# OMEGA Drift Experiment v0.1

This is a falsification-first benchmark for the proposed idea that a 4D OMEGA
reference frame could act as a stable memory anchor.

## Critical boundary

The declared `OMEGA_REFERENCE_GEOMETRY` package specifies geometry and exact
reconstruction. It does **not** specify a dynamical "drift correction" law.

Paper VII v1.6 is a Euclidean marked-kernel theorem. It does not define a
memory-drift operator.

So this experiment does not silently add one to those works. Instead it
introduces one explicit experimental candidate:

\[
R_\Omega = R(2\pi\lambda)\oplus R(2\pi\mu),
\qquad
\lambda=\phi/(\phi+\pi),\quad \mu=\pi/(\phi+\pi).
\]

Because \(\lambda+\mu=1\), these are equal-magnitude counter-rotations modulo
\(2\pi\).

That operator is a **hypothesis layer**, not part of Paper VII and not part of
the frozen geometry.

## Experiments

- **E0 — exact SRSD control:** 10,000 exact rational 4D states.
- **E1 — matched OMEGA spiral:** float32 iterative evolution vs direct anchored reconstruction.
- **E2 — adversarial mismatch:** slightly perturb the true rotation frequencies.
- **E3 — synthetic embedding proxy:** 800 clustered 64D vectors, float16, 5,000 steps.
- **E4 — random-dynamics control:** compare OMEGA to 200 random fixed anchors across 2,000 random 4D dynamics.

## Run

```bash
python3 omega_drift_experiment.py
```

Requires Python 3 and NumPy.

## Interpretation rule

A positive matched-case result is not enough. It only counts as OMEGA-specific
evidence if OMEGA beats matched generic controls on a task distribution that was
not itself constructed from OMEGA dynamics.

The published `results.json` records that, across uniformly random dynamics,
OMEGA performs like an ordinary fixed anchor. No universal privilege is
detected.

The benchmark reports absolute state fidelity and relational geometry
separately, because a common wrong orthogonal rotation can preserve pairwise
relationships while putting every individual state at the wrong absolute phase.