Clean up and update

[Al-Kindi-0]

This PR merges changes from the original Plonky3. It also renames our version of FRI to p3-miden-fri which will ease our transition to lifted FRI.

More precisely, we add the following

Crated	Based On	Purpose
p3-miden-goldilocks	p3-goldilocks	Goldilocks field with Miden compatibility APIs
p3-miden-uni-stark	p3-uni-stark	Extended Entry enum with Aux/Periodic variants
p3-miden-fri	p3-fri	Miden naive FRI implementation with higher folding factors
p3-miden-air	p3-air	Miden AIR traits and types
p3-miden-prover	-	Miden prover combining the above crates

---

1. p3-miden-goldilocks

Based on: p3-goldilocks

Purpose: Provides the Goldilocks field with additional APIs for compatibility with miden-crypto, especially const support.

Key Changes from p3-goldilocks

// Additional constructors
pub const fn new(value: u64) -> Self
pub const fn from_u64_unchecked(value: u64) -> Self
pub const fn from_u64_array<const N: usize>(values: [u64; N]) -> [Self; N]

// Accessor methods
pub const fn inner(&self) -> u64
pub const fn as_int(&self) -> u64  // Alias for as_canonical_u64()

// Validated constructor (replaces TryFrom<u64>)
pub fn try_checked(value: u64) -> Result<Self, String>

Why These Changes

• new() and from_u64_unchecked(): Const constructors needed for compile-time field element creation
• as_int(): Compatibility alias, should be easy to drop.
• try_checked(): Replaces TryFrom<u64> which conflicts with the blanket impl from From<u64>

---

2. p3-miden-uni-stark

Based on: p3-uni-stark

Purpose: Extends the Entry enum with Miden-specific variants for auxiliary traces and periodic columns.

Key Changes from p3-uni-stark

// Extended Entry enum
pub enum Entry {
    Preprocessed { offset: usize },
    Main { offset: usize },
    Permutation { offset: usize },
    Aux { offset: usize },      // NEW: Auxiliary trace columns
    Periodic,                    // NEW: Periodic columns
    Public,
    Challenge,
}

// Updated degree_multiple for new variants
impl SymbolicVariable {
    pub const fn degree_multiple(&self) -> usize {
        match self.entry {
            Entry::Preprocessed { .. }
            | Entry::Main { .. }
            | Entry::Permutation { .. }
            | Entry::Aux { .. } => 1,           // Aux has degree 1
            Entry::Public | Entry::Periodic | Entry::Challenge => 0,  // Periodic has degree 0
        }
    }
}

Re-exports from p3-uni-stark

The crate re-exports StarkGenericConfig, StarkConfig, and related types from p3-uni-stark to ensure a single trait definition across the codebase:

// config.rs
pub use p3_uni_stark::{
    Domain, PackedChallenge, PackedVal, PcsError, StarkConfig, StarkGenericConfig, Val,
};

Why These Changes

• Entry::Aux: Required for Miden's auxiliary trace columns used in permutation arguments
• Entry::Periodic: Required for periodic columns (columns with values that repeat with a fixed period)

---

3. p3-miden-fri

Based on: p3-fri

Purpose: Miden-specific naive FRI implementation supporting higher arity folding factors.

---

4. p3-miden-air

Based on: p3-air

Purpose: Miden AIR (Algebraic Intermediate Representation) traits and types.

Key Components

• AIR trait implementations for Miden VM with aux trace support

---

5. p3-miden-prover

Based on: Combines multiple crates

Purpose: The main Miden prover that orchestrates proof generation and supports aux trace generation.

Dependencies

p3-miden-goldilocks
p3-miden-uni-stark
p3-miden-fri
p3-miden-air
p3-air
p3-field
p3-matrix
p3-commit
p3-challenger

Key Components

• prove() and verify() functions
• LogUp argument implementation (could be dropped as we are not making use of it)
• Constraint folding to handle aux constraints

---

Upstream Compatibility

The following core Plonky3 crates remain unchanged from upstream:

• p3-field - Core field traits and implementations
• p3-uni-stark - Base univariate STARK framework
• p3-fri - Base FRI implementation
• p3-air - Base AIR traits
• p3-matrix - Matrix operations
• p3-commit - Polynomial commitment schemes
• p3-challenger - Fiat-Shamir challenger
• p3-symmetric - Symmetric cryptography primitives
• p3-merkle-tree - Merkle tree implementation

[Al-Kindi-0]

We changed the approach to using https://github.com/0xMiden/p3-miden