{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HFQT6WQDDIMZ6WMOJ2DAL7GV2U","short_pith_number":"pith:HFQT6WQD","canonical_record":{"source":{"id":"1603.02400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-08T07:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"6ab505a49b73456376f52d1b1309b30758db3040560d0fbdc105a500abaa3809","abstract_canon_sha256":"2e0b8c34e3161a8bae5aa85a73cd86fe3072951a315e53fce628238870ac3055"},"schema_version":"1.0"},"canonical_sha256":"39613f5a031a199f598e4e8605fcd5d5218df302ae3d09c09c2fb74effbd14ab","source":{"kind":"arxiv","id":"1603.02400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02400","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02400v1","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02400","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"HFQT6WQDDIMZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HFQT6WQDDIMZ6WMO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HFQT6WQD","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HFQT6WQDDIMZ6WMOJ2DAL7GV2U","target":"record","payload":{"canonical_record":{"source":{"id":"1603.02400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-08T07:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"6ab505a49b73456376f52d1b1309b30758db3040560d0fbdc105a500abaa3809","abstract_canon_sha256":"2e0b8c34e3161a8bae5aa85a73cd86fe3072951a315e53fce628238870ac3055"},"schema_version":"1.0"},"canonical_sha256":"39613f5a031a199f598e4e8605fcd5d5218df302ae3d09c09c2fb74effbd14ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:23.465636Z","signature_b64":"BmmApjzku2kQTDXAAskAyvb5qIuu3LH2nmkhlyWkPfv54l4KXRlf36tSWKkvgK1qx2EFwGFiXuVR4Bd9YfblBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39613f5a031a199f598e4e8605fcd5d5218df302ae3d09c09c2fb74effbd14ab","last_reissued_at":"2026-05-18T01:19:23.464839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:23.464839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.02400","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":"2026-05-18T01:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xwprn0/Cfp34AmNJO0+LzEhJU+7zEEYT5CXOFNZSjiEchIrYHFyWvz3kYr3Tqh3vRge4u8TN76Yv7dWug96EBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:03:00.491270Z"},"content_sha256":"5ffd918bd2c64503fdd741150a10293bea63d8c01c57989babc7e9c5f788ae2e","schema_version":"1.0","event_id":"sha256:5ffd918bd2c64503fdd741150a10293bea63d8c01c57989babc7e9c5f788ae2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HFQT6WQDDIMZ6WMOJ2DAL7GV2U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-sum Risk-sensitive Stochastic Games for Continuous Time Markov Chains","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":"2016-03-08T07:20:05Z","abstract_excerpt":"We study infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space. For the discounted-cost game we prove the existence of value and saddle-point equilibrium in the class of Markov strategies under nominal conditions. For the ergodic-cost game we prove the existence of values and saddle point equilibrium by studying the corresponding Hamilton-Jacobi-Isaacs equation under a certain Lyapunov condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02400","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":"2026-05-18T01:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aopv2rYkmIiyG3cPWnr7dL5V7U1RL5EpmJznPNncjpUjL9BsH3Hr5ZNDxY/2RZYAaEW8p4HbTL++ozLNfQ+8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:03:00.491621Z"},"content_sha256":"94fe2294489552d3e8a528595324a828e3805a75a0aa882d68280e0c7de27c77","schema_version":"1.0","event_id":"sha256:94fe2294489552d3e8a528595324a828e3805a75a0aa882d68280e0c7de27c77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/bundle.json","state_url":"https://pith.science/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/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":"2026-06-23T05:03:00Z","links":{"resolver":"https://pith.science/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U","bundle":"https://pith.science/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/bundle.json","state":"https://pith.science/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFQT6WQDDIMZ6WMOJ2DAL7GV2U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HFQT6WQDDIMZ6WMOJ2DAL7GV2U","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":"2e0b8c34e3161a8bae5aa85a73cd86fe3072951a315e53fce628238870ac3055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-08T07:20:05Z","title_canon_sha256":"6ab505a49b73456376f52d1b1309b30758db3040560d0fbdc105a500abaa3809"},"schema_version":"1.0","source":{"id":"1603.02400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02400","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02400v1","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02400","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"HFQT6WQDDIMZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HFQT6WQDDIMZ6WMO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HFQT6WQD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:94fe2294489552d3e8a528595324a828e3805a75a0aa882d68280e0c7de27c77","target":"graph","created_at":"2026-05-18T01:19:23Z","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 infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space. For the discounted-cost game we prove the existence of value and saddle-point equilibrium in the class of Markov strategies under nominal conditions. For the ergodic-cost game we prove the existence of values and saddle point equilibrium by studying the corresponding Hamilton-Jacobi-Isaacs equation under a certain Lyapunov condition.","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":"2016-03-08T07:20:05Z","title":"Zero-sum Risk-sensitive Stochastic Games for Continuous Time Markov Chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02400","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":"sha256:5ffd918bd2c64503fdd741150a10293bea63d8c01c57989babc7e9c5f788ae2e","target":"record","created_at":"2026-05-18T01:19:23Z","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":"2e0b8c34e3161a8bae5aa85a73cd86fe3072951a315e53fce628238870ac3055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-08T07:20:05Z","title_canon_sha256":"6ab505a49b73456376f52d1b1309b30758db3040560d0fbdc105a500abaa3809"},"schema_version":"1.0","source":{"id":"1603.02400","kind":"arxiv","version":1}},"canonical_sha256":"39613f5a031a199f598e4e8605fcd5d5218df302ae3d09c09c2fb74effbd14ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39613f5a031a199f598e4e8605fcd5d5218df302ae3d09c09c2fb74effbd14ab","first_computed_at":"2026-05-18T01:19:23.464839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:23.464839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmmApjzku2kQTDXAAskAyvb5qIuu3LH2nmkhlyWkPfv54l4KXRlf36tSWKkvgK1qx2EFwGFiXuVR4Bd9YfblBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:23.465636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ffd918bd2c64503fdd741150a10293bea63d8c01c57989babc7e9c5f788ae2e","sha256:94fe2294489552d3e8a528595324a828e3805a75a0aa882d68280e0c7de27c77"],"state_sha256":"60c8bce822572d8f63d165c355f2b18a3efd2fbeeea2fbdbe1ee04bfde24cedd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6C0LcjOaREJILPvvPdoeaZJrdZMs3G1tcxLJBM+8w874v28+S3h/G2Y9jtnpSeiIsImdb92u3HaNzZugYwLRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:03:00.493492Z","bundle_sha256":"4a099696c6f83246cce8cad85a5c63ddd3b31f602e8ba1fa6f20961f95ef7600"}}