{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:274Q2VJIBMOTJUWICTY6OBKQOD","short_pith_number":"pith:274Q2VJI","canonical_record":{"source":{"id":"1202.1443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-07T15:03:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"af8d308734cc2f7511c770dad3b28da1f8beba7d6618de893f428f2b2dc790f2","abstract_canon_sha256":"7974d2da8b99df84e2c32daf1647522f76d79fbc122cdee6fa9bf111847a2f42"},"schema_version":"1.0"},"canonical_sha256":"d7f90d55280b1d34d2c814f1e7055070c448c8640e20edcf1a76c3a774ffa584","source":{"kind":"arxiv","id":"1202.1443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1443","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1443v1","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1443","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"274Q2VJIBMOT","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"274Q2VJIBMOTJUWI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"274Q2VJI","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:274Q2VJIBMOTJUWICTY6OBKQOD","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-07T15:03:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"af8d308734cc2f7511c770dad3b28da1f8beba7d6618de893f428f2b2dc790f2","abstract_canon_sha256":"7974d2da8b99df84e2c32daf1647522f76d79fbc122cdee6fa9bf111847a2f42"},"schema_version":"1.0"},"canonical_sha256":"d7f90d55280b1d34d2c814f1e7055070c448c8640e20edcf1a76c3a774ffa584","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:53.358659Z","signature_b64":"omdFesjaLIyxdh/9NaX2cv7FL/l3mxc0F8LCGDUDNzu/IWbyQoD3tb4JCImSLdP2EDYXjmXITfqlZeMCRRRlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7f90d55280b1d34d2c814f1e7055070c448c8640e20edcf1a76c3a774ffa584","last_reissued_at":"2026-05-18T04:02:53.357820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:53.357820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1443","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":"2026-05-18T04:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpeD40HJX0HRUWcBbc21opRqKoGcAwn6jT+8ml/ZWJzazWWvmaClZgK4KZkCgLkg43roZaqRx/QMZZa3/i8CDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:20:38.835359Z"},"content_sha256":"03cfc08a6640e7ca618d8d83034ff2e489bc0b9cd6a4c2fbea58007b94d3688f","schema_version":"1.0","event_id":"sha256:03cfc08a6640e7ca618d8d83034ff2e489bc0b9cd6a4c2fbea58007b94d3688f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:274Q2VJIBMOTJUWICTY6OBKQOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Juan Li, Marc Quincampoix, Rainer Buckdahn","submitted_at":"2012-02-07T15:03:43Z","abstract_excerpt":"In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are associated with classical nonanticipative strategies (with delay). Imposing on the underlying controls for both players a conditional independence property, we obtain the existence of the value in mixed strategies as the limit of the lower as well as of the upper value functions along a sequence of partitions which mesh tends to zero. Moreover, we characterize t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1443","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":""},"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":"2026-05-18T04:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PjUdrQP0IZY4BgatAqR0mQ3X5VRZtrHOihxFFU/tujX0YzHMl1YEx3ctCg42u8QWMY3n9rXe5xD6yyDbfjXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:20:38.835721Z"},"content_sha256":"5d76fb69288bb86585f41da0de87887894a03c690333e008fb5d61c73d00f7cc","schema_version":"1.0","event_id":"sha256:5d76fb69288bb86585f41da0de87887894a03c690333e008fb5d61c73d00f7cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/274Q2VJIBMOTJUWICTY6OBKQOD/bundle.json","state_url":"https://pith.science/pith/274Q2VJIBMOTJUWICTY6OBKQOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/274Q2VJIBMOTJUWICTY6OBKQOD/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":"2026-06-02T16:20:38Z","links":{"resolver":"https://pith.science/pith/274Q2VJIBMOTJUWICTY6OBKQOD","bundle":"https://pith.science/pith/274Q2VJIBMOTJUWICTY6OBKQOD/bundle.json","state":"https://pith.science/pith/274Q2VJIBMOTJUWICTY6OBKQOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/274Q2VJIBMOTJUWICTY6OBKQOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:274Q2VJIBMOTJUWICTY6OBKQOD","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":"7974d2da8b99df84e2c32daf1647522f76d79fbc122cdee6fa9bf111847a2f42","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-07T15:03:43Z","title_canon_sha256":"af8d308734cc2f7511c770dad3b28da1f8beba7d6618de893f428f2b2dc790f2"},"schema_version":"1.0","source":{"id":"1202.1443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1443","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1443v1","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1443","created_at":"2026-05-18T04:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"274Q2VJIBMOT","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"274Q2VJIBMOTJUWI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"274Q2VJI","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:5d76fb69288bb86585f41da0de87887894a03c690333e008fb5d61c73d00f7cc","target":"graph","created_at":"2026-05-18T04:02:53Z","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":"In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are associated with classical nonanticipative strategies (with delay). Imposing on the underlying controls for both players a conditional independence property, we obtain the existence of the value in mixed strategies as the limit of the lower as well as of the upper value functions along a sequence of partitions which mesh tends to zero. Moreover, we characterize t","authors_text":"Juan Li, Marc Quincampoix, Rainer Buckdahn","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-07T15:03:43Z","title":"Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1443","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":"sha256:03cfc08a6640e7ca618d8d83034ff2e489bc0b9cd6a4c2fbea58007b94d3688f","target":"record","created_at":"2026-05-18T04:02:53Z","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":"7974d2da8b99df84e2c32daf1647522f76d79fbc122cdee6fa9bf111847a2f42","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-07T15:03:43Z","title_canon_sha256":"af8d308734cc2f7511c770dad3b28da1f8beba7d6618de893f428f2b2dc790f2"},"schema_version":"1.0","source":{"id":"1202.1443","kind":"arxiv","version":1}},"canonical_sha256":"d7f90d55280b1d34d2c814f1e7055070c448c8640e20edcf1a76c3a774ffa584","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7f90d55280b1d34d2c814f1e7055070c448c8640e20edcf1a76c3a774ffa584","first_computed_at":"2026-05-18T04:02:53.357820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:53.357820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"omdFesjaLIyxdh/9NaX2cv7FL/l3mxc0F8LCGDUDNzu/IWbyQoD3tb4JCImSLdP2EDYXjmXITfqlZeMCRRRlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:53.358659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03cfc08a6640e7ca618d8d83034ff2e489bc0b9cd6a4c2fbea58007b94d3688f","sha256:5d76fb69288bb86585f41da0de87887894a03c690333e008fb5d61c73d00f7cc"],"state_sha256":"9a1060474a25bef12f29b9e87977ff80aa473d7cc1892146cefd482f60118ef0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zChBWWFM0Qs/jlLnn+qlHtXCmD064ry11MpqBrgDruuvRsCLeBYD8/87NUg39DzmuNElYg/sPNKd+c21pn0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:20:38.837649Z","bundle_sha256":"742867af8a73cc5fdd94abeb6e64eeffee4d5078b1f1c20be56f65e09821672e"}}