The 14 Provers Ceiling: Validating Memory Backpressure with a Single Grep

In the middle of an intense optimization session for the SUPRASEAL_C2 Groth16 proof generation pipeline, a single bash command appears that, on its surface, looks trivial. The assistant runs:

grep "BUFFERS" /home/theuser/cuzk-p12-semchan-pw10.log | awk -F'provers=' '{print $2}' | awk -F' ' '{print $1}' | sort -n | tail -3

The output is just three lines: 14, 14, 14. Three identical numbers. Yet this moment crystallizes the entire arc of a multi-hour engineering investigation into memory backpressure, concurrent system design, and the subtle art of bounding in-flight work in a heterogeneous GPU proving pipeline. This article unpacks why this message was written, what it reveals, and why it matters.

The Problem: When Synthesis Outruns the GPU

To understand this message, one must first understand the architecture it monitors. The Phase 12 split GPU proving API, developed over the preceding segment ([msg 29] through [msg 31]), decouples CPU-based partition synthesis from GPU-based proof computation. In Filecoin's Proof-of-Replication (PoRep) protocol, each sector proof is split into ten partitions. Each partition undergoes synthesis (CPU-bound computation of evaluation vectors) followed by GPU proving (NTT, MSM, and related operations). The split API allows synthesis to run ahead of the GPU, with completed partitions flowing through an in-memory channel to GPU worker threads.

The problem this creates is fundamental to any producer-consumer pipeline where the producer is faster than the consumer. Synthesis for a partition takes approximately 29 seconds, while GPU proving takes about 5–6 seconds per partition (including the b_g2_msm finalization). With ten partitions per proof and two GPU workers, synthesis completes roughly five times faster than the GPU can consume. Without careful backpressure, completed synthesis outputs pile up in memory, each holding approximately 4 GiB of data (after early freeing of evaluation vectors). With ten partition workers running concurrently, the system can accumulate dozens of in-flight outputs, driving RSS into the hundreds of gigabytes and eventually causing out-of-memory (OOM) failures.

The Three-Part Fix

The assistant had just implemented a three-part memory backpressure mechanism ([msg 3161] through [msg 3167]):

  1. Early a/b/c free: The evaluation vectors a, b, and c — approximately 12 GiB per partition — are freed immediately after prove_start returns, since the GPU has already copied them to device memory and no longer needs the host copies.
  2. Channel capacity auto-scaling: The synthesis-to-GPU channel capacity was changed from a hardcoded value of 1 to max(synthesis_lookahead, partition_workers). This ensures that completed syntheses never block on send() while holding large allocations, because the channel has room for all in-flight partitions.
  3. Partition permit held through send: This was the critical semantic change. Previously, the partition semaphore permit (which limits concurrent synthesis tasks to partition_workers) was released inside the spawn_blocking closure — immediately after synthesis finished but before the result was sent to the GPU channel. This meant that a completed synthesis would release its permit, allowing a new synthesis to start, even if the completed output was still waiting to be picked up by the GPU. The fix moved the permit release to after the channel send() succeeds, so the total number of in-flight outputs (synthesizing + waiting in channel + being GPU-processed) is bounded by partition_workers. The key insight was that with channel capacity set to partition_workers, the send() is non-blocking — the channel always has room. So holding the permit through the send adds zero latency while providing a hard bound on in-flight memory.

The Benchmark Results

The assistant had just run a full 15-proof benchmark at concurrency 15 ([msg 3173]) and analyzed the results ([msg 3174]). The throughput was 38.9 seconds per proof — essentially identical to the 38.8 seconds per proof observed without the semaphore fix. This confirmed that holding the permit through the send did not add latency, because the channel capacity was large enough that sends never blocked.

The RSS data was even more telling. Without the semaphore fix, peak RSS reached 390 GiB ([msg 3157]). With the fix, peak RSS dropped to 314.7 GiB ([msg 3174]). That is a 75 GiB reduction — approximately 19% less peak memory — achieved with zero throughput regression.

But the assistant needed to verify the mechanism. Was the provers counter (which tracks how many GPU shells are in-flight) actually bounded? In the earlier run without the fix, provers peaked at 19 ([msg 3157]). With the fix, a quick check of synth_done events showed provers peaking at 14 ([msg 3175]). But that only sampled one event type. The assistant wanted a comprehensive check.

The Message Itself

This brings us to the subject message ([msg 3176]). The command is carefully constructed:

grep "BUFFERS" /home/theuser/cuzk-p12-semchan-pw10.log | awk -F'provers=' '{print $2}' | awk -F' ' '{print $1}' | sort -n | tail -3

It extracts all BUFFERS log lines (not just synth_done), parses out the provers= field, extracts the numeric value, sorts numerically, and takes the three highest values. This is a robust way to find the peak across all sampling points — every buffer counter snapshot in the entire 15-proof run.

The output is 14, 14, 14. The peak provers count is 14, and it appears at least three times (likely at different points in the run). This is consistent with the synth_done-only check and confirms that the fix is working as designed.

What 14 Means

Why 14? The theoretical bound is partition_workers + num_gpu_workers + some slack. With partition_workers=10 and num_gpu_workers=2, the bound is 12 in-flight outputs (10 in the channel or being synthesized, 2 being GPU-processed). The observed peak of 14 is slightly above this, which is expected: there are transitional states where a permit has been released but the next synthesis hasn't started yet, and the channel may have transient occupancy above its nominal capacity during concurrent send/receive operations. The important thing is that 14 is far below the previous peak of 19, and the system is stable at 314.7 GiB RSS instead of growing unboundedly toward OOM.

The Deeper Significance

This message exemplifies a critical engineering practice: validate the mechanism, not just the outcome. The assistant had already confirmed that throughput was acceptable and RSS was improved. But those are aggregate metrics — they could be influenced by many factors. By checking the provers counter specifically, the assistant verified that the causal mechanism (bounding in-flight outputs) was actually producing the expected effect. This is the difference between correlation and causation in systems engineering.

The command also reveals the assistant's mental model of the system. The provers counter is an internal instrumentation point, not a user-facing metric. The assistant knew exactly which counter to check and how to interpret it. This level of understanding comes from deep familiarity with the codebase — the assistant had read the engine.rs source code ([msg 3162], [msg 3163]), traced the permit lifecycle, and understood the relationship between the semaphore, the channel, and the GPU worker pool.

There is also a subtle assumption embedded in this check: that the provers counter is the right proxy for memory pressure. The assistant had already confirmed that RSS dropped from 390 GiB to 314.7 GiB, but the provers counter provides a more direct measure of the fix's intended effect. If provers had remained at 19 despite the RSS improvement, it would suggest that the memory savings came from a different mechanism (perhaps the early a/b/c free or the channel capacity change) and that the semaphore fix was not actually binding. The fact that provers dropped confirms that all three parts of the fix are working together.

Conclusion

A single grep command, three lines of output, and a peak value of 14. On its surface, this message is almost invisible — a routine diagnostic check in a long optimization session. But within the full context of the Phase 12 investigation, it represents the moment when a complex, multi-part fix was validated at the mechanism level. The assistant had designed a memory backpressure system with three interacting components, benchmarked it, confirmed the throughput was preserved, observed the RSS improvement, and then — crucially — verified that the internal counters matched the theory. The 14 provers ceiling is the signature of a correctly bounded pipeline, and this message is the evidence that the fix works.