{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6UJL2HJKOQ6IWOWFH7VQYPTCSM","short_pith_number":"pith:6UJL2HJK","canonical_record":{"source":{"id":"2607.16538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-17T22:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"e264c4770c1ae723463a7cf86a1545bf7c4932597116080c99e0445b998354c5","abstract_canon_sha256":"8c3da1fc622f51db33de5902e65b29108cef0356c57a5907e8f699ba56fe65a2"},"schema_version":"1.0"},"canonical_sha256":"f512bd1d2a743c8b3ac53feb0c3e62933b2e6889f829ef4136ac8e4ad8277586","source":{"kind":"arxiv","id":"2607.16538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16538","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16538v1","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16538","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"6UJL2HJKOQ6I","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_16","alias_value":"6UJL2HJKOQ6IWOWF","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_8","alias_value":"6UJL2HJK","created_at":"2026-07-21T00:20:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6UJL2HJKOQ6IWOWFH7VQYPTCSM","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-17T22:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"e264c4770c1ae723463a7cf86a1545bf7c4932597116080c99e0445b998354c5","abstract_canon_sha256":"8c3da1fc622f51db33de5902e65b29108cef0356c57a5907e8f699ba56fe65a2"},"schema_version":"1.0"},"canonical_sha256":"f512bd1d2a743c8b3ac53feb0c3e62933b2e6889f829ef4136ac8e4ad8277586","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:23.868168Z","signature_b64":"oXyNAQM+AuA3QXnF0nlcH2drDWDWd/Yune1k3bBb5Cgktgkn4q2b0UbvJ89IFAZGD+6uH4tJbvgJnVKhE7iXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f512bd1d2a743c8b3ac53feb0c3e62933b2e6889f829ef4136ac8e4ad8277586","last_reissued_at":"2026-07-21T00:20:23.867308Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:23.867308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16538","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":"2026-07-21T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Arznh+BIJ1jYdx3slY5Ps1ujvY6ZiN3ABs0ZSE5IsHyRI9BsNonqhHExBr+sG8OM6OtcGfOGO+6lWhHdqp+ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:59:23.604952Z"},"content_sha256":"aedb8e1d94bc0ab1a927c0de0fcb0eb7c15ed121408d66ac5e513752665e0095","schema_version":"1.0","event_id":"sha256:aedb8e1d94bc0ab1a927c0de0fcb0eb7c15ed121408d66ac5e513752665e0095"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6UJL2HJKOQ6IWOWFH7VQYPTCSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"History-Dependent Recursive Preferences in Markov Decision Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"William B. Haskell","submitted_at":"2026-07-17T22:25:09Z","abstract_excerpt":"In finite horizon dynamic programming with history-dependent preferences, the relevant state may be the entire realized history, even when the physical state is Markov. This paper develops a behavioral state-reduction theory for such Markov decision processes. Under behavioral axioms and a certainty-equivalent richness condition, the full-history problem admits a recursive representation composed of time and risk aggregators. We then derive a canonical preference-augmented (PA) state by quotienting histories that have the same current physical Markov state, are indifferent under every common c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16538","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/2607.16538/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":"2026-07-21T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EkMid6Su9lW7ux4TrrCQQ3EDvmxs26GUPyaWMJUCvWcK+oSvBUhtQ89mI2AzxIpLh7claErCke0DnfX9AB/gDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:59:23.605420Z"},"content_sha256":"2a1a7fbd420a8a5ccbff6ba58aa1947687d8935ed1fae13364edf110bf5a77a2","schema_version":"1.0","event_id":"sha256:2a1a7fbd420a8a5ccbff6ba58aa1947687d8935ed1fae13364edf110bf5a77a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/bundle.json","state_url":"https://pith.science/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/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":"2026-08-14T12:59:23Z","links":{"resolver":"https://pith.science/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM","bundle":"https://pith.science/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/bundle.json","state":"https://pith.science/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UJL2HJKOQ6IWOWFH7VQYPTCSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6UJL2HJKOQ6IWOWFH7VQYPTCSM","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":"8c3da1fc622f51db33de5902e65b29108cef0356c57a5907e8f699ba56fe65a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-17T22:25:09Z","title_canon_sha256":"e264c4770c1ae723463a7cf86a1545bf7c4932597116080c99e0445b998354c5"},"schema_version":"1.0","source":{"id":"2607.16538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16538","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16538v1","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16538","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"6UJL2HJKOQ6I","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_16","alias_value":"6UJL2HJKOQ6IWOWF","created_at":"2026-07-21T00:20:23Z"},{"alias_kind":"pith_short_8","alias_value":"6UJL2HJK","created_at":"2026-07-21T00:20:23Z"}],"graph_snapshots":[{"event_id":"sha256:2a1a7fbd420a8a5ccbff6ba58aa1947687d8935ed1fae13364edf110bf5a77a2","target":"graph","created_at":"2026-07-21T00:20:23Z","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/2607.16538/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In finite horizon dynamic programming with history-dependent preferences, the relevant state may be the entire realized history, even when the physical state is Markov. This paper develops a behavioral state-reduction theory for such Markov decision processes. Under behavioral axioms and a certainty-equivalent richness condition, the full-history problem admits a recursive representation composed of time and risk aggregators. We then derive a canonical preference-augmented (PA) state by quotienting histories that have the same current physical Markov state, are indifferent under every common c","authors_text":"William B. Haskell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-17T22:25:09Z","title":"History-Dependent Recursive Preferences in Markov Decision Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16538","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:aedb8e1d94bc0ab1a927c0de0fcb0eb7c15ed121408d66ac5e513752665e0095","target":"record","created_at":"2026-07-21T00:20:23Z","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":"8c3da1fc622f51db33de5902e65b29108cef0356c57a5907e8f699ba56fe65a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-17T22:25:09Z","title_canon_sha256":"e264c4770c1ae723463a7cf86a1545bf7c4932597116080c99e0445b998354c5"},"schema_version":"1.0","source":{"id":"2607.16538","kind":"arxiv","version":1}},"canonical_sha256":"f512bd1d2a743c8b3ac53feb0c3e62933b2e6889f829ef4136ac8e4ad8277586","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f512bd1d2a743c8b3ac53feb0c3e62933b2e6889f829ef4136ac8e4ad8277586","first_computed_at":"2026-07-21T00:20:23.867308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:23.867308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oXyNAQM+AuA3QXnF0nlcH2drDWDWd/Yune1k3bBb5Cgktgkn4q2b0UbvJ89IFAZGD+6uH4tJbvgJnVKhE7iXCQ==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:23.868168Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aedb8e1d94bc0ab1a927c0de0fcb0eb7c15ed121408d66ac5e513752665e0095","sha256:2a1a7fbd420a8a5ccbff6ba58aa1947687d8935ed1fae13364edf110bf5a77a2"],"state_sha256":"8e3f360732bba469b0f6a36cd158f083dd6ecb17ba8e711d27c0416d1fefbe72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQzM/kWog+5pq8yJyijHnOe2EkmcRu29JaZWHEbFXwGFfzfI9UHghM7uycZLXFb7XzkHw20rU0GcYWlpZvoADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T12:59:23.610059Z","bundle_sha256":"c972d27fc9169e9bb6817f0fa3677a2f855a5b506912bf9cac86054a5bb88a44"}}