Deterministic, Verifiable Compute at GPU Scale

1. The Hidden Problem: Floating-Point Nondeterminism

What Most Engineers Assume

Most engineers assume that mathematical operations are deterministic. They expect sin(0.5) to always return 0.4794255386... regardless of when, where, or how it executes.

This assumption is wrong.

What Actually Happens

IEEE 754 defines the behavior of individual floating-point operations, but it does not mandate the order of operations in parallel execution. When a GPU spawns thousands of threads to compute a vector operation, the order in which partial results accumulate is nondeterministic.

Example: Summing 1 million floats.

• Thread 1: 0.1 + 0.2 + 0.3 = 0.6000000238...
• Thread 2: 0.3 + 0.2 + 0.1 = 0.6000000119...

The difference is in the 8th decimal place. Over millions of operations, these differences compound.

Why This Matters

Domain	Consequence of Drift
Quantitative Finance	Monte Carlo simulations produce different P&L on re-run. Auditors cannot verify historical trades. FINRA Rule 3110 compliance fails.
Autonomous Systems	Sensor fusion algorithms produce different outputs on identical inputs. Certification bodies cannot validate behavior.
Scientific Research	Results cannot be reproduced. Peer review fails. Retraction risk increases.
Machine Learning	Model training is not reproducible. Debugging becomes guesswork.

The 2025 FINRA Annual Regulatory Oversight Report explicitly flags AI model reproducibility as an emerging compliance concern. Standard LLMs and numeric libraries "suffer from floating-point noise and non-determinism, making them unfit for audit-grade financial applications."

2. Why Reproducibility Is No Longer Optional

Regulatory Pressure

FINRA Rule 3110 requires broker-dealers to maintain systems that can reproduce the basis for any trade recommendation. If your Monte Carlo simulation cannot produce the same output on re-run, you cannot prove why a trade was made.

DO-178C (aerospace software certification) requires deterministic, predictable behavior for safety-critical systems. Floating-point nondeterminism is a certification blocker for Level A software, the category covering catastrophic failure scenarios.

EU AI Act classifies financial and safety-critical AI as high-risk, requiring explainability and reproducibility.

Operational Reality

Beyond regulation, nondeterminism creates operational problems:

• Debugging: If you cannot reproduce a failure, you cannot fix it.
• Testing: If outputs vary between runs, test suites become probabilistic.
• Auditing: If historical outputs cannot be regenerated, audit trails are worthless.

3. Deterministic Compute as a First-Class Primitive

The Solution

A deterministic compute engine enforces strict execution invariants:

• Deterministic execution: Regardless of thread scheduling, results are identical across all platforms.
• Platform-independent rounding: Results are identical across ARM, x86, and GPU.
• Stateless execution: No hidden state accumulates between calls.

Lu(x)iEdge Guarantees

Lu(x)iEdge achieves bit-exact determinism across all supported platforms. The implementation is protected under a Track 1 non-provisional patent filing with the United States Patent and Trademark Office.

Guarantee	Description
Deterministic execution	Identical results regardless of thread scheduling, parallelism, or hardware platform
Memory-safe core	Built with memory-safe systems programming for zero memory corruption risk
Cross-platform verification	Bit-exact results across ARM, x86, and GPU architectures
Cryptographic audit trail	SHA-256 output hashing for tamper-evident verification

Given identical inputs, Lu(x)iEdge produces identical outputs down to the last bit, regardless of hardware or execution time.

4. From Reproducibility to Verifiability

The Audit Problem

Reproducibility alone is not enough. An auditor needs to verify that a claimed output actually came from a claimed input without re-executing the computation.

SHA-256 Verification

Lu(x)iEdge hashes output buffers with SHA-256:

{
  "expr": "sin(x)*cos(x)",
  "x": [0.5, 1.0, 1.57, 2.0, 3.14],
  "y": [0.4207, 0.4546, 0.0007, -0.3784, -0.0014],
  "hash": "98bd97026a738671ec7c3d302efa6aa8ff078a5fb9183f7fdf51a1c4ff938321"
}

Verification workflow:

• Store the hash at computation time
• Re-run computation months later
• Compare hashes

If match: computation is verified. If mismatch: tampering or drift detected.

5. The Art of Fugue: A Polyphonic Determinism Benchmark

The Art of Fugue benchmark applies the concept of polyphonic musical structure to floating-point verification. It launches multiple "Voices" (threads) of conflicting mathematical intensity to create maximum opportunity for scheduler drift.

Platform	Architecture	FPBench Hash
Apple M1 Pro	ARM64 (Neon)	98bd97...ac19 ✓
NVIDIA H100	CUDA	98bd97...ac19 ✓
NVIDIA L4	Vulkan	98bd97...ac19 ✓

Lu(x)iEdge produces the exact same hash across all platforms. Bit-exact identity across heterogeneous hardware.

6. Performance Without Compromise

Validated Performance (TestFort QA Lab, December 2025):

• Aggregate Throughput: 286.94 billion ops/sec
• Error Rate: 0.00% (over 444.4 trillion operations)
• Hardware: NVIDIA H100 SXM, 80GB HBM3

Validation scope: non-linear function suite, cross-platform determinism, and GPU endurance. Validation of remaining function categories is in progress.

7. Power, Heat, and Cooling

Race to Idle: Faster computation means less time at peak power, which means less heat generated. At 2.35B ops/joule, Lu(x)iEdge allows hardware to idle sooner, reducing total energy consumed and cooling costs.

Conclusion

Floating-point nondeterminism is a hidden tax on modern computing. Lu(x)iEdge eliminates this tax. Bit-exact results. SHA-256 verification. 286.94 billion ops/sec. 2.35 billion ops/joule. Determinism is not a feature. It is infrastructure.

How to Cite

BibTeX

@misc{waller2026luxiedge,
  title     = {Deterministic, Verifiable Compute at GPU Scale},
  author    = {Waller, Eric},
  year      = {2026},
  note      = {Lu(x)iEdge: Deterministic Numeric Computation Engine, v0.1.0},
  url       = {https://luxiedge.com/whitepaper}
}

APA

Waller, E. (2026). Deterministic, verifiable compute at GPU scale.
Lu(x)iEdge: Deterministic Numeric Computation Engine (v0.1.0).
https://luxiedge.com/whitepaper