Where Polanyi Meets Galois: Tacit Knowing as an Algebro-Deterministic Operation, Toward Re-rooting AI-Generated Science

arXiv:2610.16102v2 Announce Type: replace Abstract: We argue that tacit knowing is better modelled as an operating regime of a memory than as a kind of content. Our substrate is VaCoAl, an algebro-deterministic XOR-and-shift hyperdimensional memory over GF(2), realized as CASRAM and PyVaCoAl. In it, a DAG reads two ways. Repairing every collision (Rescue) makes the trace exactly auditable but ranks no path higher; tolerating them (Don't Care) yields a path confidence, CR$_2$, silently favouring direct routes. This audit-valuation complementarity formalizes Polanyi's claim that tacit and explicit are not sharply divided. It separates contingent tacitness, which a new query brings out (AlphaGo's game tree), from regime-bound tacitness, statable only once it is gone (AlphaGo's hunches). (1) Polanyi's from-to structure reads as non-commutative binding. (2) Explicating the valuation destroys it, as with Polanyi's pianist, yet a closed-form law states it. Polanyi, Nonaka, Tsoukas and Collins each capture part of this, narrowly; even Nonaka and von Krogh's continuum cannot tell the classes apart. (3) Collins's three tacit knowledges become strata, one outside the substrate. (4) Our mentor-student DAG is a tacit-transmission graph. (5) Tao's remark that AI-solved problems spawn few follow-ups reveals rootless explicit knowledge: checkable results no one can trace or yet understands. To re-root them, LLMs generate, VaCoAl/PyVaCoAl keeps an auditable trace with its confidence, and people value, a role virtue epistemology shows cannot be offloaded. Art, craft and skill show the same decoupling of form from the maker's becoming. (6) On Mercier and Sperber's account an LLM is reason's arguing side set loose, a sophist; truth-seeking lies deeper, in Polanyi's conviviality, which we conjecture is the root of evolvability and, as the Buddhist idea that plants and lands attain buddhahood suggests, reaches beyond humans. Testable predictions follow.