We formalize the "Butterfly's Secret" — the prediction that the four major fields of the Book of Knowledge (BOK) undergo bilateral symmetry transformations in which Quadrant II maps onto Quadrant I *simultaneously* with Quadrant III mapping onto Quadrant IV. This bilateral simultaneous mapping is identified as a complex reflection: z → −z̄ (negation of the real part, preserving the imaginary part). We then compare this operation with the action of the four-chambered heart, which implements a *cyclic* bilateral operation (a 90° rotation through the GILE quadruplet) rather than a reflective one. The key result: the butterfly generates the reflection subgroup of the dihedral group D₄, the heart generates the rotation subgroup, and **together they generate the complete dihedral group D₄ — the full symmetry group of the Book of Knowledge.** D₄ is the symmetry group of a square and has 8 elements: 4 rotations and 4 reflections. This is identified as "the rhythm of computation itself." A remarkable external validation: the same D₄ symmetry governs the Riemann zeta function via its functional equation and complex conjugate symmetry — the BOK symmetry group and the symmetry group of the prime number distribution are identical.
Brandon Charles Emerick (Tue,) studied this question.