# Liquidity Pool Smart Contracts as Decoherence-Free Subspace Volumes within a Hilbert Space

***Smart contracts can be seen as isolated clusters of decoherence-free subspace volumes within a Hilbert space, where local logic breaks away from general logic*** [1]. Decoherence-free subspaces represent portions of a quantum system that remain coherent and unaffected by **environmental noise, allowing for the preservation of quantum information [2].**

In the context of smart contracts, local singularities within free subspace volumes could lead to altered states via shockwaves, such as the **initiation of spiraling singularities and ever-altering states** [3]. Local singularities in an ideal fluid, for example, are points where the fluid's properties become infinite or undefined, such as the formation of a shock wave. Shock waves can form when a fluid encounters a sudden change in its environment, like a collision or expansion, resulting in the fluid's density, pressure, and **velocity becoming infinite** at the **shock front** [3].

The concept of local singularities in smart contracts could potentially be applied to understand the **emergence of complex pricing dynamics** within decentralized systems, such as blockchain technology.

# Local singularities from emerging complexity and diversity within decoherence-free subspace volumes (smart contracts) leading to altered Automated Market Marker Network states via shockwave propagation:

**Initiation of spiraling singularities:** the origins of ever-altering states:

A local singularity in an ideal fluid is a point at which the fluid's properties become infinite or undefined. This can occur when the fluid's density, pressure, or other physical characteristics become too large to be accurately measured or modeled.

One example of a **local singularity in an ideal fluid** is the formation of a **shock wave**. Shock waves are discontinuities in the fluid that **propagate** through the fluid at supersonic speeds, and they can occur when a fluid encounters a **sudden change in its environment, such as a collision or an expansion**. When a shock wave forms, the fluid's **density, pressure, and velocity can become infinite** at the shock front, leading to a local singularity.

**50/50 Weights liquidity pool I/O**

<iframe type="gif" src="https://upload.wikimedia.org/wikipedia/commons/b/b8/Inviscid_flow_around_a_cylinder.gif" width="650" height="500" ></iframe>

Image credit: Wikipedia.org

**Multiassets/Multiweights liquidity pool I/O**

One common example of a singularity in fluid dynamics is the point of separation in a flow, where the fluid separates from a solid surface and **forms a turbulent wake**. This can occur when the fluid flow is too fast or the surface is too smooth, causing the fluid to separate from the surface and form **eddies**.

<iframe type="gif" src="https://upload.wikimedia.org/wikipedia/commons/d/d2/Flow_around_a_wing.gif" width="650" height="500" ></iframe>

Image credit: Wikipedia.org

It is important to note that local singularities in ideal fluids are purely theoretical constructs, as it is impossible for the physical properties of a real fluid to become infinite. However, they can serve as useful tools for understanding the behavior of fluids under certain conditions. The following suggested computational environment may allow to remove for friction and get closer to a appromixates via virtualization and softwarization of the above-described phenomenas.

We suggest that transient states may allow for such model of informational shockwave propagation to exist in computational reality within Automated Market Makers networks.

<b>References:</b>
<span>[1] <a href='https://www.sciencedirect.com/science/article/pii/S1364032121012764' target='_blank' class='text-purple-1 underline'>Smart contracts in energy systems: A systematic review of ...</a></span>
<span>[2] <a href='https://www.mdpi.com/2078-2489/14/2/117' target='_blank' class='text-purple-1 underline'>Smart Contracts in Blockchain Technology: A Critical Review</a></span>
<span>[3] <a href='https://academic.oup.com/rfs/article-abstract/32/5/1754/5427778' target='_blank' class='text-purple-1 underline'>Blockchain Disruption and Smart Contracts - Oxford Academic</a></span>

<b>Other sources:</b>

Hamann, A., Sekatski, P. and Dür, W. (2021) Approximate decoherence free subspaces for distributed sensing, arXiv.org. Available at: https://arxiv.org/abs/2106.13828 (Accessed: 17 May 2023).

Lidar, D.A., Chuang, I.L. and Whaley, K.B. (1998) Decoherence free subspaces for Quantum Computation, arXiv.org. Available at: https://arxiv.org/abs/quant-ph/9807004 (Accessed: 17 May 2023).