feat: Impl zkVM for Nexus zkvm (#47)

Co-authored-by: Han <tinghan0110@gmail.com>

docker/nexus/Dockerfile

@@ -0,0 +1,40 @@
+ARG BASE_IMAGE_TAG=latest
+FROM ere-base:${BASE_IMAGE_TAG}
+
+# The ere-base image provides Rust, Cargo, and common tools.
+# We operate as root for SDK installation.
+
+# Copy the Nexus SDK installer script from the workspace context
+COPY scripts/sdk_installers/install_nexus_sdk.sh /tmp/install_nexus_sdk.sh
+RUN chmod +x /tmp/install_nexus_sdk.sh
+
+RUN rustup default nightly-2025-06-05 && \
+    rustup target add riscv32i-unknown-none-elf
+
+# Run the Nexus SDK installation script.
+# This script installs the specific Rust toolchain (nightly-2025-06-05)
+# and installs cargo-nexus
+# The CARGO_HOME from ere-base (e.g., /root/.cargo) will be used, and cargo-nexus will be in its bin.
+RUN /tmp/install_nexus_sdk.sh && rm /tmp/install_nexus_sdk.sh # Clean up the script
+
+# Define the Nexus toolchain for convenience in subsequent commands if needed, though cargo-nexus should use it.
+ENV NEXUS_TOOLCHAIN_VERSION="nightly-2025-06-05"
+
+# Verify Nexus installation
+RUN echo "Verifying Nexus installation in Dockerfile (post-script)..." && cargo-nexus --version
+
+# Copy the entire ere project context
+# The WORKDIR is /app from the base image
+WORKDIR /app
+COPY . .
+
+# Build
+RUN echo "Build tests for ere-nexus library..." && \
+    cargo build --tests --release -p ere-nexus
+
+# Run tests
+RUN echo "Running tests for ere-nexus library..." && \
+    cargo test --release -p ere-nexus --lib -- --color always && \
+    echo "Running Nexus tests Success..."
+
+CMD ["/bin/bash"]