pith. sign in
def

f2sq_card

definition
show as:
module
IndisputableMonolith.Mathematics.FourColorTheoremFromRS
domain
Mathematics
line
33 · github
papers citing
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plain-language theorem explainer

f2sq_card defines the cardinality of the vector space F₂² as four. Researchers deriving the four color theorem from Recognition Science cite this value when equating colors to the size of the 2-bit field at D=3. The definition is a direct power computation with no lemmas required.

Claim. The cardinality of the finite vector space $F_2^2$ equals 4.

background

The module derives the four color theorem from Recognition Science by identifying four colors with the elements of F₂², the two-dimensional vector space over the field with two elements. This space contains the pairs (0,0), (0,1), (1,0), (1,1). The module states that four equals D+1 at spatial dimension D=3 and also equals 2², with all equalities decided by computation.

proof idea

The declaration is a direct definition that evaluates 2 raised to the power 2.

why it matters

This supplies the explicit integer value used inside the FourColorCert structure and the theorem four_eq_F2sq. It completes the identification of four colors with 2², which the module links to the D=3 recognition lattice from the forcing chain T8.

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