powerSetQ3_2_2D
plain-language theorem explainer
The cardinality of the power set of the recognition lattice Q₃ equals 2 raised to 2 cubed. Researchers deriving set theory from recognition principles cite this to equate the lattice size 256 with spatial dimension three. The proof is a direct numerical evaluation via the decide tactic.
Claim. The power set of the recognition lattice Q₃ satisfies $|P(Q_3)| = 2^{2^3}$.
background
Recognition Science constructs set theory from the recognition lattice Q₃, a structured set whose power set encodes the five canonical ZF axioms (extensionality, pairing, union, power set, infinity) scaled by configDim D. The module states that |F(F₂³)| = 2^8 = 256, with the upstream definition powerSetQ3 fixing this value as 2^8. This supplies the concrete cardinality that the present equality identifies with the expression 2^(2^3).
proof idea
One-line wrapper that applies the decide tactic to confirm the numerical identity between the defined powerSetQ3 and 2^(2^3).
why it matters
The declaration supplies the structure_match field inside setTheoryCert, thereby certifying that the ZF power-set axiom reproduces the lattice cardinality 256. It directly instantiates the module proposition 256 = 2^(2^D) and aligns with the eight-tick octave and D = 3 spatial dimensions from the forcing chain T8. The computation is closed; no scaffolding remains.
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