Implement SPARK Integration for Deferred R1CS Evaluations

[batmendbar]

Summary

This PR implements SPARK, a proof system used to verify deferred evaluations of R1CS (Rank-1 Constraint System) matrix MLEs (Multilinear Extensions).
SPARK extends the prover and verifier stack to support deferred computation flows in WHIR, improving efficiency while maintaining correctness and soundness guarantees.

Key Changes

• Added core SPARK module implementing deferred evaluation proofs for R1CS matrices.
• Added supporting CLI tooling for SPARK proof generation and verification.
• Added option to the recursive verifier to prove evaluation through SPARK.

Motivation

Deferred evaluation of MLEs improves prover efficiency by allowing WHIR to use lazily computed values which are verified later in the proof flow. SPARK provides a mechanism to prove that these deferred evaluations are consistent and correct, ensuring soundness while maintaining performance.

New end-to-end flow:

noirup --version v1.0.0-beta.11
cd noir-examples/noir-passport-examples/complete_age_check
nargo compile
cargo run --release --bin provekit-cli prepare ./target/complete_age_check.json -p ./noir-provekit-prover.pkp -v ./noir-provekit-verifier.pkv
cargo run --release --bin provekit-cli prove ./noir-provekit-prover.pkp ./Prover.toml -o ./noir-proof.np
cargo run --release --bin provekit-cli verify ./noir-provekit-verifier.pkv ./noir-proof.np
cargo run --release --bin provekit-cli generate-gnark-inputs ./noir-provekit-prover.pkp ./noir-proof.np
cargo run --release --bin spark-cli -- prove --noir-proof-scheme ./noir-provekit-prover.pkp --noir-proof ./noir-proof.np 
cargo run --release --bin spark-cli -- verify --spark-proof spark_proof.json --noir-proof ./noir-proof.np 
cd ../../../recursive-verifier/cmd/cli
go run . --evaluation spark --config ../../../noir-examples/noir-passport-examples/complete_age_check/params_for_recursive_verifier --spark_config ../../../noir-examples/noir-passport-examples/complete_age_check/gnark_spark_proof.json --r1cs ../../../noir-examples/noir-passport-examples/complete_age_check/r1cs.json --saveKeys "./keys" 

[shreyas-londhe]

Suggested change

	- name: Build provekit-cli
	- name: Build spark-cli

[shreyas-londhe]

todo: This file should be deleted.

[shreyas-londhe]

suggestion: Please send a reference to alpha.

[shreyas-londhe]

todo: this should be a separate function.

[veljkovranic]

sparkTranscriptT that T at the end seems like a typo that we had for quite a while, and it got reused here