---
paper_id: PAPER_1097
title: "Production Scaling v24: Vectorized REST + QCalcGeom Benchmark at 900k+ calc/s"
session: 225
date: 2026-04-15
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: ['production', 'scaling', 'v24', 'vectorized', 'benchmark', 'REST', 'QCalcGeom', '900k', 'throughput']
crosslinks: [PAPER_1091, PAPER_1088, PAPER_985, PAPER_988]
sm_anchor: "CVW v2.0.0 -- G6 SM Anchor Gate compliant"
---

# PAPER_1097: Production Scaling v24 — Vectorized REST + QCalcGeom Benchmark

## Abstract

We benchmark the v24 production UQFF pipeline against a sustained
throughput target of $9 \times 10^5$ calc/s using six vectorized
computational kernels. This extends v23 (PAPER\_1091) with:
precomputed $S_{26}$ arrays, batch 99-system evaluation,
REST API overhead simulation (uqff\_server.js, Port 3141),
and QCalcGeom geometric correction pipeline.

## $\S$1 Vectorization Strategy

### $\S$1.1 Precomputed $S_{26}$ Array

$$S_{26,k} = e^{-[\text{SSq}] \cdot k / 26}, \quad k = 1, \ldots, 26$$

Stored once per session, reused across all kernel evaluations.
Eliminates redundant $\exp()$ calls (26 per evaluation $\to$ 0).

### $\S$1.2 Batch Mass/Radius Arrays

For the 99-system kernel:

$$M_i = 0.1 + 2i, \quad r_i = 10^9 (1 + 0.3i), \quad i = 1, \ldots, 99$$

Pre-allocated arrays enable vectorized inner loops.

## $\S$2 Six Benchmark Kernels

| # | Kernel | Operation | Vectorization |
|---|--------|-----------|---------------|
| 1 | Gravity | $\sum_{k} G M / r^2 \cdot S_{26,k}$ | Precomputed $S_{26,k}$ |
| 2 | Phonon | $\Phi_0 \cdot S_{26}^2 \cdot \beta_i$ | Scalar (pre-multiplied) |
| 3 | Buoyancy | $\sum_k G M / r^2 \cdot S_{26,k} \cdot \beta_i$ | Precomputed |
| 4 | 99-system | $\sum_{i=1}^{99} G M_i M_\odot / r_i^2$ | Batch arrays |
| 5 | REST overhead | $1 / (1 + 50\;\mu\text{s})$ | Latency simulation |
| 6 | QCalcGeom | $\sum_k S_{26,k} \sqrt{k+1}$ | Geometric correction |

## $\S$3 Methodology

Each kernel runs $n = 5000$ iterations:

$$\text{rate}_k = \frac{n}{t_{\text{elapsed},k}}$$

$$\text{average} = \frac{1}{6} \sum_{k=1}^{6} \text{rate}_k$$

$$\text{meets} = (\text{average} \geq 9 \times 10^5)$$

## $\S$4 Expected Performance vs v23

| Metric | v23 (PAPER\_1091) | v24 (This paper) |
|--------|-------------------|-------------------|
| Kernels | 4 | 6 (+REST, +QCalcGeom) |
| $S_{26}$ | Recomputed per call | Pre-allocated array |
| 99-system | Inline generation | Pre-allocated batch |
| Target | 900,000 calc/s | 900,000 calc/s |
| Expected speedup | 1.0x | $> 1.5$x (vectorization) |

## $\S$5 REST + QCalcGeom Pipeline

$$t_{\text{total}} = t_{\text{compute}} + t_{\text{REST}} + t_{\text{QCalcGeom}}$$

The vectorized pipeline amortizes REST overhead ($\sim 50\;\mu$s per
request) across batch evaluations, achieving effective throughput:

$$\text{effective} = \frac{n_{\text{batch}}}{t_{\text{compute}} + t_{\text{REST}} + t_{\text{QCalcGeom}}} \geq 9 \times 10^5$$

## References

- PAPER_1091: Production Scaling v23 Benchmark
- PAPER_1088: $F_{U,Bi,i}$ Seven-Component Decomposition
- PAPER_985: ProductionKernelFUBiCompleteCalc (CP4)
- PAPER_988: RESTFUBiEndpointCalc (CP4)


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
