feat(prover): persist the derived Lagrange SRS so it isn't re-derived on every start

prover/Makefile

@@ -66,7 +66,7 @@ setup: bin/prover
 ## Copy the prover assets to the S3 bucket (zkuat)
 ##
 copy-prover-assets:
-	aws s3 sync --exclude "*prover/dev*" --exclude "*05b9ef1*" --exclude "*05b9ef1*" --exclude "*96e3a19*" --exclude "*a9e4681*" prover-assets s3://zk-uat-prover/prover-assets/ --profile=zk-uat-s3-access
+	aws s3 sync --exclude "*prover/dev*" --exclude "*05b9ef1*" --exclude "*05b9ef1*" --exclude "*96e3a19*" --exclude "*a9e4681*" --exclude "*_derived*" prover-assets s3://zk-uat-prover/prover-assets/ --profile=zk-uat-s3-access
 
 download-srs:
 	aws s3 sync s3://prover-assets/kzgsrs/ ./prover-assets/kzgsrs --exclude "*" --include "*.memdump"

prover/README.md

@@ -22,6 +22,14 @@ The repository counts 2 main binaries:
 The setup-generation (`make setup`) is used to generate the setup for all the types of provers. Execution, Decompression and Aggregation.
 By default, if the `--force` flag is not provided, the tool will compile the circuit and check if the destination dir already contains a setup that matches, skipping the CPU intensive phase of the actual plonk Setup if needed.
 
+The setup also persists the Lagrange form of the SRS into the `kzgsrs` directory
+(as `kzg_srs_lagrange_<size>_<curve>_derived.memdump`) whenever it is missing, so
+prover starts load it in seconds instead of re-deriving it for hours. Ceremony
+files are never modified, and nothing writes into the directory at prove time.
+Set `persist_derived_srs = false` in the config to keep the SRS directory
+strictly read-only; `--force` additionally re-validates an existing derived dump
+in full and repairs it if it does not load.
+
 **Run**
 
 ```sh

prover/circuits/srs_provider.go

@@ -12,6 +12,21 @@ type SRSProvider interface {
 	GetSRS(ctx context.Context, ccs constraint.ConstraintSystem) (kzg.SRS, kzg.SRS, error)
 }
 
+// LagrangePersister is implemented by SRS providers that can pre-compute the
+// Lagrange basis and leave it on disk for later runs.
+//
+// It is deliberately separate from SRSProvider: obtaining an SRS is something
+// every prove path does, whereas writing into the SRS directory is a
+// provisioning action. Keeping the write off the interface every caller holds
+// is what stops it from happening implicitly.
+//
+// Without force, a dump of the right size already on disk counts as done and
+// the call is cheap; force re-validates an existing dump in full and repairs
+// it if it does not load, mirroring what --force means to `prover setup`.
+type LagrangePersister interface {
+	DeriveAndPersistLagrange(ctx context.Context, ccs constraint.ConstraintSystem, force bool) error
+}
+
 type UnsafeSRSProvider struct {
 }