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We study SHARD, which splits PCA coordinates into a short routing prefix and a residual protected by independent cell-local orthogonal keys. It supports CKKS ciphertext--plaintext reranking but is evaluated as a leakage trade-off, not a cryptographic document-privacy guarantee.\n  Corrected scoring uses centered document coordinates and an uncentered scoring query, preserving raw ranking up to a query-dependent constant. Across ten BEIR/MIRACL configurations it reproduces raw nDCG@10 and recall, whereas centering both sides loses up to 0.080 nDCG. Cell keys spread diffuse known-pair evidence across compartments, but minimum-norm alignment recovers useful signal far below full key rank, so there is no hard de-anonymization threshold.\n  Real CKKS has maximum score error 2.29e","title":"SHARD: cell-keyed residual splitting for alignment-resistant private dense retrieval","url":"https://arxiv.org/abs/2606.27976","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.27976v3 Announce Type: replace-cross \nAbstract: Dense retrieval systems expose document geometry when vector stores are compromised, and a global protective transform can often be aligned from known pairs. We study SHARD, which splits PCA coordinates into a short routing prefix and a residual protected by independent cell-local orthogonal keys. It supports CKKS ciphertext--plaintext reranking but is evaluated as a leakage trade-off, not a cryptographic document-privacy guarantee.\n  Corrected scoring uses centered document coordinates and an uncentered scoring query, preserving raw ranking up to a query-dependent constant. Across ten BEIR/MIRACL configurations it reproduces raw nDCG@10 and recall, whereas centering both sides loses up to 0.080 nDCG. Cell keys spread diffuse known-pair evidence across compartments, but minimum-norm alignment recovers useful signal far below full key rank, so there is no hard de-anonymization threshold.\n  Real CKKS has maximum score error 2.29e","title":"SHARD: cell-keyed residual splitting for alignment-resistant private dense retrieval","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-15T04:44:03Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.27976"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c3edd0858c0973c464081b5db939e689b4aedd726362006c51f7d43255ddf65e05963d32d304a326abf62faa2a45ac263538a91e34fce54932a592217573fb02","signer":"crovia.substrate","subject":{"observed_at":"2026-07-15T04:44:03Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.27976"},"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":"8c32cec67a0d622b7c2d170d090a772b38b85dde0a6ca7e8bbf4b2eee53298fe","leaf_index":316594,"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":"ff13548052a483b8a418d7ff6fc974392cabcfba4276e39ac34b102f2dff964b","side":"right"},{"sibling":"b8a8d7459e19d4fe8ad98928aa0e6610d43cf7c75d96861ca4c2ea3f83e8cb8c","side":"left"},{"sibling":"5199549222f76330d494f774a43542005879f99cd053c85ec455b7f398a5b271","side":"right"},{"sibling":"6160e775a23f4324e573b98036cd55149434454f5cecce7622d2e194a2c720d4","side":"right"},{"sibling":"7f55c7b07c52d9a9adb79590ac12a193771d2f53892c111dfa8e51a972748ea0","side":"left"},{"sibling":"fc5fe414d03440bed7aa3c8fdd956b2cb0a844eb7ddc3f58126f36dc3900245e","side":"left"},{"sibling":"33661ca420513ca9092e711309245c4602733fe2714484fedf48cb9c8664fd0e","side":"right"},{"sibling":"af39fefe9ccf50e1288b21fab97d8bc62d8495b7dbe9a55a9ffa363740e34285","side":"left"},{"sibling":"1c7f1bf97993e3a126824f8350788b168c4c13264fb03a73b3ede312035d3527","side":"right"},{"sibling":"84a7590e6b24dd07ed46597f19deb75d9ad247b4227b17f30857ec7cc0fc5c21","side":"right"},{"sibling":"c8d3d8cb0183b912107f9781ad2a1b6c0c9424906c5907c09deeb5bea9d7b571","side":"left"},{"sibling":"0cb62c0ada57a2406a6bcb100889d3e8b29a15efeed07adaff5bb90a5e80612a","side":"right"},{"sibling":"0b69289b25462ddd6166f6f49004cfc8ada0ab4f10adafe188347817bdd46e37","side":"left"},{"sibling":"1418b281cd985b5ed411ef25f2017a1826cc14919b6fad3934e6ceeec693699b","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"abe4a8c706e530484d1e96a8988cb09eab85928b2050985500ab289753fe3eec","side":"right"},{"sibling":"f436dccf82aa2c1eb7bfa3eb84316e116aaf64dc55cd9592597118f6cb0648f6","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":316730,"merkle_root":"a8e6e5be81ea6f5b5f2227422459bf39455fe9f0b6602b4d1ce6977dbfd78bc7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260715T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-15T05:38:24Z","sig_algorithm":"ed25519","signature":"df1678d268b5a07413e2ca6e748c3f40b6cfedea930a18d843489a4ab513da791bf0a886caab1b918d0989f8ebaaf3d0035ca2aa777913b1ad29979f1deb9a0c","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_4bbe286d0c6619b63b97e5eee73d8f11c7454ad0f983d401af418460ab855f86"}}