{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YTPXSVFRTCIHIRA6EFRKWYEH5O","short_pith_number":"pith:YTPXSVFR","canonical_record":{"source":{"id":"2606.08428","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:56:30Z","cross_cats_sorted":[],"title_canon_sha256":"2d1f9bb2ad48ccec11bfa4a7ec7f965e866e5bdcc6915a85da260853ba9eda04","abstract_canon_sha256":"66621551206bdc92e55557d1d04d8ac8ff4d18df837db7870b55d92bd0398f11"},"schema_version":"1.0"},"canonical_sha256":"c4df7954b1989074441e2162ab6087eba8da1c8252851d05664b880c458c28a3","source":{"kind":"arxiv","id":"2606.08428","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08428","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08428v1","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08428","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"YTPXSVFRTCIH","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"YTPXSVFRTCIHIRA6","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"YTPXSVFR","created_at":"2026-06-09T01:05:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YTPXSVFRTCIHIRA6EFRKWYEH5O","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08428","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:56:30Z","cross_cats_sorted":[],"title_canon_sha256":"2d1f9bb2ad48ccec11bfa4a7ec7f965e866e5bdcc6915a85da260853ba9eda04","abstract_canon_sha256":"66621551206bdc92e55557d1d04d8ac8ff4d18df837db7870b55d92bd0398f11"},"schema_version":"1.0"},"canonical_sha256":"c4df7954b1989074441e2162ab6087eba8da1c8252851d05664b880c458c28a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:36.341947Z","signature_b64":"XMjjEfJdZjofhYhfS5iHnhQUASZUWa7IPV5Wj0B4YarG+euEQF5rlY5opkqwo+XLfMiAnna6zR6PsL+SmkZVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4df7954b1989074441e2162ab6087eba8da1c8252851d05664b880c458c28a3","last_reissued_at":"2026-06-09T01:05:36.341598Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:36.341598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08428","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":"2026-06-09T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8iOD5bT7UbSP+6N4hPx4oAw6moO1xUYyuuDOfJlvaQ9OzNlDOWDdb5WBFUOtQF7B3+P7S8a9x7tok3KCRDqsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:37.042185Z"},"content_sha256":"26a13931e278d0ae96f8338b92bfacd9515f7572e36d36d1f165dd88e271c62b","schema_version":"1.0","event_id":"sha256:26a13931e278d0ae96f8338b92bfacd9515f7572e36d36d1f165dd88e271c62b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YTPXSVFRTCIHIRA6EFRKWYEH5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Harvesting under Stochastic Control: HJB Equation and Feynman-Kac Representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fatamatuj Johora, Paramahansa Pramanik","submitted_at":"2026-06-07T02:56:30Z","abstract_excerpt":"Sustainable resource management requires harvesting strategies that account for environmental variability and ecological uncertainty. This study investigates optimal harvesting of renewable biological resources within a stochastic framework, where population dynamics are influenced by random environmental fluctuations and modeled using stochastic differential equations. Two complementary approaches are employed: the Hamilton-Jacobi-Bellman (HJB) equation and the Feynman-Kac representation. The HJB framework provides a dynamic optimization rule and characterizes the value function through a non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08428","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/2606.08428/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":"2026-06-09T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vpUhYFlDhOnkbHJ1GJkvr0qm3VGb+AdazKk06637Jpul0HeLut58mrOHHke7GCHTaZpzrg/QDJSxKYRYac2sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:37.042572Z"},"content_sha256":"caa89f504c3242ec86e691e0266d5f5f40b9c8ed24e9a320bbecfccdf37754b5","schema_version":"1.0","event_id":"sha256:caa89f504c3242ec86e691e0266d5f5f40b9c8ed24e9a320bbecfccdf37754b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/bundle.json","state_url":"https://pith.science/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/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":"2026-07-02T12:38:37Z","links":{"resolver":"https://pith.science/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O","bundle":"https://pith.science/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/bundle.json","state":"https://pith.science/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTPXSVFRTCIHIRA6EFRKWYEH5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YTPXSVFRTCIHIRA6EFRKWYEH5O","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":"66621551206bdc92e55557d1d04d8ac8ff4d18df837db7870b55d92bd0398f11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:56:30Z","title_canon_sha256":"2d1f9bb2ad48ccec11bfa4a7ec7f965e866e5bdcc6915a85da260853ba9eda04"},"schema_version":"1.0","source":{"id":"2606.08428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08428","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08428v1","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08428","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"YTPXSVFRTCIH","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"YTPXSVFRTCIHIRA6","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"YTPXSVFR","created_at":"2026-06-09T01:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:caa89f504c3242ec86e691e0266d5f5f40b9c8ed24e9a320bbecfccdf37754b5","target":"graph","created_at":"2026-06-09T01:05:36Z","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/2606.08428/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sustainable resource management requires harvesting strategies that account for environmental variability and ecological uncertainty. This study investigates optimal harvesting of renewable biological resources within a stochastic framework, where population dynamics are influenced by random environmental fluctuations and modeled using stochastic differential equations. Two complementary approaches are employed: the Hamilton-Jacobi-Bellman (HJB) equation and the Feynman-Kac representation. The HJB framework provides a dynamic optimization rule and characterizes the value function through a non","authors_text":"Fatamatuj Johora, Paramahansa Pramanik","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:56:30Z","title":"Optimal Harvesting under Stochastic Control: HJB Equation and Feynman-Kac Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08428","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":"sha256:26a13931e278d0ae96f8338b92bfacd9515f7572e36d36d1f165dd88e271c62b","target":"record","created_at":"2026-06-09T01:05:36Z","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":"66621551206bdc92e55557d1d04d8ac8ff4d18df837db7870b55d92bd0398f11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:56:30Z","title_canon_sha256":"2d1f9bb2ad48ccec11bfa4a7ec7f965e866e5bdcc6915a85da260853ba9eda04"},"schema_version":"1.0","source":{"id":"2606.08428","kind":"arxiv","version":1}},"canonical_sha256":"c4df7954b1989074441e2162ab6087eba8da1c8252851d05664b880c458c28a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4df7954b1989074441e2162ab6087eba8da1c8252851d05664b880c458c28a3","first_computed_at":"2026-06-09T01:05:36.341598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:36.341598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMjjEfJdZjofhYhfS5iHnhQUASZUWa7IPV5Wj0B4YarG+euEQF5rlY5opkqwo+XLfMiAnna6zR6PsL+SmkZVAQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:36.341947Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26a13931e278d0ae96f8338b92bfacd9515f7572e36d36d1f165dd88e271c62b","sha256:caa89f504c3242ec86e691e0266d5f5f40b9c8ed24e9a320bbecfccdf37754b5"],"state_sha256":"c0f53420bb3e9983aef32d0f70b49f338299ac46f52e99930731950f637a2c71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtYUfD3+W2yzysS81ZuxfB8jJthI02t8IST7EUD0xQxq1gxlElvgA6vOmFvIMWpkm+JoPCGOYD9BLxFR4jegCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:38:37.044961Z","bundle_sha256":"87a9892c4b90701a2b2fe25e563febac43986f6e0b3a0be0f384fe0006b72017"}}