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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:2605.15652v5 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":"2026-05-25T04:43:48Z","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":"ed25519:9387abbcb204df64df945cd10acb1424c77f239e5587c010dc249f90e6d95f8ea95919503f3fe06e3cdb7b945a5d9d0094291423a1bc3e55aa43a371d173ba04","signer":"crovia.substrate","subject":{"observed_at":"2026-05-25T04:43:48Z","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":"2bc2420eafcaee22106b0fe0892d16c26972f87bc6c828b0f9f57a128f0e3f3f","leaf_index":149760,"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":"735924e190c430daba0cc46e1172f314b5397121331b5e358787121cc97a7906","side":"right"},{"sibling":"904d6217c9de016e53ca38aff0b9c45930c78640265a6fabb932e4aced67adf7","side":"right"},{"sibling":"6ee96c5806589324f66f8bb50f8f080b8ff312b3da410c230c009a3c1f53c460","side":"right"},{"sibling":"1fbd7344b27514ed9955dce9fa0d93accec16ddeb01d9f2580e8440b5cc82355","side":"right"},{"sibling":"118099894ddfd88f4b7cacaef273730c50e1543a013b86dd86be1e819e9de6f8","side":"right"},{"sibling":"0056ee67f86a31be6331b48f491dfa370c69a2c85230b156659bff6177e119f9","side":"right"},{"sibling":"92ad4fc36e2d8bd64a4d83e76fd8e6e0c9cc03786f4e389a46451d49428799b6","side":"right"},{"sibling":"5203bb116cea5471bab102351ae528fe783239665ad8c3a791a604a7146f231b","side":"right"},{"sibling":"b4b5fac84e1432ae7c3747859a1ce8e49081cee98975ffeee0646d5da13dd35d","side":"left"},{"sibling":"6be461ecf12dedf98a31921aa7b5c32d4a32df6897e0f697b8bf1a4ba3e2d324","side":"right"},{"sibling":"c2861a8cef3eb66bf2726aa377c24a6bf6e8b7489dcd0e870b61d62a35ccadfb","side":"right"},{"sibling":"134949308b15cffd6792ee2cf678119af34d69a64764d7c89cd47573c94e1cda","side":"left"},{"sibling":"debbc1a6232ea7970009b91bdc2345041b2de5ac59551f955855d579001e512c","side":"right"},{"sibling":"216869846f40bd905626884f58cb67b9019e488b3656946a7808c436ab7339ac","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e734b0c6d6d13acb5f4cf00367b3913e5bbf1aa717377aa4e4820c6de24b7673","side":"right"},{"sibling":"4bbb7f78e96179bb9cdd06d7207b66b3503ab68e4880438263025b04ebe8f7ec","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":149835,"merkle_root":"51484a548bc0cf3d178eec868e98935c87f0aa83369143b7c96b048585e5ba01","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260525T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-25T05:37:33Z","sig_algorithm":"ed25519","signature":"99a657e53a015ace0bade5d7fbb3f60f950b6d1e1128251a63afcc454a492422cae5efdc0c18503b4f7e62f371bd48f2889be78d9048c4681d6c1e73f754d705","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_8d0f032be08804348e8c8f6129da07f744e282c14a4a3d946e5238c3e3df51e0"}}