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Human iEEG shows that hippocampal sharp-wave ripples (SWRs) gate episodic recall, ripple-locked cortical reactivation recapitulates encoding-time patterns, and multi-hop replay fidelity decays multiplicatively along sequence length. These literatures have advanced in parallel without a shared algebraic object. We show that VaCoAl, an algebro-deterministic hyperdimensional memory architecture built from Galois-field LFSRs, supplies that object. Specifically, deterministic Galois-field diffusion provides a substrate-level alternative to Vector-HaSH's random scaffold-to-hippocampus projection that satisfies the same quasi-orthogonality requirement, with matched second-moment statistics, stronger avalanche behavior, and bi","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:2605.15652v1 Announce Type: cross \nAbstract: Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose that the hippocampal-entorhinal circuit factorizes content from a prestructured grid-cell scaffold and supports compositional memory via ripple-mediated replay. Human iEEG shows that hippocampal sharp-wave ripples (SWRs) gate episodic recall, ripple-locked cortical reactivation recapitulates encoding-time patterns, and multi-hop replay fidelity decays multiplicatively along sequence length. These literatures have advanced in parallel without a shared algebraic object. We show that VaCoAl, an algebro-deterministic hyperdimensional memory architecture built from Galois-field LFSRs, supplies that object. Specifically, deterministic Galois-field diffusion provides a substrate-level alternative to Vector-HaSH's random scaffold-to-hippocampus projection that satisfies the same quasi-orthogonality requirement, with matched second-moment statistics, stronger avalanche behavior, and bi","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":"2026-05-18T04:43:11Z","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":"ed25519:15e99ff7a72e6092a4297ad25495ba3a18517c0b11f522f99fc933f288b084f69d3bd71b0a6507e9667733d1d0441cae7e3bb7825b34fd7f77fcc0b304a2d005","signer":"crovia.substrate","subject":{"observed_at":"2026-05-18T04:43:11Z","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":"e38d9bc1326a966bc3e1b3fee24d14aeef5b9781300a219e43f262df3ddfd529","leaf_index":140621,"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":"30e765b180e1d0af62b3b1ce5d60eed5c9ae572f39486a98d85cc55db976e00b","side":"left"},{"sibling":"41a6221429c902a5cdc01d2e9bad325f6f5202c3851f77674f3fd34d827c54db","side":"right"},{"sibling":"b803c9ebee0dad01b45690867c1ae8adb4dcb1d7be0cad6e9400aa51e6afd245","side":"left"},{"sibling":"9f8fb99086ce75c338b3fd865412e2c952eb99316ba16ea6de74d5581e7e5fe0","side":"left"},{"sibling":"1bed136be1b4ea3e9cc07b06eedb51bc35fb6aa8481dd003da922207e468ff6f","side":"right"},{"sibling":"98d5140aed30c0c7d91961eb0b59182f26a7143dcf5fb8034051461962c32b58","side":"right"},{"sibling":"5c5831ea238589ca34ebaf3b0f0f0a78017dbf0ef2a7b97c29b6180efe9bafc5","side":"left"},{"sibling":"b29bcbd6adca3228d98aa21ca6aabf98e279340820cd7a960b41569223eebf29","side":"right"},{"sibling":"6bedf73520cf3dd8758d8bdedf3be245de9aea97abd42934aae25539176ae1b2","side":"left"},{"sibling":"07abc3bad689e74e6304772503dc9372a118e6f66883b8e88c43414efddac063","side":"right"},{"sibling":"28b78fb112bcf26b6801664db97eb8f52a9bccbf0a7ae6766e11845d443692df","side":"left"},{"sibling":"68d0a4634c1460a19c92edd9480df3aa733b814463e7420d1e14471bf61b2f83","side":"right"},{"sibling":"8af64f275b862349aa3bbb9d5cd7fa9a7fdd5620af3bf1b36b2a4519b0b53bdf","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"b98c2afadb358e5387e88f19588f8343a81b488d9b44a6f7e57a032db3a1b030","side":"right"},{"sibling":"11b0c1591747f09f7c8971a6caa19befcd81317ca9dfd417b143234df4e10c79","side":"right"},{"sibling":"87206f3bcc342797c990d87f7235c01f78d32ca59cfaf8ad18d71afc879ba477","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":140892,"merkle_root":"6cca56ead155990456b8a014cc50bddbe710f409b26e3d1bfa6fb12b0bfcf6bf","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260518T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-18T05:37:30Z","sig_algorithm":"ed25519","signature":"1e1135f7595f79b14fb11f5fa81a2e17ad31b11b44b427a5e40a7d511cd86447daf492babd368ab571cf26404c8c74c450d460130fca4b064eb2760367489a0f","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_39fbc94ee8e4c9188e57254170688b9c5f2515e90b08970ed2156008beb104ff"}}