{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:HW5DOX2ANFONIFB76FWXICZI6J","short_pith_number":"pith:HW5DOX2A","canonical_record":{"source":{"id":"2009.07842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-16T17:59:25Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"629819525ac72e33d3c626860fa50b5316f78530ee31a084f0c9290f8cc0eb54","abstract_canon_sha256":"cee4ddc56517efcb42fc5db61802624f40ef9587d19137d909713022a761f24b"},"schema_version":"1.0"},"canonical_sha256":"3dba375f40695cd4143ff16d740b28f25f9f8335d071bf84f28e50d782993754","source":{"kind":"arxiv","id":"2009.07842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07842","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07842v1","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07842","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"HW5DOX2ANFON","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_16","alias_value":"HW5DOX2ANFONIFB7","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_8","alias_value":"HW5DOX2A","created_at":"2026-07-05T01:35:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:HW5DOX2ANFONIFB76FWXICZI6J","target":"record","payload":{"canonical_record":{"source":{"id":"2009.07842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-16T17:59:25Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"629819525ac72e33d3c626860fa50b5316f78530ee31a084f0c9290f8cc0eb54","abstract_canon_sha256":"cee4ddc56517efcb42fc5db61802624f40ef9587d19137d909713022a761f24b"},"schema_version":"1.0"},"canonical_sha256":"3dba375f40695cd4143ff16d740b28f25f9f8335d071bf84f28e50d782993754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:35:59.031912Z","signature_b64":"f1EOH7zIEBUvnjYQJG4FJzIacK4Mb4n9zHrIQi7tw9n2ZpxS1LYQSZoyp7bQWKCpeq773ukTFlcEBmwDRsIQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dba375f40695cd4143ff16d740b28f25f9f8335d071bf84f28e50d782993754","last_reissued_at":"2026-07-05T01:35:59.031488Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:35:59.031488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.07842","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":"2026-07-05T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvVjD7zpgXWcYzMli/8edjOO20QZna5pkCCRXOhGf+aoYVAroHliZsvQOgJy2qUQFP/nQ8OvBhNJDi+QuuRSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T14:52:20.943406Z"},"content_sha256":"37fe780d69aa789c42bb0241287a7f94cfddb148e700eb6ba3d4dcfc60a4932f","schema_version":"1.0","event_id":"sha256:37fe780d69aa789c42bb0241287a7f94cfddb148e700eb6ba3d4dcfc60a4932f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:HW5DOX2ANFONIFB76FWXICZI6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower Bounds for Policy Iteration on Multi-action MDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bhishma Dedhia, Kumar Ashutosh, Parthasarathi Khirwadkar, Sahil Shah, Sarthak Consul, Shivaram Kalyanakrishnan","submitted_at":"2020-09-16T17:59:25Z","abstract_excerpt":"Policy Iteration (PI) is a classical family of algorithms to compute an optimal policy for any given Markov Decision Problem (MDP). The basic idea in PI is to begin with some initial policy and to repeatedly update the policy to one from an improving set, until an optimal policy is reached. Different variants of PI result from the (switching) rule used for improvement. An important theoretical question is how many iterations a specified PI variant will take to terminate as a function of the number of states $n$ and the number of actions $k$ in the input MDP. While there has been considerable p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07842","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/2009.07842/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":"2026-07-05T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZWpC9uVWQZECdQzgES94DVL7xS2ThNrHl1qVn3cnptOzlM0MB4jsBAKZKntx/ESWHrQ+AnSVS++JDJR76e9qCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T14:52:20.943796Z"},"content_sha256":"48590c37adac93b671cdefdb706d6c7e9e66927717e5372a5f4152704cb1930a","schema_version":"1.0","event_id":"sha256:48590c37adac93b671cdefdb706d6c7e9e66927717e5372a5f4152704cb1930a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HW5DOX2ANFONIFB76FWXICZI6J/bundle.json","state