reduceConfig
plain-language theorem explainer
Freely reduces every loop in an utterance by applying free reduction to each word. Loom users cite it as the total, linear normaliser that erases spelling before checking or evaluating. The body is a one-line list map of free reduction, so every downstream question about the result stays cheap and always answerable.
Claim. For a configuration $c$ (a finite list of words representing closed walks that share one basepoint), return the configuration obtained by freely reducing each word of $c$.
background
Loom treats a finished recognition history as a configuration: a finite list of words in the free group of rank five on the eight-state, three-axis window (the closed walks up to homotopy). Spelling is not content, so words are read up to free reduction; the module supplies a total checker, a computable invariant, and theorems that the invariant is blind to free reduction and simultaneous conjugation.
A Config is an utterance: List Word. Free reduction of a single word is total and linear: it walks the list and cancels adjacent inverse pairs via a cons-with-cancel step. Mapping that operation across the list is the configuration-level normaliser. Upstream free reduction is documented as the reason every question the language can ask is cheap and always answerable.
proof idea
One-line definition: map free reduction over the list of words. No proof obligations; the computational content is exactly list map of the already-total word reducer.
why it matters
This is the spelling normaliser for the whole Loom stack. Downstream, every reduced configuration is pointwise reduced (all_isReduced_reduceConfig); the SL(2, Z/3Z) invariant is unchanged by it ("Spelling is not content"); and framing then reducing yields a well-formed utterance the checker always accepts. The grammar's weaver builds content by framing a body and calling this reducer, so every honest utterance is well formed in linear time. Gauge images (automorphism, optional global reverse, basepoint move, free respelling) also finish by reducing, so quotienting by non-content operations stays computable. It sits under the module's two non-content premises: free reduction and basepoint conjugation, aligned with the eight-tick window and free group of rank five from the forcing chain.
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