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Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520","title":"Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory \"VaCoAl\" as a Substrate for Vector-HaSH and TEM","url":"https://arxiv.org/abs/2605.15652","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.15652v4 Announce Type: replace-cross \nAbstract: Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. 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Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520","title":"Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory \"VaCoAl\" as a Substrate for Vector-HaSH and TEM","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-22T04:43:12Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.15652"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:ea495ef5c720fd1f1217a747d649a9ebb23491a52506834152beef3e5a9a4b59a7c4336509f7e00766e0993823b108b57e7c9015f22f9dfe92ee9a283bfde404","signer":"crovia.substrate","subject":{"observed_at":"2026-05-22T04:43:12Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.15652"},"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":"81a2131bb46f11c59e36c7b521e912497e8c0667a70ab43485487e801cfa4099","leaf_index":148486,"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":"c8a6ae31daf5c8a02f5d1a0edc1f8f9a79f736956e3d7e503e5d22d95097b284","side":"right"},{"sibling":"1430eea05bbc6bfcae06d10a30eb26c10d185924d75545875efbb3473c8153c3","side":"left"},{"sibling":"af762c5a8df947428e50356c1232f468a21eb4b8f08e091e0cd7bc861778d44d","side":"left"},{"sibling":"152ff989204d7d635c5590fbaf8996790064dbd6a5564384e03ec150e685e7f7","side":"right"},{"sibling":"605d6ba350761e671e4664c774ed862e17ff5eb181c0895db1413e050b8126f7","side":"right"},{"sibling":"29c83f92eefcf37fd5647bf9965bae343542cc3cafabe85a14c353be2579820c","side":"right"},{"sibling":"b2b3e1dd273a89fa858097a49ad18f7a787e5f5108ffd3d34e2db914ff0f8893","side":"right"},{"sibling":"c2464e6156ff209e78b1366fb55bf2f9d9ab654edb687e533a50f92f1ec063fe","side":"right"},{"sibling":"45d7b77845fd951e51c069dff3d17eaf26d1981d61660baa90643a8a3e33efac","side":"right"},{"sibling":"46ba1960714c5ca099e764bc8d2a0242369a84e0255d7a9e3bb6ab00ffa50417","side":"right"},{"sibling":"5c4ff01819c3dfe5105c2c31139b878c525a66d2ed2f835e2d6579c68da04611","side":"left"},{"sibling":"79a713e1e345ccb99c5fe994a11708c8e9bcfa2e91f940d70421cb7d8d77ecc6","side":"right"},{"sibling":"249870fb494bef050c409081e5de45f9042938d7b2823524ee496f296aa63667","side":"right"},{"sibling":"96c48ee8328f1b7925a4cc4421df5cb0bd81c92a5d8354c93126fa5f0166d225","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"4e13b4a3e69bb83d13913477a782913ce03937edd65046853c1964d3cbb6564b","side":"right"},{"sibling":"0f7b2df1c4580bf7bb7c24b9158ba20593a06af18a5f18d0973e5eff20c35cd8","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":148601,"merkle_root":"44900cffd986f40535c83f46a250e86fbf1019d41f27080a00fbf9b8d77ec33a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260524T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-24T13:37:32Z","sig_algorithm":"ed25519","signature":"059e428c3c5241de303721ad6ac7b748758372180f3f0a717810312aecd6fab073abb3ea264157666de581a2b361c4c6e2aa8ca081b08ce9be090721f0e3400e","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_9cd98be74b680f97f980b416ab97e49baa0b73edaff376bb3ed7d6ac7029d019"}}