f42d2d2c5e846375005cb853e463f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cd8a4a0ecfbc0c64a3c1fa3a0bbbdebdf5f42d2d2c5e846375005cb853e463f","first_computed_at":"2026-05-21T00:04:21.306656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T00:04:21.306656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhOmVmc2tBne7A+uKlIIYJZkFOeD39iK1qOtb+7N9792hQZ62/KqZ5H27Je56mKAtYlna1U9CKMyE5evsvYPDA==","signature_status":"signed_v1","signed_at":"2026-05-21T00:04:21.307420Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a3fdde4454fce1caf8b2e540d0f9935deb5e6cb7b9e6f238f35781e921d0805","sha256:029cebb276398a73c4def57ffbff963671655df81f31d029ef163318d668514c"],"state_sha256":"ce5dc5da4af1de7255e3cc1e779d5b1cf84d5d3c0af5d87da60300660b6faba6"}