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Coherence Law - Abstract

The Law of Coherence is a field equation, not a slogan.

Coherence across many-body degrees of freedom is governed by a simple empirical law. Defining the global order parameter C = √(⟨X⟩² + ⟨Y⟩²) from phase samples θᵢ, we observe (i) Gaussian dephasing C(σ) ≈ e−ασ², (ii) return-to-attractor dynamics Ċ = −κ(C − C∗), and (iii) finite-size scaling C(N) ≈ C₀ − βN⁻¹, with a stable fixed point C∗ ≈ 1. The same relations hold in simulation and hardware-stress surrogates over wide sweeps of disorder and scale. These regularities define a minimal framework for coherent computing.

Law of Coherence(TM) - conceptual field model by Rucker Labs.

01 - Relaxation
Return to a target
Ċ = −κ(C − C∗)
At any point in the field, coherence C(t) is pulled toward a target level C∗. The constant κ sets how quickly you snap back; because C∗ shifts with context and attention, the field never truly stops moving.
02 - Dephase
Gaussian dephasing
C(σ) ≈ e−ασ²
Noise broadens phases and drops C along a Gaussian curve. The slope α captures how aggressively coherence decays under disorder; across constructions, the same curve reappears.
03 - Scale
Finite-size scaling
C(N) ≈ C₀ − βN⁻¹
Finite ensembles saturate toward a common asymptote. As N grows, the gap closes like β/N, revealing the fixed point C∗ ≈ 1 that anchors the field across scales.

The toy model is a thin slice of the field evolving over time: a one-dimensional band of coherence that relaxes toward a drifting target, rides on a gentle wave of motion, and runs into a few fixed feature zones.

In higher dimensions, patterns get richer, not different. Ridges form where motion, structure, and attention line up; troughs mark places where the law fights noise. OpenSpace is the part where you feel those ridges directly, instead of only looking at the math.

Toy coherence field