Data Entropment Labs https://entropment.com
Author: Jack Kowalski <jack@entropment.com>

Patent Pending

NOTE: Crawling of zero divisors in sedonions leading to NaN

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 ε-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. ∞−∞, 0·∞). 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.