feat: liquid alpha

[distributedstatemachine]

Description

This PR implements

• Liquid Alpha feature.
• moves the maths unit tests to the tests folder

Supercedes: #503

Related Issue(s)

• Closes #417

Type of Change

• [ ] Bug fix (non-breaking change which fixes an issue)
• [x] New feature (non-breaking change which adds functionality)
• [ ] Breaking change (fix or feature that would cause existing functionality to not work as expected)
• [ ] Documentation update
• [ ] Other (please describe):

Breaking Change

If this PR introduces a breaking change, please provide a detailed description of the impact and the migration path for existing applications.

Checklist

• [x] I have performed a self-review of my own code
• [x] I have commented my code, particularly in hard-to-understand areas
• [x] I have run cargo fmt and cargo clippy to ensure my code is formatted and linted correctly
• [x] I have made corresponding changes to the documentation
• [x] My changes generate no new warnings
• [ ] I have added tests that prove my fix is effective or that my feature works
• [x] New and existing unit tests pass locally with my changes
• [ ] Any dependent changes have been merged and published in downstream modules

Screenshots (if applicable)

Please include any relevant screenshots or GIFs that demonstrate the changes made.

Additional Notes

Please provide any additional information or context that may be helpful for reviewers.