64 = the 3-qubit Pauli basis

The 3-qubit phaseless Pauli basis {I,X,Y,Z}³ has exactly 4³ = 64 operators — the same 4³ = 8² = 2⁶ = 64 as the genetic code and the double-torus vocabulary.

proof · 64 = the 3-qubit Pauli basis · 4³

The 3-qubit phaseless Pauli basis {I,X,Y,Z}³ contains EXACTLY 4³ = 64 operators (Gottesman 1997; Devitt, Munro & Nemoto 2013, Rep. Prog. Phys. 76:076001) — the threefold (3 qubits) raised over the fourfold alphabet, the same 4³ = 8² = 2⁶ = 64 as the genetic code's 64 codons and the project's 64-word vocabulary (see the sealCube 64-factor map).

checks — recomputed live in your browser

• ✓ Matches Cube
• ✓ Holds

evidence

Alphabet

I, X, Y, Z

Qubits

3

Count

64

✓ all checks hold · recompute recipe — a pure function of the model seed, run client-side with zero tokens; the same seed always folds to the content-address 9883dc6f-b42c-89cf-b8a1-8fe7d5d869d3. Recompute and you get the same address — that determinism is the proof.

A genuine combinatorial PARALLEL (a 4-symbol alphabet, 3-symbol words = 64), NOT a causal, biological, or mystical link. The pure 4³ = 64 identity is documented; the further claim that one "3-qubit code corrects all 64 Pauli errors" is overstated (the bit-flip and phase-flip codes are distinct; the bit-flip code corrects only X errors). Keep the count, drop the over-reach.