{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:64RNX6DIR7ZHMWVSGCB2T5WR2N","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":"0833fccf19b4b533e07619dc44dc003434d43f4943b5aa1e36341b2e2464fdd5","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-03T15:04:44Z","title_canon_sha256":"d67927365285e6e5920e2e44926da61afe9aa02db2e814f177b817a08d063e51"},"schema_version":"1.0","source":{"id":"1509.01118","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01118","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01118v2","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01118","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"64RNX6DIR7ZH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"64RNX6DIR7ZHMWVS","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"64RNX6DI","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:53c11455fcbe84e5cf2a3d5fc2c7f325a0d80ec728278814e976d83a54ce73f1","target":"graph","created_at":"2026-05-18T00:56:38Z","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":"Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in $\\mathbb{R}_+$ with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.","authors_text":"Anup Biswas, Hitoshi Ishii, Lin Wang, Subhamay Saha","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-03T15:04:44Z","title":"On viscosity solution of HJB equations with state constraints and reflection control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01118","kind":"arxiv","version":2},"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:fc10c2ff581225fafcfdd4826fdb7b18c8dc45a72b7d0b57a11da4440a645717","target":"record","created_at":"2026-05-18T00:56:38Z","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":"0833fccf19b4b533e07619dc44dc003434d43f4943b5aa1e36341b2e2464fdd5","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-03T15:04:44Z","title_canon_sha256":"d67927365285e6e5920e2e44926da61afe9aa02db2e814f177b817a08d063e51"},"schema_version":"1.0","source":{"id":"1509.01118","kind":"arxiv","version":2}},"canonical_sha256":"f722dbf8688ff2765ab23083a9f6d1d35a270fc6cdfede3690824cb1135aec86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f722dbf8688ff2765ab23083a9f6d1d35a270fc6cdfede3690824cb1135aec86","first_computed_at":"2026-05-18T00:56:38.179923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:38.179923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4NjwvLSGSfd8gED2WbZB7JQHJpRBflE7RJVoZWjhOMVx/w396oZBRjjFceQmIitWWQDoZLqDMefGdXXYfL6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:38.180652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01118","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc10c2ff581225fafcfdd4826fdb7b18c8dc45a72b7d0b57a11da4440a645717","sha256:53c11455fcbe84e5cf2a3d5fc2c7f325a0d80ec728278814e976d83a54ce73f1"],"state_sha256":"1218971cbdfa84d2d3483c5a7f31b36797b0578ce89bf63dd5f039ca53a43f1c"}