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Even though rewards are linear and the agent has no utility curvature, probability weighting, or framing dependence, standard Bellman optimality produces three prospect-theory-like signatures: an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient $\\lambda^*(S) > 1$, and a reflection-effect policy reversal. Across 495 configurations, the optimal policy plays safe near catastrophe in positive-drift (growth) regimes despite the risky action's higher immediate expected value, and plays risky near catastrophe in negative-drift (decline) regimes despite the safe action's lower immediate expected loss. We derive a closed-form expression for the asymptotic loss-aversion plateau $\\bar{\\lambda}$ that depends only on win probability $p$, payoff asymmetry $r = |\\Delta_\\ell/\\","title":"Prospect-Theory Behavior from Bellman Optimality in MDPs with Catastrophic States","url":"https://arxiv.org/abs/2606.00970","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.00970v2 Announce Type: replace \nAbstract: We study risk-neutral control in Markov decision processes with an absorbing catastrophic state. Even though rewards are linear and the agent has no utility curvature, probability weighting, or framing dependence, standard Bellman optimality produces three prospect-theory-like signatures: an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient $\\lambda^*(S) > 1$, and a reflection-effect policy reversal. Across 495 configurations, the optimal policy plays safe near catastrophe in positive-drift (growth) regimes despite the risky action's higher immediate expected value, and plays risky near catastrophe in negative-drift (decline) regimes despite the safe action's lower immediate expected loss. We derive a closed-form expression for the asymptotic loss-aversion plateau $\\bar{\\lambda}$ that depends only on win probability $p$, payoff asymmetry $r = |\\Delta_\\ell/\\","title":"Prospect-Theory Behavior from Bellman Optimality in MDPs with Catastrophic States","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-01T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.00970"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d5f0597322cb3d69d8d19f37eb18974f3b319a0f235da0c264b50f8010e1a85f0bf26eda2a266a32704b394a1a5f8eda772ff67eaedd0a37a3feadecb6a01a04","signer":"crovia.substrate","subject":{"observed_at":"2026-07-01T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.00970"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"90689bd0a6a5541a6018532b4e070c91e4d69650a1c9b0311ed180e9a87d7a57","leaf_index":268642,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"e76c9cd18aa34561cb39f864732c27d55306c1a1ec2ae2999fd07ab5e9da9cba","side":"right"},{"sibling":"0300ebe83ece781a7eaee82c515ee28629228ae1d3f246acb8fea9a183a746de","side":"left"},{"sibling":"bd236433f5bf13434cd4a0eb8ddcac61fa8e475bcfcda23a6ee4ed92ec1714de","side":"right"},{"sibling":"f140725fc7ce461fadbe3893eaff43a2f2bb70ee09c50940d324e14991a4dbec","side":"right"},{"sibling":"7c3081b113c9bce1a40bc373d953eb619d4c00c9911f7ec5d3af2f087e37284f","side":"right"},{"sibling":"7caf50a8d663be3d397380d87998b2f8be0601e4f183578903035b3b15cf798b","side":"left"},{"sibling":"0eb4eb96022242f95e819116ec215f97662a006e19b7a97219e1ee83a96f4d60","side":"left"},{"sibling":"09d2631e35e497faf605540c596009624dcf181a796c7acf51592f060eb3f046","side":"right"},{"sibling":"4b14e8ccae46b588748944ffaf410222f66cebc2ac58d936cbe16847b7be9508","side":"left"},{"sibling":"bbd9a20451913e8c7b910f616d5661d9b281a94af70d201ba50b3112d429521b","side":"right"},{"sibling":"85af80e45748c1e0da1e2f42d9d66da8996016888a034f20eb17ff0a73b69eab","side":"right"},{"sibling":"4575fde969d1d9a2984cc01a37ac8441238f74527d42874272dc5582dadebb4f","side":"left"},{"sibling":"f536de281672cbf0b583a3dc46faef1de2823b72bd9265c7b60e889131cc268d","side":"left"},{"sibling":"95b8b0f67237052a17c41fa8cbdce2b79bcb5aeeba3fdb239d4c4497e598115d","side":"right"},{"sibling":"c2f351f771cee329448890504d9436792ba482e50250ca9a19289311131f96c8","side":"right"},{"sibling":"c39bfb2e911ca37ae997690bfc04128ae32e6806ee1cb3908781a7e6685022a0","side":"right"},{"sibling":"a101b4c60ef6854ac3d750eef02d8e2e06c153284b5ecb7111302f97eb129797","side":"right"},{"sibling":"eae2a3de5cb35455ad60125e196cfadaba8a590c53146e95028469f53f70349c","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":268860,"merkle_root":"d098f25810d0569730b6c0e170d57f329a70359d483b47874b5f2fc51d23de65","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260701T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-01T05:38:05Z","sig_algorithm":"ed25519","signature":"64f37f0e3df0556baa55b924a736cab8005643fa0ab65b503f22407de30eab293e6e0bd62904270fda38d05084bb350c8c0d0aadb2c5a6bae5f1c54598e6d30c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_08fba2d01cdd4f1aba0b4ad863eff64eb2e543bcd811709b95c65b4402a1184f"}}