{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:55IU5DU5JSD4R7OBKBCUHTZUNZ","short_pith_number":"pith:55IU5DU5","canonical_record":{"source":{"id":"1604.01142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-05T05:43:58Z","cross_cats_sorted":[],"title_canon_sha256":"57eca4b797980e67d630f50f235282bef75ceda81f707034497045c6af159722","abstract_canon_sha256":"875fdc39bfc333373abb73dc8fdea3674a948a089f3d40cea3e03d1ebb6fe42b"},"schema_version":"1.0"},"canonical_sha256":"ef514e8e9d4c87c8fdc1504543cf346e663c985dc2953f53a558abf830eb4e60","source":{"kind":"arxiv","id":"1604.01142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01142","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01142v1","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01142","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"55IU5DU5JSD4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55IU5DU5JSD4R7OB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55IU5DU5","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:55IU5DU5JSD4R7OBKBCUHTZUNZ","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-05T05:43:58Z","cross_cats_sorted":[],"title_canon_sha256":"57eca4b797980e67d630f50f235282bef75ceda81f707034497045c6af159722","abstract_canon_sha256":"875fdc39bfc333373abb73dc8fdea3674a948a089f3d40cea3e03d1ebb6fe42b"},"schema_version":"1.0"},"canonical_sha256":"ef514e8e9d4c87c8fdc1504543cf346e663c985dc2953f53a558abf830eb4e60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:44.662791Z","signature_b64":"3q0mKdw3m6wg9DEVnhNdAR4uQDfLi6o4FV27nLuUuZXD/wMnMHDifXOcfCvl1YFmb9Dh/v2s4NmYopO2vndfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef514e8e9d4c87c8fdc1504543cf346e663c985dc2953f53a558abf830eb4e60","last_reissued_at":"2026-05-18T01:17:44.662124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:44.662124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01142","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":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/luCsqgHCBVREHBjcb51ShtkraIUZ2MA9+wbF8/9omkkZkqAkSk2FAzq5VOoYHgePR7ixaCGH/1VRTItkU6PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:32:57.473903Z"},"content_sha256":"98b5182b7adaf9a091922f5d1c362131e2f4ac3424e0c9721778203aedb7a2fe","schema_version":"1.0","event_id":"sha256:98b5182b7adaf9a091922f5d1c362131e2f4ac3424e0c9721778203aedb7a2fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:55IU5DU5JSD4R7OBKBCUHTZUNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonzero-sum risk-sensitive stochastic differential games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chandan Pal, K. Suresh Kumar, Mrinal K. Ghosh","submitted_at":"2016-04-05T05:43:58Z","abstract_excerpt":"We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a Nash equilibrium in stationary strategies for the ergodic cost criterion. We achieve our results by studying the relevant systems of coupled HJB equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01142","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":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6fmbn2XGGAZyGV+spBJXtgwfaxJTvODZ92PpFce5bb6tie3ytHMioQRGiuGELJKnahZsrzH72wNE0gFMVaDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:32:57.474595Z"},"content_sha256":"e11e54f0c7dde7a40e6350c94190558d7d9474fc1c7d33e1c2f6c5098747a480","schema_version":"1.0","event_id":"sha256:e11e54f0c7dde7a40e6350c94190558d7d9474fc1c7d33e1c2f6c5098747a480"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/bundle.json","state_url":"https://pith.science/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/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":"2026-06-23T01:32:57Z","links":{"resolver":"https://pith.science/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ","bundle":"https://pith.science/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/bundle.json","state":"https://pith.science/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55IU5DU5JSD4R7OBKBCUHTZUNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:55IU5DU5JSD4R7OBKBCUHTZUNZ","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":"875fdc39bfc333373abb73dc8fdea3674a948a089f3d40cea3e03d1ebb6fe42b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-05T05:43:58Z","title_canon_sha256":"57eca4b797980e67d630f50f235282bef75ceda81f707034497045c6af159722"},"schema_version":"1.0","source":{"id":"1604.01142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01142","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01142v1","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01142","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"55IU5DU5JSD4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55IU5DU5JSD4R7OB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55IU5DU5","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:e11e54f0c7dde7a40e6350c94190558d7d9474fc1c7d33e1c2f6c5098747a480","target":"graph","created_at":"2026-05-18T01:17:44Z","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":"We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a Nash equilibrium in stationary strategies for the ergodic cost criterion. We achieve our results by studying the relevant systems of coupled HJB equations.","authors_text":"Chandan Pal, K. Suresh Kumar, Mrinal K. Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-05T05:43:58Z","title":"Nonzero-sum risk-sensitive stochastic differential games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01142","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":"sha256:98b5182b7adaf9a091922f5d1c362131e2f4ac3424e0c9721778203aedb7a2fe","target":"record","created_at":"2026-05-18T01:17:44Z","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":"875fdc39bfc333373abb73dc8fdea3674a948a089f3d40cea3e03d1ebb6fe42b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-05T05:43:58Z","title_canon_sha256":"57eca4b797980e67d630f50f235282bef75ceda81f707034497045c6af159722"},"schema_version":"1.0","source":{"id":"1604.01142","kind":"arxiv","version":1}},"canonical_sha256":"ef514e8e9d4c87c8fdc1504543cf346e663c985dc2953f53a558abf830eb4e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef514e8e9d4c87c8fdc1504543cf346e663c985dc2953f53a558abf830eb4e60","first_computed_at":"2026-05-18T01:17:44.662124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:44.662124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3q0mKdw3m6wg9DEVnhNdAR4uQDfLi6o4FV27nLuUuZXD/wMnMHDifXOcfCvl1YFmb9Dh/v2s4NmYopO2vndfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:44.662791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98b5182b7adaf9a091922f5d1c362131e2f4ac3424e0c9721778203aedb7a2fe","sha256:e11e54f0c7dde7a40e6350c94190558d7d9474fc1c7d33e1c2f6c5098747a480"],"state_sha256":"9fbea9d23747b425817ed1072e029a6098bc8492f31135eaab2d3b9a94169e62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ACmkf46R5IYzoX86c7U4j6/jw6JcwLD1f/fwrjGtVF1glQBT+rQFnCgPR+Y1Ze/RzVgVvpD9P1FG58BXoTOuBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:32:57.477641Z","bundle_sha256":"cd561446ee502c9f36d20256b52022a25d9fec4dd88a29a77127377c21e73415"}}