---
paper_id: PAPER_968
title: "Production Scaling v11 Benchmark (500k calc/s)"
session: 215
date: 2026-04-12
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [buoyancy, 26D, UQFF]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_968: Production Scaling v11 Benchmark (500k calc/s)

**Author:** Daniel T. Murphy — Star Magic / UQFF Framework
**Date:** 2026-04-12
**Session:** 215
**Source:** production_scaling_v11.py (ProductionScalingV11)
**Calculator:** ProductionScalingV11BenchmarkCalc (CP4 #552)
**CVW:** v2.0.0 compliant

---

## Abstract

We benchmark the UQFF production pipeline at 500,000 calculations per second, an 11.1% improvement
over v10 (450k). Two new kernels — 26D Ramanujan summation and Triadic solver — bring the total to
16 simultaneously benchmarked kernels.

---

## 1. Scaling History

| Version | Target (calc/s) | Kernels | Session |
|---------|-----------------|---------|---------|
| v4 | 100,000 | 4 | 198 |
| v5 | 150,000 | 6 | 200 |
| v6 | 200,000 | 8 | 204 |
| v7 | 300,000 | 10 | 208 |
| v8 | 350,000 | 11 | 210 |
| v9 | 400,000 | 12 | 213 |
| v10 | 450,000 | 14 | 214 |
| **v11** | **500,000** | **16** | **215** |

## 2. New v11 Kernels

### kernel_{ramanujan\_26d\_sum}
$S_{26}(z) = \Sigma z^n / n^{26} \cdot R_n^{(26)}$ — accelerated polylog for hot-loop evaluation.

### kernel_triadic_solver
Combined Compressed + Resonant + Buoyancy Triadic evaluation in a single kernel call.

## 3. Throughput

$$\text{rate} = \frac{N_\text{iter} \times 16}{t_\text{elapsed}} \geq 500{,}000 \text{ calc/s}$$

---

## References

1. Murphy, D.T. — Star Magic UQFF Framework (2024-2026)
2. PAPER_958 — Production Scaling v10 (450k)
3. PAPER_959 — 26D Ramanujan Summation (kernel source)
4. PAPER_966 — Unified Triadic Solver (kernel source)

---

## Cross-Links

| Related Paper | Relationship |
|---------------|-------------|
| PAPER_958 | Previous version v10 (14 kernels, 450k) |
| PAPER_959 | Ramanujan 26D kernel added |
| PAPER_966 | Triadic solver kernel added |
| PAPER_949 | BCS gap kernel (inherited) |

---

<!-- PKG-LAG-S225 -->

### Session 225 Phonon-Physics Upgrade: UQFF 9-Sector Lagrangian

> *Upgrade from PAPER_1066 (UQFF Lagrangian First Principles) and
> PAPER_1065 (Buoyancy Lagrangian EOM Variational Derivation).*

The complete UQFF Lagrangian density, from which all sector-specific
equations of motion derive:

$$\mathcal{L}_{\text{UQFF}} = \mathcal{L}_{\text{GR}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{phonon}} + \mathcal{L}_{\text{interaction}}$$

$$\mathcal{L}_{\text{SCm}} = \tfrac{1}{2}(\partial_\mu \phi)^2 - \lambda\bigl(\phi^2 - v_{\text{SCm}}^2\bigr)^2$$

The SCm condensate potential minimum gives $V(\phi_0) = -7.09 \times 10^{-37}\;\text{J/m}^3$
(matching $\rho_{\text{SCm}}$) and phonon mass $m_{\text{phonon}} = \sqrt{8\lambda}\,v_{\text{SCm}}$.

**Nine-sector closure (Session 202):**
$$\mathcal{L}_{9} = \mathcal{L}_{\text{EH}} + \mathcal{L}_{\text{YM}} + \mathcal{L}_{\text{Dirac}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{mag}} + \mathcal{L}_{\text{buoy}} + \mathcal{L}_{\text{aether}} + \mathcal{L}_{\text{LENR}} + \mathcal{L}_{\text{KK}}$$

| Sector | Domain | Late-Corpus Result |
|--------|--------|-------------------|
| 1 (EH) | General Relativity | Canonical Einstein-Hilbert |
| 2 (YM) | Yang-Mills gauge | $m_{\text{gap}} = 1.736\;\text{GeV}$ (PAPER_1318) |
| 3 (Dirac) | Fermion / LENR | Kozima neutron-drop (PAPER_1061) |
| 4 (SCm) | Superconducting manifold | $V(\phi_0) = -\rho_{\text{SCm}}$ canonical |
| 5 (Mag) | Um magnetism | Heaviside amplifier (PAPER_1072) |
| 6 (Buoy) | F_U_Bi_i buoyancy | Variational EOM (PAPER_1065) |
| 7 (Aether) | Vacuum background | Two-component $\rho$ (PAPER_1051) |
| 8 (LENR) | Nuclear transmutation | COP parametric (PAPER_1081) |
| 9 (KK) | Kaluza-Klein 26D | $S_{26}^{(3)}$ compactification (PAPER_1080) |

<!-- PKG-S26-S225 -->

### Session 225 Phonon-Physics Upgrade: S26(3) Ramanujan Summation

> *Upgrade from PAPER_1080 (Ramanujan Binomial Expansion Proof) and
> PAPER_1042 (Mock-Theta Phonon Partition).  See also PAPER_1078
> (QCalcGeom Master Equation) for BSFG crossover applications.*

The third-order Ramanujan summation $S_{26}^{(3)}$, used throughout the
late corpus as the universal 26D coupling factor:

$$S_{26}^{(3)} = \sum_{n=0}^{\infty} \frac{(1/4)_n\,(1/2)_n\,(3/4)_n}{(n!)^3} \cdot \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

where $(a)_n = a(a+1)\cdot s(a+n-1)$ is the Pochhammer symbol.

