{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_64229bf6c94d70eb3881e0b49fdaade15bce664cce635f6f73da891895054376","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_64229bf6c94d70eb3881e0b49fdaade15bce664cce635f6f73da891895054376","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"a1d7525b71f42614cb946bbb6d6fca1993a9292ebe4721efa6439cac92b82b7f","published":"Tue, 16 Jun 2026 00:00:00 -0400","receipt_hash":"a1d7525b71f42614cb946bbb6d6fca1993a9292ebe4721efa6439cac92b82b7f","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"a1d7525b71f42614cb946bbb6d6fca1993a9292ebe4721efa6439cac92b82b7f","observed_at":"2026-06-16T04:43:43.281320Z","parent_run_hash":"eb6edcf82c3507c59161a4ab46d2e904e507004f44677402bb24d106997ed7c2","published":"Tue, 16 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2606.16846v1 Announce Type: cross \nAbstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions. In value-based reinforcement learning, each Q-learning or DQN update is built from a Bellman optimality target; our analysis isolates this target in a diffusion setting and studies its regularity and approximation complexity. Under uniform ellipticity and H\\\"older-regular coefficients, we show that a Bellman update maps bounded inputs into an anisotropic regularity class, smoothing the state variable while leaving only Lipschitz dependence on the action variable. This yields a compact family of Bellman iterates and motivates a tensor-product DeepONet architecture adapted to the mixed regularity of the problem. We then derive explicit approximation and resource bounds, together with a stiffness--complexity trade-off as the time step $\\delta \\to 0$. The resulting theory makes a direct contribution to Q-learning the","title":"Deep Q-Learning on H\\\"older Spaces","url":"https://arxiv.org/abs/2606.16846","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.16846v1 Announce Type: cross \nAbstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions. In value-based reinforcement learning, each Q-learning or DQN update is built from a Bellman optimality target; our analysis isolates this target in a diffusion setting and studies its regularity and approximation complexity. Under uniform ellipticity and H\\\"older-regular coefficients, we show that a Bellman update maps bounded inputs into an anisotropic regularity class, smoothing the state variable while leaving only Lipschitz dependence on the action variable. This yields a compact family of Bellman iterates and motivates a tensor-product DeepONet architecture adapted to the mixed regularity of the problem. We then derive explicit approximation and resource bounds, together with a stiffness--complexity trade-off as the time step $\\delta \\to 0$. The resulting theory makes a direct contribution to Q-learning the","title":"Deep Q-Learning on H\\\"older Spaces","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-16T04:43:43Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.16846"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:2a03f9d67e7b86b7353fa993402eb19eaeea952f71eef3c66b11b784b32e9c95418730ccdadd7309d7d475992161a370cc7bf537b28ca0027be85bd6983c0600","signer":"crovia.substrate","subject":{"observed_at":"2026-06-16T04:43:43Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.16846"},"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":"92e5f7d53709f8412d5ceb2ffde7e39f98c4d6d25b4527f36a0d9ebb4ec45578","leaf_index":230589,"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":"cd18f8efe9b0a0c38f47c2f7e5d50418309b7e7b059ece93af0dc47e4494371b","side":"left"},{"sibling":"eef557695ad7c1924cd80ab234dd7aa16906e594e618dcc33dd5b47d11ae2eda","side":"right"},{"sibling":"3db011cebf3d3f31d9dd546a43e05f0306e32301dc4caa9dcae03a231b7d322a","side":"left"},{"sibling":"28c088ec0f0447e15ae0d89a1cbf094e67d4acbf097052f6e5e84a65c116a70d","side":"left"},{"sibling":"46769b676bd3b4df810c95eb50470861a95d2706ef591f2ee2574c9b373af710","side":"left"},{"sibling":"612233d88c667c0240d517966bd8d2fb32129b2de5671dd583f373ae2fd7a88f","side":"left"},{"sibling":"b49ca064746e7e6295be61ea90a8ad7b8ae51e000a19ff00ba9ac201b696c28b","side":"right"},{"sibling":"f5958932b707fbb8d9de8cb158fe61200709928e9e5d860d183ba06f040858b6","side":"left"},{"sibling":"63d6b9d8af7ae8348285d3493af29f64992ecec42f5f1cae99c8604cd1703487","side":"right"},{"sibling":"0c5669692381d605223c74b8d30f70cd308e77e33d5e40ea84bb7b4f84f2d4d9","side":"right"},{"sibling":"d5b9f8b1a2c9f6a46e17982dfbe6ce1f3b5fa4e730220397f2253d114dcc8486","side":"left"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_64229bf6c94d70eb3881e0b49fdaade15bce664cce635f6f73da891895054376"}}