{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:US55XHA4ZP2JIY5VHSVCRSX5NQ","short_pith_number":"pith:US55XHA4","canonical_record":{"source":{"id":"2606.25707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-06-24T11:19:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1ac28a8eab4db96d25c4499b626abb1d5d066b3a917471538cca83d4122cd2a3","abstract_canon_sha256":"377a4db643c48418fe5de4be018913bec0918541dea50730cbb5698d62c5b8ee"},"schema_version":"1.0"},"canonical_sha256":"a4bbdb9c1ccbf49463b53caa28cafd6c1fa8382420de9a31aa7d97f3adf45fe2","source":{"kind":"arxiv","id":"2606.25707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25707","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25707v1","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25707","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"US55XHA4ZP2J","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"US55XHA4ZP2JIY5V","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"US55XHA4","created_at":"2026-06-25T01:18:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:US55XHA4ZP2JIY5VHSVCRSX5NQ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.25707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-06-24T11:19:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1ac28a8eab4db96d25c4499b626abb1d5d066b3a917471538cca83d4122cd2a3","abstract_canon_sha256":"377a4db643c48418fe5de4be018913bec0918541dea50730cbb5698d62c5b8ee"},"schema_version":"1.0"},"canonical_sha256":"a4bbdb9c1ccbf49463b53caa28cafd6c1fa8382420de9a31aa7d97f3adf45fe2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:13.280637Z","signature_b64":"rYAQP4IJKobtQD7QYNL9P8aBbZADyQ5i+1NimR2AZN6x9eZaFQW31ol1sH1e3C9Z4lnnR7W5zNBhMAG/sjy/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4bbdb9c1ccbf49463b53caa28cafd6c1fa8382420de9a31aa7d97f3adf45fe2","last_reissued_at":"2026-06-25T01:18:13.280240Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:13.280240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.25707","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGyEdXXptUGddBV8EAGW+iaXRqM3osmUtUfW3G5bDD9gdwFI1Y0MJVF7A0DQPAxhM/CjgTAbd4Y3n1W/MylbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:23:38.595828Z"},"content_sha256":"3446f067492c1d730ee66ee99c6c91b258278012165f235e824495b255788a25","schema_version":"1.0","event_id":"sha256:3446f067492c1d730ee66ee99c6c91b258278012165f235e824495b255788a25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:US55XHA4ZP2JIY5VHSVCRSX5NQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium and Infeasibility: A new solution concept for games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.GT","authors_text":"Anne Reulke (LIA), LIA), Mika\\\"el Touati, Rachid El-Azouzi (FR 3621","submitted_at":"2026-06-24T11:19:44Z","abstract_excerpt":"Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $\\psi$-penalized solution as a strategy profile maximizing every player's uti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25707","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/2606.25707/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RtM6DZLbrSWZhrAqBLV1woXI1R4c/aTMTwDH9p8JFNvTzzeCjtvG1xFbpBvCMdqWqLpDMnw87oGEWaapG5ucDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:23:38.596219Z"},"content_sha256":"c58b02e9ead36b8126f6757e8b1d581864099531be9f64ded43063935dc63a5f","schema_version":"1.0","event_id":"sha256:c58b02e9ead36b8126f6757e8b1d581864099531be9f64ded43063935dc63a5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/bundle.json","state_url":"https://pith.science/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T11:23:38Z","links":{"resolver":"https://pith.science/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ","bundle":"https://pith.science/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/bundle.json","state":"https://pith.science/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/US55XHA4ZP2JIY5VHSVCRSX5NQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:US55XHA4ZP2JIY5VHSVCRSX5NQ","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":"377a4db643c48418fe5de4be018913bec0918541dea50730cbb5698d62c5b8ee","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-06-24T11:19:44Z","title_canon_sha256":"1ac28a8eab4db96d25c4499b626abb1d5d066b3a917471538cca83d4122cd2a3"},"schema_version":"1.0","source":{"id":"2606.25707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25707","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25707v1","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25707","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"US55XHA4ZP2J","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"US55XHA4ZP2JIY5V","created_at":"2026-06-25T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"US55XHA4","created_at":"2026-06-25T01:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:c58b02e9ead36b8126f6757e8b1d581864099531be9f64ded43063935dc63a5f","target":"graph","created_at":"2026-06-25T01:18:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.25707/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $\\psi$-penalized solution as a strategy profile maximizing every player's uti","authors_text":"Anne Reulke (LIA), LIA), Mika\\\"el Touati, Rachid El-Azouzi (FR 3621","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-06-24T11:19:44Z","title":"Equilibrium and Infeasibility: A new solution concept for games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25707","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":"sha256:3446f067492c1d730ee66ee99c6c91b258278012165f235e824495b255788a25","target":"record","created_at":"2026-06-25T01:18:13Z","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":"377a4db643c48418fe5de4be018913bec0918541dea50730cbb5698d62c5b8ee","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-06-24T11:19:44Z","title_canon_sha256":"1ac28a8eab4db96d25c4499b626abb1d5d066b3a917471538cca83d4122cd2a3"},"schema_version":"1.0","source":{"id":"2606.25707","kind":"arxiv","version":1}},"canonical_sha256":"a4bbdb9c1ccbf49463b53caa28cafd6c1fa8382420de9a31aa7d97f3adf45fe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4bbdb9c1ccbf49463b53caa28cafd6c1fa8382420de9a31aa7d97f3adf45fe2","first_computed_at":"2026-06-25T01:18:13.280240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:13.280240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rYAQP4IJKobtQD7QYNL9P8aBbZADyQ5i+1NimR2AZN6x9eZaFQW31ol1sH1e3C9Z4lnnR7W5zNBhMAG/sjy/Aw==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:13.280637Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3446f067492c1d730ee66ee99c6c91b258278012165f235e824495b255788a25","sha256:c58b02e9ead36b8126f6757e8b1d581864099531be9f64ded43063935dc63a5f"],"state_sha256":"52c0703720e8e3ba9805fe4e43fa11ecd63fbec738df118085290b6fd7f41f2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQPZysij7uS660Krm1GuODjKijz7TwsgYWGiDs/vCj0R1S+95BVnT3+xlfq1DPa7RGwLBCIQq3vE4R2ayB9iCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T11:23:38.598222Z","bundle_sha256":"8b7553d7aa881f4e17c5342dbb11b7f64b4973317ceb9370ee486cfbe3c26a97"}}