Author: Jack Kowalski <jack@entropment.com>

Crawling of zero divisors in sedonions leading to NaN

• 1. This behavior is expected.
• 2. Key points:

This behavior is expected.

The implementation operates on a 16D Cayley–Dickson algebra (sedonions), which is non-alternative, non-normed, and contains non-trivial zero divisors. The arithmetic is performed using IEEE-754 floating-point numbers, i.e. a finite-precision projection of the underlying real algebra.

Key points:

1. Zero divisors are not isolated points. In sedonions, zero divisors form extended manifolds rather than single algebraic elements. When projected onto finite-precision floats, these manifolds become \varepsilon-thick regions instead of exact null sets.

2. Deterministic drift under iteration. The system is fully deterministic. Apparent randomness arises from sensitivity to rounding and cancellation in IEEE-754 arithmetic, not from stochastic input. Small perturbations caused by rounding errors result in systematic drift of zero-divisor components between coordinates.

3. "Crawling" is a structural effect, not instability. Under repeated nonlinear mixing (e.g. sedonion → octonion → quaternion projections), zero-divisor states do not remain fixed but migrate across components. This crawling behavior is a natural consequence of iterating a non-normed algebra on a discrete numerical lattice.

4. NaN is a boundary marker, not a bug. NaN values arise when trajectories intersect algebraic singularities amplified by finite-precision projection (e.g. \infty - \infty, 0 \cdot \infty). In this context, NaN acts as an absorbing boundary condition in the IEEE-754 state space, not as an implementation error.

5. No physical randomness is involved. The computation is entirely deterministic. The observed loss of reproducibility at the real-number level is due to the impossibility of "hitting the same point" exactly in a discretized algebra with zero divisors.

In summary, this code does not approximate real-valued sedonions; it defines a deterministic dynamical system on the IEEE-754 projection of a zero-divisor algebra. The crawling of zero divisors and occasional collapse into NaN are intrinsic and expected properties of this system.