logical-connectives
Logical Connectives
Every Boolean function of two inputs can be written as a four-bit output column. The sixteen possible columns are the vertices of the Boolean tesseract Q₄ and form the rank structure 1–4–6–4–1.
Interactive field guide
The dependency-free site in docs/ turns the tesseract into an interactive
catalogue. Every connective has one canonical four-bit definition from which
the index card, prose description, truth table, and live evaluator are
generated. This keeps the explanation and executable behaviour aligned.
Open docs/index.html directly, or serve the repository root with any static
file server and visit /docs/. Run the catalogue check with:
node tests/connectives.test.mjs
The site is an interactive companion to The Geometry of Expressibility: Logic at the Corners of a Continuous Relational Space, originally developed under the title From NAND to Xanadu. The complete LaTeX manuscript is available at essay/geometry-of-expressibility.tex.
The complete three-input Boolean-function space has 2⁸ = 256 vertices and is therefore Q₈. Any Q₄ → Q₅ extension denotes one additional independent coordinate on the two-input function space rather than the complete three-input function space.