Experimental control · v0.1

OMEGA drift experiment

A hypothesis that a 4D OMEGA frame could stabilize drifting representations is tested rather than assumed. The experimental operator is not a theorem of Paper VII and is not a drift-correction law in the reference-geometry prototype. The published run finds no universal privilege.

This is not a source paper and not part of Paper VII. It does not modify frozen SRSD. A matched-case reconstruction advantage is the generic advantage of a correct model, not evidence that Ω₀ is privileged. Interactive pair clocks and torus winding: /geometry/pair-dynamics.

Scope boundary

Paper VII v1.6 specifies a Euclidean marked kernel and exact reconstruction. The OMEGA_REFERENCE_GEOMETRY/0.1 prototype specifies state coordinates and frozen SRSD encode/decode. Neither work specifies a dynamical drift-correction law.

This experiment therefore does not silently add one. It introduces an explicit experimental candidate and tests it against generic controls, including adversarial mismatch and uniformly random 4D dynamics. All floating-point uses of φ, π, and Ω₀ here are noncanonical numerical approximations used only for simulation. Seed 20260831.

Real AI embedding model used: false.
Embedding test is a synthetic proxy: true.
Spiral operator is a new experimental operator: true.
SRSD is frozen and external: true.

Hypothesis operator

R_\Omega=R(2\pi\lambda)\oplus R(2\pi\mu),\qquad\lambda=\varphi/(\varphi+\pi),\;\mu=\pi/(\varphi+\pi).

Because $\lambda+\mu=1$ , the two plane rotations are equal-magnitude counter-rotations modulo $2\pi$ . Approximate constants in this run: λ = 0.33994977134477894, μ = 0.660050228655221, α+β over 2π = 0.9999999999999999.

E0 — exact SRSD control

10,000 exact rational 4D states. Failures: 0. Exact encode/decode is lossless; representation alone cannot correct or create drift.

E1 — matched OMEGA spiral

Direct procedural reconstruction prevents cumulative roundoff when the dynamics are known exactly. A generic direct renderer with the same true dynamics gives the same advantage.

Mean state error versus step count. Log–log. Direct reconstruction of the known dynamics does not accumulate roundoff; iterative float32 does. Any correct model has the same advantage.

E2 — adversarial mismatch

True frequencies are perturbed by Δα = 0.00001, Δβ = -0.000017. A fixed OMEGA anchor becomes wrong if the actual dynamics are not OMEGA-aligned. The correct generic model remains stable.

E3 — synthetic embedding proxy

N = 800, D = 64, 20 clusters, 5,000 steps, float16.Relational geometry (kNN) can remain nearly intact even while absolute state is wrong under a common wrong rotation. Absolute fidelity and relational fidelity must be scored separately.

E3 synthetic embedding proxy. Absolute fidelity and 10-NN retention scored separately.
Setting	Method	Mean state error	Mean cosine	kNN-10 retention
matched OMEGA dynamics	iterative float16	2.400e+0	0.966473	0.978875
matched OMEGA dynamics	direct OMEGA anchor float16	2.898e-4	1.000000	0.999625
mismatched dynamics	iterative float16	6.632e-1	0.879650	0.977625
mismatched dynamics	OMEGA wrong-model anchor	5.713e-1	0.836736	0.999625
mismatched dynamics	generic true-model anchor	4.043e-4	1.000000	0.999250

Under a common wrong rotation the kNN graph can remain almost intact (retention 0.9996) while absolute cosine falls to 0.837. Relational geometry is not a substitute for absolute state fidelity.

E4 — uniform random dynamics

2,000 random 4D tasks, 200 random fixed anchors, horizon 1,000 steps. Across uniformly random dynamics, OMEGA performs like an ordinary fixed anchor; no universal privilege is detected.

OMEGA anchor mean state error: 1.333999
Random-anchor mean of means: 1.331828 ± 0.005437
Fraction of random anchors better than OMEGA: 0.56
Best random anchor: 1.320583
Worst random anchor: 1.340939

no universal privilege detected56% of random fixed anchors scored better than the OMEGA pair on this distribution.

Files

omega_drift_experiment.py · 12776 bytes · SHA-256 1ba1d3d24360fae96bb98d3822a2b91b5de3cd319e5e3ce3e6cca52d29b03bd4
results.json · 7038 bytes · SHA-256 02708842d1f0682d92dd25d03418f2cbf28125554750929c2cf5f6af5613b0fb
SPEC_SCOPE.md · README.md

Run: python3 omega_drift_experiment.py. Requires NumPy. Passing a rerun is a numerical reproducibility check of this experimental script, not a theorem of Papers I–VII.

Return to Paper VII geometry. The archive makes no blanket claim of novelty, priority, peer review, or independent validation. Some displayed identities are standard or definitional and are included to make the computational specification self-contained. Any claim of originality must concern a specifically stated formulation or derived result and must be evaluated separately against the relevant prior literature.