Tile the cell and the cube doesn't vanish — it changes job. A 3-cell neighbourhood (left, centre, right), each {−1,0,+1}, has exactly 27 configurations, so the unit cube is now the lookup table of a ternary cellular automaton. Time runs downward. The honest scaling result is on the right: the global state space is 3ᴺ and exhaustive enumeration dies immediately — but the local rule stays 27 entries you can read in full at any size, and for structured (additive) rules superposition lets you prove global behaviour without ever enumerating it. Keep the rule linear and auditability survives the tiling; go nonlinear and it's gone.
Bridge-Burners LLC · Fiddler · 27 = the rule table · global = 3ᴺ · additive ⇒ provable · (0) = held vacuum · anchor: AKASHA
−1 0 (held vacuum) +1
The local rule = the 27
27 neighbourhood configs → 27 outputs. The whole rule, visible, at any lattice size.
Global state space = 3ᴺ
Enumerating the whole lattice dies fast. Coverage ≠ scale.
Can you prove it without enumerating?
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Superposition: does evolve(A⊕B) = evolve(A)⊕evolve(B)? If yes, predict any config as a sum of single-cell impulses — no 3ᴺ.
What tiling does to audit
SurvivesThe local rule (27 entries) stays fully auditable at any size; the held vacuum (0) persists; additive rules are provable by superposition — N impulse responses, never 3ᴺ states.
TransformsAudit shifts from "enumerate every global state" to "verify the rule + prove an invariant that lifts." Same rigor, different object.
LostFor nonlinear/generic rules there's no shortcut — and ternary CA can be Turing-complete, so global prediction is formally undecidable. Exhaustive global audit is genuinely gone.