Kadena proof server is not progressing

Following the documentation, if I run
```
RECONSTRUCT_COMMITMENTS=false SHARD_BATCH_SIZE=0 SHARD_CHUNKING_MULTIPLIER=64 SHARD_SIZE=4194304 RUSTFLAGS="-C target-cpu=native -C opt-level=3" cargo run --release --bin proof_server -- --mode "single" -a 127.0.0.1:8080
```

Produced the following (using `RUST_LOG=debug`):
```
...
[2024-11-21T08:03:18Z DEBUG tracing::span] generate preprocessed traces;
[2024-11-21T08:03:18Z DEBUG tracing::span] commit to preprocessed traces;
[2024-11-21T08:03:18Z INFO p3_dft::radix_2_dit_parallel] coset_lde_batch; dims=36x65536
[2024-11-21T08:03:18Z INFO p3_dft::radix_2_dit_parallel] coset_lde_batch; dims=2x65536
[2024-11-21T08:03:18Z DEBUG p3_merkle_tree::merkle_tree] build merkle tree; dimensions="[36x1048576, 2x1048576]"
[2024-11-21T08:03:23Z DEBUG tracing::span] setup;
[2024-11-21T08:03:23Z DEBUG tracing::span] setup machine;
[2024-11-21T08:03:23Z DEBUG tracing::span] generate preprocessed traces;
[2024-11-21T08:03:23Z DEBUG tracing::span] commit to preprocessed traces;
[2024-11-21T08:03:23Z INFO p3_dft::radix_2_dit_parallel] coset_lde_batch; dims=6x65536
[2024-11-21T08:03:23Z INFO p3_dft::radix_2_dit_parallel] coset_lde_batch; dims=11x65536
[2024-11-21T08:03:23Z INFO p3_dft::radix_2_dit_parallel] coset_lde_batch; dims=37x32768
[2024-11-21T08:03:23Z DEBUG p3_merkle_tree::merkle_tree] build merkle tree; dimensions="[6x131072, 11x131072, 37x65536]"
[2024-11-21T08:03:23Z INFO proof_server] Server running on 127.0.0.1:8080
```
The proof server is not producing any additional output. Running the light-client results in
```
[2024-11-21T08:05:04Z INFO client] Starting proving process for the longest chain
[2024-11-21T08:05:04Z DEBUG reqwest::connect] starting new connection: http://localhost:8080/
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::connect::dns] resolve; host=localhost
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::connect::dns] resolving host="localhost"
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::connect::http] connecting to [::1]:8080
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::connect::http] connecting to 127.0.0.1:8080
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::connect::http] connected to 127.0.0.1:8080
[2024-11-21T08:05:04Z DEBUG hyper_util::client::legacy::pool] pooling idle connection for ("http", localhost:8080)
thread 'main' panicked at light-client/src/proofs/mod.rs:125:15:
index out of bounds: the len is 0 but the index is 0
```

Reproduce the documented `cargo run --release --bin proof_server` command with the shown environment and debug logs, then run the light-client. Start at `light-client/src/proofs/mod.rs:125` and compare its request/response handling with the proof server output; done means identifying why the client receives an empty result and documenting or correcting the failure.

Written by the indexing model from the issue text.