{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:S2U6GEKGJHQDDY57EQVI7MHDGM","short_pith_number":"pith:S2U6GEKG","canonical_record":{"source":{"id":"1909.00387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-01T12:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"75a9621a4f216b86b8640887ec07525d2a6b11cac228cebc263b50786d8a8f2d","abstract_canon_sha256":"4219f850d27d464bf31f94c8dc96d85dea42dcaee977d9f19532a57e785495fd"},"schema_version":"1.0"},"canonical_sha256":"96a9e3114649e031e3bf242a8fb0e333053ab08c7b8c422c8e77e9822ba78ad1","source":{"kind":"arxiv","id":"1909.00387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.00387","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"1909.00387v1","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00387","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"S2U6GEKGJHQD","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"S2U6GEKGJHQDDY57","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"S2U6GEKG","created_at":"2026-07-05T00:01:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:S2U6GEKGJHQDDY57EQVI7MHDGM","target":"record","payload":{"canonical_record":{"source":{"id":"1909.00387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-01T12:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"75a9621a4f216b86b8640887ec07525d2a6b11cac228cebc263b50786d8a8f2d","abstract_canon_sha256":"4219f850d27d464bf31f94c8dc96d85dea42dcaee977d9f19532a57e785495fd"},"schema_version":"1.0"},"canonical_sha256":"96a9e3114649e031e3bf242a8fb0e333053ab08c7b8c422c8e77e9822ba78ad1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:01:08.583582Z","signature_b64":"MPLVOinSH4kRm+X0zflbZoCYiRyhW8lq3EcCYhbxFJtnF+drlQVJYQSnq0qvisxY76Rw4Lj1fMDnYVkvZJ4JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a9e3114649e031e3bf242a8fb0e333053ab08c7b8c422c8e77e9822ba78ad1","last_reissued_at":"2026-07-05T00:01:08.583243Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:01:08.583243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.00387","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":"2026-07-05T00:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LPf/cm3c8jjbRafSO9hlPh6qaLcRF1+4C0TDl7YdqqCMfWqnSn7a3zJIoXsoKg7bLEhQ8iQWomm1Cb5fI87Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:41:15.592105Z"},"content_sha256":"e6010554ea119112b9ebbda918f05cb5496689cc4bef4f40f4e838761fe889db","schema_version":"1.0","event_id":"sha256:e6010554ea119112b9ebbda918f05cb5496689cc4bef4f40f4e838761fe889db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:S2U6GEKGJHQDDY57EQVI7MHDGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subdifferentials of Value Functions in Nonconvex Dynamic Programming for Nonstationary Stochastic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Nobusumi Sagara","submitted_at":"2019-09-01T12:15:22Z","abstract_excerpt":"The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity assumptions. Unlike to standard stochastic DP with stationary Markov processes, we investigate here stochastic DP in $L^p$ spaces to deal with nonstationary stochastic processes, which describe a more flexible learning procedure for the decision-maker. Our main concern is to calculate generalized subgradients of the corresponding value function and to derive ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00387","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/1909.00387/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":"2026-07-05T00:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQqsVB2fcFRGg8uaf+hGmjr4bMm1EpugMGPd0Sx2SuzBOkHQ3hTS3YbPHyTgdeg65uePh4q5j1f8eIUW4Li9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:41:15.593023Z"},"content_sha256":"dc8b9e754bf5f6dc314351097342e4929f62dae4203135f2d3277d891c907916","schema_version":"1.0","event_id":"sha256:dc8b9e754bf5f6dc314351097342e4929f62dae4203135f2d3277d891c907916"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/bundle.json","state_url":"https://pith.science/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/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":"2026-08-18T07:41:15Z","links":{"resolver":"https://pith.science/pith/S2U6GEKGJHQDDY57EQVI7MHDGM","bundle":"https://pith.science/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/bundle.json","state":"https://pith.science/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2U6GEKGJHQDDY57EQVI7MHDGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:S2U6GEKGJHQDDY57EQVI7MHDGM","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":"4219f850d27d464bf31f94c8dc96d85dea42dcaee977d9f19532a57e785495fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-01T12:15:22Z","title_canon_sha256":"75a9621a4f216b86b8640887ec07525d2a6b11cac228cebc263b50786d8a8f2d"},"schema_version":"1.0","source":{"id":"1909.00387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.00387","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"1909.00387v1","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00387","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"S2U6GEKGJHQD","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"S2U6GEKGJHQDDY57","created_at":"2026-07-05T00:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"S2U6GEKG","created_at":"2026-07-05T00:01:08Z"}],"graph_snapshots":[{"event_id":"sha256:dc8b9e754bf5f6dc314351097342e4929f62dae4203135f2d3277d891c907916","target":"graph","created_at":"2026-07-05T00:01:08Z","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/1909.00387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity assumptions. Unlike to standard stochastic DP with stationary Markov processes, we investigate here stochastic DP in $L^p$ spaces to deal with nonstationary stochastic processes, which describe a more flexible learning procedure for the decision-maker. Our main concern is to calculate generalized subgradients of the corresponding value function and to derive ne","authors_text":"Boris S. Mordukhovich, Nobusumi Sagara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-01T12:15:22Z","title":"Subdifferentials of Value Functions in Nonconvex Dynamic Programming for Nonstationary Stochastic Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00387","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:e6010554ea119112b9ebbda918f05cb5496689cc4bef4f40f4e838761fe889db","target":"record","created_at":"2026-07-05T00:01:08Z","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":"4219f850d27d464bf31f94c8dc96d85dea42dcaee977d9f19532a57e785495fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-01T12:15:22Z","title_canon_sha256":"75a9621a4f216b86b8640887ec07525d2a6b11cac228cebc263b50786d8a8f2d"},"schema_version":"1.0","source":{"id":"1909.00387","kind":"arxiv","version":1}},"canonical_sha256":"96a9e3114649e031e3bf242a8fb0e333053ab08c7b8c422c8e77e9822ba78ad1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96a9e3114649e031e3bf242a8fb0e333053ab08c7b8c422c8e77e9822ba78ad1","first_computed_at":"2026-07-05T00:01:08.583243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:01:08.583243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MPLVOinSH4kRm+X0zflbZoCYiRyhW8lq3EcCYhbxFJtnF+drlQVJYQSnq0qvisxY76Rw4Lj1fMDnYVkvZJ4JBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:01:08.583582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.00387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6010554ea119112b9ebbda918f05cb5496689cc4bef4f40f4e838761fe889db","sha256:dc8b9e754bf5f6dc314351097342e4929f62dae4203135f2d3277d891c907916"],"state_sha256":"370fefd93d379e096bdbb1be67435c088e9cc55076b3e8aa2a45d1cd18af3826"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uupTeNbalcfcLYIwR3MH1EZ9nFIEwtSyZGWHCLtoiWbbby4cy27zZ//0L7UZyg6HCHVXLhplUY/5LSqq3gfCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:41:15.604641Z","bundle_sha256":"faad4753f30ed52177334b9dfd61f1d067f6d8f761f9ebf886205e012a2b86b2"}}