fix: solvable intermediate gates for csat

[guipublic]

Description

Problem*

The width reduction creates intermediate variables from an expression. However, if an unknown variable is used for the intermediate one, from the expression, the intermediate is also unknown. In that case the csat generates an arithmetic gate with 2 unknowns and it cannot be resolved in one step.

Resolves

Summary*

We only use 'known' witnesses when generating intermediate variables.
To do this, we track the 'known' witness in a map, after each opcode that the transformation pass processes.

Additional Context

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[TomAFrench]

Thanks for this! Will do a full review next week.

[TomAFrench]

I think we should track this on the Circuit struct as a "required witnesses to begin execution" field.

I thought a bit more about this and decided that we should instead track the private inputs to the circuit rather than the full set of witnesses required to start execution. We can then calculate this from private+public parameters.