Триединството на кубита
Един кубит има точно 3 безследови наблюдаеми — матриците на Паули X, Y, Z — генераторите на SU(2) и трите оси на Блох; dim su(2) = 2²−1 = 3 е принуден инвариант.
proof · the qubit's trinity · X Y Z
A qubit has exactly 3 independent traceless observables — the Pauli matrices X, Y, Z — the generators of SU(2) and the 3 Cartesian axes of the Bloch sphere; dim su(2) = 2²−1 = 3 is a forced algebraic invariant, not a chosen coincidence (Pauli 1927, Z. Phys. 43:601; Nielsen & Chuang 2000). The project's "trinity" has a genuine quantum-physics instance — and these are the same X, Y, Z the 64-seal already names as its three axis-generators.
checks — recomputed live in your browser
- ✓ Is Trinity
- ✓ Holds
evidence
- Pauli Axes
X, Y, Z- Dim SU2
3
✓ 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 179b549b-01cb-85c8-839c-e148bd8a58a5. Recompute and you get the same address — that determinism is the proof.
A real algebraic threefold of ONE qubit. It is independent of the 3 QCD colour charges and the 3 fermion generations: they share the numeral 3 but no common cause. Uniting them into one "3-6-9 trinity" is numerology — SU(3) has 8 gluons not 9, and the n-qubit Pauli basis is 4ⁿ not 3ⁿ.