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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":"2026-07-07T04:43:08Z","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:ab5847899e536bc6af13111aa849f967d3baf84890353ec161676b2f7fa5ab8b14400685b9cbd1b939e7c3bce49fe1bfbad70f47b9c984a15aa87164877ae00e","signer":"crovia.substrate","subject":{"observed_at":"2026-07-07T04:43:08Z","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":"7745298ac509b877988f33a5bb37254dd7c32c1f15028fbd8b5723f3985895cd","leaf_index":289424,"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":"fe5edd98fe6f93e88e7685b62913c7e6d662e36c83984e59da496009ccd0609f","side":"right"},{"sibling":"68d625d70212a15730b6c15fd5d23af08c8f40f08014ee52c2627508932e0b7d","side":"right"},{"sibling":"e9758b111280d9537c4810758c0ecf0d205ae1d8b8c673ee39b5babd8cf7c47d","side":"right"},{"sibling":"46bdac46d1377070a5d63d9603d0821f0e363b46eddf98cd04b7eb21398c9d21","side":"right"},{"sibling":"bb8e787cf63025e1d2f21b397d82d53f33249227ed0e5c41e76b57d45d6abe96","side":"left"},{"sibling":"12382744d3cf0eb10b0c9f653c1650ffad4facf8e1eb998522c263815c8e1292","side":"right"},{"sibling":"60e5ea8d44fd25d64c4c1597dc225e2b98776766a056422a59c03da2180c9c39","side":"right"},{"sibling":"338d253a141554cbceab9dd091d805059d5d74af3605e7c62bd7529bdce399ff","side":"left"},{"sibling":"f6a26c200957df5b056969d2ac473b7e794709bf54454460f447a4af62c6bd58","side":"right"},{"sibling":"c6f2478caecaf381e6b06b04f99195339b88d0db4da957bf2106979ee4a0375c","side":"left"},{"sibling":"19d6dfd29bc47f35fa02e8fe765277ba9cc3e6da5072309f24ebaac5b5f295e3","side":"right"},{"sibling":"8e0ad7889eb2d4b40e5b6c3d8e2eb19d4e202374983f468aa76321823de07a9f","side":"left"},{"sibling":"aae716235efcb893a1f219dbcd5095070d08a497769fc6d50c14976aa26d5750","side":"right"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"1b72ad8d12164fdf329e7871711be99d8569d140b21f94056e6962da21da9ce1","side":"right"},{"sibling":"5f5109c2bfdcc7a7e70554bba25862e2d7ce86b6b0cd48a72eb66d2eb735f321","side":"right"},{"sibling":"05fd8a05dddb2e7f72bbb5b290ca55c378f1aed709f132277908d9a5f30eb605","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":289613,"merkle_root":"dc428b9d9ba248d4f93f63147bf7c700bf5be7f500cec6c3507b9df6e9401601","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260707T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-07T05:38:15Z","sig_algorithm":"ed25519","signature":"c468b0e183383ab71992be40bda451093e6cd8cd8efb0d26f68e135a804b287c209d12a0f4fdd95c69c835c04b78df8cb1903dee1f53d4730b36f5332a29fe05","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_ebed22a98c6c3a68ef092eac47a4d208fb805a89336050b766fd5eb660c2446b"}}