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

Patent Pending

NOTE: Ontological status of IEEE-754 arithmetic in this construction
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This code deliberately treats floating-point behavior (IEEE-754)
as a *primary algebraic structure*, not as an approximation of ℝ.

Key design stance:

1. IEEE-754 arithmetic is NOT assumed to be an implementation of the
   real numbers ℝ.
   It is treated as a discrete, projective numerical space with:
   - minimal scale ε (machine epsilon),
   - non-numeric states (NaN, ±Inf),
   - path-dependent evaluation (ordering matters),
   - loss of global associativity and distributivity.

2. From this perspective, deviations from ℝ are NOT "errors".
   They are structural properties of the underlying numerical space.

3. Zero divisors and near-zero states are treated as *dynamical objects*,
   not algebraic defects.
   Under iteration, they may:
   - persist,
   - drift ("crawl") across rounds,
   - fall below ε and collapse to 0,
   - or escape to NaN,
   depending on the number and coupling of perturbed floating-point
   operations.

4. Over ℝ, the corresponding algebra (e.g. CD algebras, sedenions)
   exhibits fixed zero-divisor structure.
   Over IEEE-754, this structure becomes a *pseudo-orbit*:
   - deterministic,
   - architecture-consistent,
   - but no longer stationary.

5. This behavior is EXPECTED and intentional.
   It arises from projecting a continuous algebra with zero divisors
   onto a discrete numerical lattice with finite mantissa.

6. The resulting dynamics are:
   - deterministic (no randomness involved),
   - highly stable with respect to rounding modes,
   - sensitive to global scale (mantissa/exponent geometry),
   - and unsuitable for interpretation within classical ℝ-based algebra.

This code therefore operates in a different ontological regime:
not "real-number algebra with errors",
but "projected algebra with intrinsic numerical dynamics".