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We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width, ruling out uniform Gaussian safety in the class and matching the empirical empty middle. The diagonal inverse-Fisher release $\\Sigma^\\star_{\\mathrm{diag}}(\\mathcal{K}) = (2\\mathcal{K}/d)\\,\\mathrm{diag}(1/F_{ii})$ is the unique minimax-optimal diagonal mechanism at first-order KL budget $\\mathcal{K}$ and the only release with worst-attacker top-1 $\\le 0.001$ at every point of a 32 model-layer grid, but it sits on a privacy/utility edge rather than filling the middle. 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The diagonal inverse-Fisher release $\\Sigma^\\star_{\\mathrm{diag}}(\\mathcal{K}) = (2\\mathcal{K}/d)\\,\\mathrm{diag}(1/F_{ii})$ is the unique minimax-optimal diagonal mechanism at first-order KL budget $\\mathcal{K}$ and the only release with worst-attacker top-1 $\\le 0.001$ at every point of a 32 model-layer grid, but it sits on a privacy/utility edge rather than filling the middle. A generalized-eigen mechanism reaching $13\\times$ Pareto reduction under Euclidean retrieval collap","title":"Hidden-State Privacy Has an Empty Middle","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-27T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.24042"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:2f45efbb1530d841f0ea56433ec8920975e2a20901b04ea94a34123f0f4739c512171dcb968269ff1592b5cca0230d8f39fd656d3598d8db3dfcd47481bfd700","signer":"crovia.substrate","subject":{"observed_at":"2026-05-27T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.24042"},"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":"c5fbd5a9b36319cc52d826affecdd779178302e8e16c497f5b3a9ea131beaf0c","leaf_index":154009,"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":"01763b2fcaf24e5a8c15cfe1adc7d6c110926b5be14c65d81d27bd0b797b23f4","side":"left"},{"sibling":"78720e0561d46797ffc66d921f1825f8e8e79b44a8ef22ff85f004daf040d23e","side":"right"},{"sibling":"2eee3916ea9fdfd53588365e82e638bf2908ffe1c8ba6bc95e6f05f01eaa4cff","side":"right"},{"sibling":"5f79b7571a5da18d9e04110a719dc982014092419e88ac4238132c43786f7463","side":"left"},{"sibling":"bdab384782c8f46c42b2d20c722e44775a1dc82aa539824853fd1584b03c24dd","side":"left"},{"sibling":"3f8a4c1da74f8ace63125682e65daad3f027c83e12545bed4e5e502497a69769","side":"right"},{"sibling":"cc672c1300e7193c9ebe208defb6285b8c64e30c3301a5c7d7a31eb02ac23e5d","side":"right"},{"sibling":"78f1bf1ac0323860fbf9acf5cd7ad4ff9898b7360db2cfe79e3301d2eb634202","side":"left"},{"sibling":"c14a4eb4b07d22a6a83f548cf6c304559dc63f0e53071e550ecc566dbba50b14","side":"left"},{"sibling":"3165125427a29042fc9d02858a59a68858dbdcb2e19d1afa5f6dd6a95cfbce6a","side":"right"},{"sibling":"04b9a68b8ec6fa37251564383c685c23ce69e5e031df4eae69f79a3a334b68bf","side":"right"},{"sibling":"816f233274bb10f5a122aac086a0c8c697b78fec67a4af55190bb596b7506fab","side":"left"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"374c02d15fb12bd356c179c94766043a982052c6132af8bfc15361b431ffa9f7","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"990705096edf483cc877217308f731dc42d6f6d99f82880167bbdbbfef32560a","side":"right"},{"sibling":"dd265753d95fa2e2fb4f5768e37fab6f691ccff09ad60d0910ff7dc23bac9226","side":"right"},{"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":154065,"merkle_root":"4993cfdc172e7880b60667f16789dc2e831ff000f81bb1ecba248e73f1510eca","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260527T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-27T05:37:36Z","sig_algorithm":"ed25519","signature":"76ecf118011540405e96506e6219752df04a2850632f2903dc6f10e08b98bc5a42c8d9e1cb5b7c5bf714479806a403df5f34399afa40c23fbb71493a1f77bd0c","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_81bde545d11dff43fff55d1822f238a541adb65d22bb48f1bd72ee3f1169140e"}}