{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BBUYKZZQEZMB7VF2IIWNOBQXXQ","short_pith_number":"pith:BBUYKZZQ","canonical_record":{"source":{"id":"1207.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-11T14:43:21Z","cross_cats_sorted":[],"title_canon_sha256":"eef04ee0c217469c8f7a393f8c6a9cffcc86e68cb588ed3b42728024ce9dfadf","abstract_canon_sha256":"fc37c232aba2258112ae8db9b9eb8ab8c73bfdccc2ee85281c968b37746e3857"},"schema_version":"1.0"},"canonical_sha256":"086985673026581fd4ba422cd70617bc2adb46321dd116df926ba6c9b992e9ed","source":{"kind":"arxiv","id":"1207.4115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4115","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4115v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4115","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"BBUYKZZQEZMB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BBUYKZZQEZMB7VF2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BBUYKZZQ","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BBUYKZZQEZMB7VF2IIWNOBQXXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-11T14:43:21Z","cross_cats_sorted":[],"title_canon_sha256":"eef04ee0c217469c8f7a393f8c6a9cffcc86e68cb588ed3b42728024ce9dfadf","abstract_canon_sha256":"fc37c232aba2258112ae8db9b9eb8ab8c73bfdccc2ee85281c968b37746e3857"},"schema_version":"1.0"},"canonical_sha256":"086985673026581fd4ba422cd70617bc2adb46321dd116df926ba6c9b992e9ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:47.943211Z","signature_b64":"3PQ19rzrCY1LjXTPTqQ/Jyk1GC2rCRyNb4De5qKBdYcKMDq/oioFeV2EsTK8vgMPr06enp3zgZZAgmXJeVU3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"086985673026581fd4ba422cd70617bc2adb46321dd116df926ba6c9b992e9ed","last_reissued_at":"2026-05-18T03:50:47.942643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:47.942643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.4115","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":"2026-05-18T03:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eAP7kUv4v7x0Pwiaw0CJwfhW+0nN7SDQrPkLoUF6tk3w7ZDbR5CvoLFcdSCc0ztLZ+a8kSxGj77V12++6hzhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:07:34.383502Z"},"content_sha256":"22ab185ff61b54c00e7886d13862f1e287e22c8d4b75fadaf218e6869171953f","schema_version":"1.0","event_id":"sha256:22ab185ff61b54c00e7886d13862f1e287e22c8d4b75fadaf218e6869171953f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BBUYKZZQEZMB7VF2IIWNOBQXXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Programming for Structured Continuous Markov Decision Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Nicolas Meuleau, Richard Dearden, Richard Washington, Zhengzhu Feng","submitted_at":"2012-07-11T14:43:21Z","abstract_excerpt":"We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4115","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":"2026-05-18T03:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uo18G/6xb6GXzuyyzZ9NFw9LnGc8C4jgXso5lTY/P3NgJfD/xy2SURyfif9g+Mug49xLRklYn14qtRhNEO93Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:07:34.384141Z"},"content_sha256":"6f019452874efe0451572be6cbc045343e7ca00eb65fc6f9b8c65887283aff1b","schema_version":"1.0","event_id":"sha256:6f019452874efe0451572be6cbc045343e7ca00eb65fc6f9b8c65887283aff1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/bundle.json","state_url":"https://pith.science/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/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":"2026-05-27T11:07:34Z","links":{"resolver":"https://pith.science/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ","bundle":"https://pith.science/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/bundle.json","state":"https://pith.science/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBUYKZZQEZMB7VF2IIWNOBQXXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BBUYKZZQEZMB7VF2IIWNOBQXXQ","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":"fc37c232aba2258112ae8db9b9eb8ab8c73bfdccc2ee85281c968b37746e3857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-11T14:43:21Z","title_canon_sha256":"eef04ee0c217469c8f7a393f8c6a9cffcc86e68cb588ed3b42728024ce9dfadf"},"schema_version":"1.0","source":{"id":"1207.4115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4115","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4115v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4115","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"BBUYKZZQEZMB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BBUYKZZQEZMB7VF2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BBUYKZZQ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:6f019452874efe0451572be6cbc045343e7ca00eb65fc6f9b8c65887283aff1b","target":"graph","created_at":"2026-05-18T03:50:47Z","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 describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions ","authors_text":"Nicolas Meuleau, Richard Dearden, Richard Washington, Zhengzhu Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-11T14:43:21Z","title":"Dynamic Programming for Structured Continuous Markov Decision Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4115","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":"sha256:22ab185ff61b54c00e7886d13862f1e287e22c8d4b75fadaf218e6869171953f","target":"record","created_at":"2026-05-18T03:50:47Z","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":"fc37c232aba2258112ae8db9b9eb8ab8c73bfdccc2ee85281c968b37746e3857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-11T14:43:21Z","title_canon_sha256":"eef04ee0c217469c8f7a393f8c6a9cffcc86e68cb588ed3b42728024ce9dfadf"},"schema_version":"1.0","source":{"id":"1207.4115","kind":"arxiv","version":1}},"canonical_sha256":"086985673026581fd4ba422cd70617bc2adb46321dd116df926ba6c9b992e9ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"086985673026581fd4ba422cd70617bc2adb46321dd116df926ba6c9b992e9ed","first_computed_at":"2026-05-18T03:50:47.942643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:47.942643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3PQ19rzrCY1LjXTPTqQ/Jyk1GC2rCRyNb4De5qKBdYcKMDq/oioFeV2EsTK8vgMPr06enp3zgZZAgmXJeVU3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:47.943211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22ab185ff61b54c00e7886d13862f1e287e22c8d4b75fadaf218e6869171953f","sha256:6f019452874efe0451572be6cbc045343e7ca00eb65fc6f9b8c65887283aff1b"],"state_sha256":"ea90d5dedf9021eb7bc75604876be5e8910cb9cfad8b2e2cf98a6ccaf6e31a0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cm9aP6gREvwElnVR8dISA17KuUVNyEeTbTl+N/eghSU+uzw4asEzbNkjpTjAFBVUU9TKPxA5ZkmoD7IOpVroAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:07:34.387887Z","bundle_sha256":"2d3ef34252fa8e1fa5f30cd4e3057b67d2b4266c824ab3163801fd67685a81d4"}}