_url":"https://pith.science/pith/HW5DOX2ANFONIFB76FWXICZI6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HW5DOX2ANFONIFB76FWXICZI6J/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":"2026-07-16T14:52:20Z","links":{"resolver":"https://pith.science/pith/HW5DOX2ANFONIFB76FWXICZI6J","bundle":"https://pith.science/pith/HW5DOX2ANFONIFB76FWXICZI6J/bundle.json","state":"https://pith.science/pith/HW5DOX2ANFONIFB76FWXICZI6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HW5DOX2ANFONIFB76FWXICZI6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HW5DOX2ANFONIFB76FWXICZI6J","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":"cee4ddc56517efcb42fc5db61802624f40ef9587d19137d909713022a761f24b","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-16T17:59:25Z","title_canon_sha256":"629819525ac72e33d3c626860fa50b5316f78530ee31a084f0c9290f8cc0eb54"},"schema_version":"1.0","source":{"id":"2009.07842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07842","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07842v1","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07842","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"HW5DOX2ANFON","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_16","alias_value":"HW5DOX2ANFONIFB7","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_8","alias_value":"HW5DOX2A","created_at":"2026-07-05T01:35:59Z"}],"graph_snapshots":[{"event_id":"sha256:48590c37adac93b671cdefdb706d6c7e9e66927717e5372a5f4152704cb1930a","target":"graph","created_at":"2026-07-05T01:35:59Z","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/2009.07842/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Policy Iteration (PI) is a classical family of algorithms to compute an optimal policy for any given Markov Decision Problem (MDP). The basic idea in PI is to begin with some initial policy and to repeatedly update the policy to one from an improving set, until an optimal policy is reached. Different variants of PI result from the (switching) rule used for improvement. An important theoretical question is how many iterations a specified PI variant will take to terminate as a function of the number of states $n$ and the number of actions $k$ in the input MDP. While there has been considerable p","authors_text":"Bhishma Dedhia, Kumar Ashutosh, Parthasarathi Khirwadkar, Sahil Shah, Sarthak Consul, Shivaram Kalyanakrishnan","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-16T17:59:25Z","title":"Lower Bounds for Policy Iteration on Multi-action MDPs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07842","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":"sha256:37fe780d69aa789c42bb0241287a7f94cfddb148e700eb6ba3d4dcfc60a4932f","target":"record","created_at":"2026-07-05T01:35:59Z","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":"cee4ddc56517efcb42fc5db61802624f40ef9587d19137d909713022a761f24b","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-16T17:59:25Z","title_canon_sha256":"629819525ac72e33d3c626860fa50b5316f78530ee31a084f0c9290f8cc0eb54"},"schema_version":"1.0","source":{"id":"2009.07842","kind":"arxiv","version":1}},"canonical_sha256":"3dba375f40695cd4143ff16d740b28f25f9f8335d071bf84f28e50d782993754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dba375f40695cd4143ff16d740b28f25f9f8335d071bf84f28e50d782993754","first_computed_at":"2026-07-05T01:35:59.031488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:35:59.031488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1EOH7zIEBUvnjYQJG4FJzIacK4Mb4n9zHrIQi7tw9n2ZpxS1LYQSZoyp7bQWKCpeq773ukTFlcEBmwDRsIQBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:35:59.031912Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37fe780d69aa789c42bb0241287a7f94cfddb148e700eb6ba3d4dcfc60a4932f","sha256:48590c37adac93b671cdefdb706d6c7e9e66927717e5372a5f4152704cb1930a"],"state_sha256":"e08c25879453b23c96f499dc72b3f0c5b9afe09d95f6cae071a88dc8244a697e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xc7YkbMR7LCpGtH/KDFwuiA/SO4EcR3IyY/qr12o+SH4VLEAuxzSK7kr8DU2wYnAvmvGY9XxQKPLIH4bdhx5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-16T14:52:20.946019Z","bundle_sha256":"d0ceb3b6266d3f85f325b475a9a5f50b7ffdb6dd104f73084c4482ccce615a1a"}}