{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AM37NEN2ETFLGEIXJIETCO4KOM","short_pith_number":"pith:AM37NEN2","canonical_record":{"source":{"id":"1507.01026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-03T20:41:40Z","cross_cats_sorted":["cs.DS","math.NA","math.OC"],"title_canon_sha256":"05db5cd0ff083dbff1e17f1396c3ef9a03b51672be71f391b2597ed000baa987","abstract_canon_sha256":"f21c88e1c8fb87c4592957e9bb2407ba7e8cdd5fc51517ca43c1a5906441b8fc"},"schema_version":"1.0"},"canonical_sha256":"0337f691ba24cab311174a09313b8a731232abf3f877127354ef064528d1ee90","source":{"kind":"arxiv","id":"1507.01026","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01026","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01026v2","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01026","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"AM37NEN2ETFL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AM37NEN2ETFLGEIX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AM37NEN2","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AM37NEN2ETFLGEIXJIETCO4KOM","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-03T20:41:40Z","cross_cats_sorted":["cs.DS","math.NA","math.OC"],"title_canon_sha256":"05db5cd0ff083dbff1e17f1396c3ef9a03b51672be71f391b2597ed000baa987","abstract_canon_sha256":"f21c88e1c8fb87c4592957e9bb2407ba7e8cdd5fc51517ca43c1a5906441b8fc"},"schema_version":"1.0"},"canonical_sha256":"0337f691ba24cab311174a09313b8a731232abf3f877127354ef064528d1ee90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:13.499912Z","signature_b64":"ugmxG4S6Qpx+HZY8Ykhd5F4MpsA8iHtgwJKcYdfzvMmbJ1xW1xPawbgHn9f2+ptd+cFx4tNN52++opQtwtWBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0337f691ba24cab311174a09313b8a731232abf3f877127354ef064528d1ee90","last_reissued_at":"2026-05-18T01:31:13.499271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:13.499271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01026","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dsqRoycAj/Uzkl0eTY4w7IRtI2l2lQhL+D+oKE4nyhFyXZ7w8kBKQD3+cHDC2JyMXgcFa6OTtzvBE4/lDRRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:33:38.547150Z"},"content_sha256":"fde551edccbfff189966d8d8d9af2bd1a0639cf9d730567733cadea03f8e1c3d","schema_version":"1.0","event_id":"sha256:fde551edccbfff189966d8d8d9af2bd1a0639cf9d730567733cadea03f8e1c3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AM37NEN2ETFLGEIXJIETCO4KOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Value and Policy Iteration in Optimal Control and Adaptive Dynamic Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.NA","math.OC"],"primary_cat":"cs.SY","authors_text":"Dimitri P. Bertsekas","submitted_at":"2015-07-03T20:41:40Z","abstract_excerpt":"In this paper, we consider discrete-time infinite horizon problems of optimal control to a terminal set of states. These are the problems that are often taken as the starting point for adaptive dynamic programming. Under very general assumptions, we establish the uniqueness of solution of Bellman's equation, and we provide convergence results for value and policy iteration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01026","kind":"arxiv","version":2},"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":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzv/wB14fXTQDVU76cylhtR4z9mAqScuuPZhnbPs58eaPXtlbrj58YYdu8CA0yHsfBDwmD8FLjJOsgunGMYmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:33:38.547536Z"},"content_sha256":"de7a91897f7fe6952684155b497761b5b6c75833eb42dba119bb6f4c2219ceda","schema_version":"1.0","event_id":"sha256:de7a91897f7fe6952684155b497761b5b6c75833eb42dba119bb6f4c2219ceda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AM37NEN2ETFLGEIXJIETCO4KOM/bundle.json","state_url":"https://pith.science/pith/AM37NEN2ETFLGEIXJIETCO4KOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AM37NEN2ETFLGEIXJIETCO4KOM/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":"2026-06-30T08:33:38Z","links":{"resolver":"https://pith.science/pith/AM37NEN2ETFLGEIXJIETCO4KOM","bundle":"https://pith.science/pith/AM37NEN2ETFLGEIXJIETCO4KOM/bundle.json","state":"https://pith.science/pith/AM37NEN2ETFLGEIXJIETCO4KOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AM37NEN2ETFLGEIXJIETCO4KOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AM37NEN2ETFLGEIXJIETCO4KOM","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":"f21c88e1c8fb87c4592957e9bb2407ba7e8cdd5fc51517ca43c1a5906441b8fc","cross_cats_sorted":["cs.DS","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-03T20:41:40Z","title_canon_sha256":"05db5cd0ff083dbff1e17f1396c3ef9a03b51672be71f391b2597ed000baa987"},"schema_version":"1.0","source":{"id":"1507.01026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01026","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01026v2","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01026","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"AM37NEN2ETFL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AM37NEN2ETFLGEIX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AM37NEN2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:de7a91897f7fe6952684155b497761b5b6c75833eb42dba119bb6f4c2219ceda","target":"graph","created_at":"2026-05-18T01:31:13Z","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":"In this paper, we consider discrete-time infinite horizon problems of optimal control to a terminal set of states. These are the problems that are often taken as the starting point for adaptive dynamic programming. Under very general assumptions, we establish the uniqueness of solution of Bellman's equation, and we provide convergence results for value and policy iteration.","authors_text":"Dimitri P. Bertsekas","cross_cats":["cs.DS","math.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-03T20:41:40Z","title":"Value and Policy Iteration in Optimal Control and Adaptive Dynamic Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01026","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:fde551edccbfff189966d8d8d9af2bd1a0639cf9d730567733cadea03f8e1c3d","target":"record","created_at":"2026-05-18T01:31:13Z","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":"f21c88e1c8fb87c4592957e9bb2407ba7e8cdd5fc51517ca43c1a5906441b8fc","cross_cats_sorted":["cs.DS","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-03T20:41:40Z","title_canon_sha256":"05db5cd0ff083dbff1e17f1396c3ef9a03b51672be71f391b2597ed000baa987"},"schema_version":"1.0","source":{"id":"1507.01026","kind":"arxiv","version":2}},"canonical_sha256":"0337f691ba24cab311174a09313b8a731232abf3f877127354ef064528d1ee90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0337f691ba24cab311174a09313b8a731232abf3f877127354ef064528d1ee90","first_computed_at":"2026-05-18T01:31:13.499271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:13.499271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ugmxG4S6Qpx+HZY8Ykhd5F4MpsA8iHtgwJKcYdfzvMmbJ1xW1xPawbgHn9f2+ptd+cFx4tNN52++opQtwtWBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:13.499912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fde551edccbfff189966d8d8d9af2bd1a0639cf9d730567733cadea03f8e1c3d","sha256:de7a91897f7fe6952684155b497761b5b6c75833eb42dba119bb6f4c2219ceda"],"state_sha256":"6ccd28e1dd0673f39286deeea86dc1712f1e7931b85ffc09fccfd04e206eef10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0raDDKjLuRo8JM1sXkeSxgTwzmPJqXOstoZyrOUFO33CY8rHZJu8ykqlWQ5JS/BAx27S3Bl0ITEiocB784q6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T08:33:38.549521Z","bundle_sha256":"47ca86d86f6ab43eedf0a2dc1846957fa175394c2ede8e9c49d59d133ffba35f"}}