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On a panel of small games this match is exact, with one apparent exception: in Kuhn poker R-NaD lands at bluff coordinate 0.180 while the maximum-entropy member sits at 0.201, a coordinate gap of about 0.021, even though R-NaD attains 99.7 percent of the maximum entropy. We ask whether this gap is a genuine selection bias or an artifact, and answer it quantitatively. We show that for selection on a one-dimensional Nash manifold the coordinate gap factorizes as $\\mathrm{gap} \\approx \\sqrt{2\\delta/\\kappa}$, where $\\delta$ is the entropy shortfall of the solver and $\\kappa$ is the curvature of the entropy landscape at its peak. Across five games this relation holds to within $2 \\tim","title":"The Curvature Shadow: An Apparent Failure of Maximum-Entropy Equilibrium Selection is a Removable Artifact","url":"https://arxiv.org/abs/2607.17543","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.17543v1 Announce Type: new \nAbstract: In two-player zero-sum games whose Nash equilibria form a convex set, regularized solvers such as Regularized Nash Dynamics (R-NaD) empirically select the maximum-entropy member: the information projection (I-projection) of a uniform reference onto the Nash set. On a panel of small games this match is exact, with one apparent exception: in Kuhn poker R-NaD lands at bluff coordinate 0.180 while the maximum-entropy member sits at 0.201, a coordinate gap of about 0.021, even though R-NaD attains 99.7 percent of the maximum entropy. We ask whether this gap is a genuine selection bias or an artifact, and answer it quantitatively. We show that for selection on a one-dimensional Nash manifold the coordinate gap factorizes as $\\mathrm{gap} \\approx \\sqrt{2\\delta/\\kappa}$, where $\\delta$ is the entropy shortfall of the solver and $\\kappa$ is the curvature of the entropy landscape at its peak. Across five games this relation holds to within $2 \\tim","title":"The Curvature Shadow: An Apparent Failure of Maximum-Entropy Equilibrium Selection is a Removable Artifact","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-21T04:43:35Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.17543"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:7a769bcc3c2d930d1c402b89667b283f65495153393e70f202342ea0c87829c1a62c40cfbac0287e2210f91fccc858dd206c291d17eab0a2b386355163700b0b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-21T04:43:35Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.17543"},"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":"b4b04dbe102fe038cf40ed5829b5d3ee2a918e149aa05e6fc23a6985178c306e","leaf_index":336585,"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":"be6f973c576a0b26151733943e3d4071311e5d5644c0e5245ae5aaa0951b3f3c","side":"left"},{"sibling":"f1f6f629a9d66481ea200e2c45895ef7db0eba3a94c73f3d464aec64dc99993c","side":"right"},{"sibling":"a1e6efdcad35afa85f6b06a74f8eaf9a9ab14c39f26578a3b89b4984d8cde232","side":"right"},{"sibling":"533f6864356a5fc5023677aae85e0c8850d4aa924e51e0265e9797c414232d04","side":"left"},{"sibling":"54c8abff7a167f90216e52f759babd710117bfd687ddcb2dbb7dc7cfdc78d433","side":"right"},{"sibling":"3af7f5627ece0b0aa3b8a46ebfe8c72367f02051656ed4864d6f665c93e28044","side":"right"},{"sibling":"78afb98e8815c9330b3a7e74c8b56112eb0284b980a66d5b96cce812169af054","side":"left"},{"sibling":"e6f9d6d6c760446a7b30dd4e30a28f58c0817f4bee09529ee009c470d86f5564","side":"left"},{"sibling":"38e5827f7c9f72ad34a2b97042f2fb5f7e868db899d074b7819af4f2209b9caa","side":"right"},{"sibling":"7b927551b5db06b6571913b4e6792ffcce5291a3eca5a0df4a3b6e296271105f","side":"left"},{"sibling":"b77a0b5ae4607c8fe6ba73449d46b35076e3dedc0c82a2c65a05780d42a7bc2e","side":"right"},{"sibling":"9eb5077edfb3dc553857d4794b925bfce117e0f8a1d049af5d0dd9026b470eef","side":"right"},{"sibling":"414b1a70fd1dcb25489a194714b97492b066684b15d0b7a48a176c4b9b5bc713","side":"right"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"613f015699131eb89bd755dee67133be95af25cf5f16c1c8ce4b99d963b8dd86","side":"right"},{"sibling":"a729b574b1135956436ded5eef1fe8f08014ff6a0729749d307ab1bca93fcdc9","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"4bf21052e085e8ac81f1dec1d2b310bd12bf948992de6177d12e9d2fda8d39f0","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":337144,"merkle_root":"5e969cc01afa67e4dbe5d37b712cdb10f4aa1fd74404e02eab724cf487c8d6d9","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260721T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-21T05:38:38Z","sig_algorithm":"ed25519","signature":"5c0c1a8dd2793d787ccd5e49e8b4d70eed136352555518589f05c74be357fc171702e42a76c3a556d90e3d51ff36cb3d292aaac83c66566de7b943f318bda50c","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_5e50160fbb4026a93653fccc981d08408143c553e7b4c34afe957663e7862d28"}}