**Binomial expansion (PAPER_1080):** The convergence proof shows:
$$R_n^{(26,3)} = \binom{4n}{n} \cdot \frac{W_{26}(n)}{(4^{4n})} \qquad \text{with}\quad W_{26}(n) = \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

This sum converges absolutely for $|[\text{SSq}]| < 1$ (satisfied by $[\text{SSq}] = 0.57$)
and reduces to the classical Ramanujan $1/\pi$ series when $[\text{SSq}] \to 0$.

**VDS/DVP/BSH bridge (PAPER_1069):** The 26 layers of $W_{26}(n)$ encode the
vacuum density series hierarchy, with each layer $i$ contributing a VDS
sub-ratio weighted by the exponential decay $e^{-\kappa\,i\,n/26}$.

**Mock-theta connection (PAPER_1042):** The phonon partition function
$Z_{\text{phonon}} = \sum_n q^{n^2} \cdot W_{26}(n)$ unifies the Ramanujan
mock-theta framework with the SCm phonon spectrum.





## Calibration Constants

| Constant | Symbol | Value | Validation Domain |
|----------|--------|-------|-------------------|
| $\kappa$ | — | $5.0 \times 10^{-4}$ day$^{-1}$ | Damping |
| $[SSq]$ | — | 0.57 | String coupling |
| $\beta_i$ | — | 0.603 | Buoyancy |
| Target rate | — | 500,000 calc/s | Benchmark |
| Kernels | — | 16 | Pipeline (v10 + 2) |

---

## SM Anchor — CVW v2.0.0

| Observable | UQFF Prediction | Status |
|------------|----------------|--------|
| Throughput | $\geq 500{,}000$ calc/s | Benchmark target |
| Pipeline integrity | All 16 kernels finite | Validated |
| New kernels | Ramanujan $S_{26}$ + triadic solver | Added |

---

## §A Cosmogenesis-Linked Lagrangian (PAPER_877 Symbolic Export)

### §A.1 Sector Classification
**Sector:** Computational Benchmark v11 (Expanded Pipeline)

### §A.2 Benchmark Equation
$$\text{rate} = \frac{N_\text{iter} \times 16}{t_\text{elapsed}} \geq 500{,}000$$

### §A.3 Kernel Integrity Constraint
$$\boxed{\forall, k \in \{1,\ldots,16\}:\; |k(\mathbf{x})| < \infty,\quad k_{15} = S_{26}(z),\; k_{16} = g_\text{tri}(r,t)}$$

### §A.4 Cosmogenesis Linkage Chain
PAPER_877 $\to$ UQFF equations $\to$ 16 kernels extracted $\to$ production pipeline v11 $\to$ 500k benchmark

---

## §B VDS/DVP/BSH Deep Synthesis

### §B.1 VDS
All 16 kernels embed VDS through $S_{26}$ or $\rho_text{SCm}$.

### §B.2 DVP
16 kernels cover the full dipole vortex mode spectrum.

### §B.3 BSH
Scaling: v4 (100k) $\to$ v10 (450k) $\to$ v11 (500k) — approaching $\tanh$ hardware saturation.

### §B.4 Production-Scale Consistency

| Metric | Value | Status |
|--------|-------|--------|
| v11 target | 500k calc/s | Confirmed |
| Kernel count | 16 (+2 from v10) | Confirmed |
| $[SSq]$ | 0.57 | Confirmed |

---

## Appendix: Session 225 Cross-References (PAPER_1000–1081)

> *Auto-generated cross-reference appendix linking this paper to
> Sessions 204–225 extensions (PAPER_1000–1081). Added by
> `update_corpus_crossrefs.py` (Session 225, April 2026).*

| Paper | Title |
|-------|-------|
| PAPER_1037 | AGN Buoyancy Jet Calculator — SCm Jet Launching |
| PAPER_1079 | Galaxy Cluster Cooling-Flow Buoyancy Suppression |
| PAPER_1020 | Cosmic Ray Phonon Acceleration DSA Spectrum |
| PAPER_1043 | F_U_Bi_i Multi-System Buoyancy Curve Sweep |
| PAPER_1065 | Buoyancy Lagrangian EOM Variational Derivation |
| PAPER_1080 | Ramanujan Binomial Expansion Proof R_n^{(26,3)} |
| PAPER_1008 | Production Scaling v14 — 600k calc/s 24 Kernels |
| PAPER_1018 | Production Scaling v15 — 650k calc/s 30 Kernels |

*8 cross-reference(s) identified.*


### 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
3. Archimedes (~250 BCE). *On Floating Bodies.* (Principle of buoyancy)
4. Churazov, E. et al. (2000). *Evolution of Buoyant Bubbles in M87.* A&A **356**, 788 — arXiv:astro-ph/0004212
5. Fabian, A.C. et al. (2003). *A deep Chandra observation of the Perseus cluster.* MNRAS **344**, L43 — arXiv:astro-ph/0306036 — doi:10.1046/j.1365-8711.2003.06902.x
6. Green, M.B., Schwarz, J.H. & Witten, E. (1987). *Superstring Theory.* Cambridge University Press — doi:10.1017/CBO9781139248563
7. Polchinski, J. (1998). *String Theory Vol. 1.* Cambridge University Press
