---
title: Max-Cut at 16.5 Billion to 200 Billion Variables on One 8×H100 Node | SpinForge
url: https://spin-forge.com/proof/p2
description: 16.5 billion: variables (mean degree 3): 89.4392% of 2.475×10¹⁰ edges cut; recount difference 3.2×10⁻⁷. To our knowledge the largest max-cut instance ever…
---

RESEARCH RECORD · P2

# Max-Cut at 16.5 Billion to 200 Billion Variables on One 8×H100 Node

To our knowledge the largest max-cut instance ever solved. Every reported cut is recomputed from the saved solution in exact integer arithmetic on the CPU, with no code shared with the solver, and the proof bundles carry hashes.

16.5 billion variables (mean degree 3): 89.4392% of 2.475×10¹⁰ edges cut; recount difference 3.2×10⁻⁷

200 billion variables, 6×10¹¹ edges: 77.42% cut in 11.4 h (quench solution at 73.39% recounted in 21.4 s)

0.0027 pp spread over 4 independent 10¹⁰-variable instances (79.5930–79.5957%)

1.8×10⁻⁶ largest difference between solver and recount, every record

Independent recount of every record

| Run (mean degree) | Solver | Recount (exact) | Relative difference |

| 1.65×10¹⁰ (3) | 2.21362×10¹⁰ | 22,136,207,143 | 3.2×10⁻⁷ |

| 1.03×10¹⁰ (6) | 2.45949×10¹⁰ | 24,594,910,829 | 4.4×10⁻⁷ |

| 10¹⁰ instance 1, seed 1 | 2.38787×10¹⁰ | 23,878,697,460 | 1.1×10⁻⁷ |

| 10¹⁰ instance 1, seed 2 | 2.38787×10¹⁰ | 23,878,706,730 | 2.8×10⁻⁷ |

| 10¹⁰ instance 3 | 2.38780×10¹⁰ | 23,877,997,940 | 8.6×10⁻⁸ |

| 10¹⁰ instance 4 | 2.38779×10¹⁰ | 23,877,908,021 | 3.4×10⁻⁷ |

| 10¹⁰ instance 5 | 2.38779×10¹⁰ | 23,877,943,348 | 1.8×10⁻⁶ |

| 2×10¹¹ quench bundle | 440,350,966,067 | 440,350,966,067 | 0 |

| 5×10¹⁰ quench bundle | 110,087,659,633 | 110,087,659,633 | 0 |

| Control: instance 3 spins on instance 1 | none | 49.9998% (random) | no match |

- Recounts agree with the solver within 1.8×10⁻⁶; proof bundles match exactly
- A control (one instance's solution scored on another instance's graph) gives 49.9998%, as random should
- Four independent 10¹⁰-variable instances agree within 0.0027 percentage points
- The 200-billion-variable run is near-optimal (77.42%), below the converged band (79.596%)
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## More research records

- [Time-to-Target Scaling on D-Wave's Pegasus Instances: Exponent 0.44 vs 1.69 for Quantum Annealing with Error Correction](https://spin-forge.com/proof/p1)
- [Ground-State Statistics of Sparse Max-Cut at 10⁸ to 10¹⁰ Spins: Extrapolations Bracket the Parisi Constant](https://spin-forge.com/proof/p0)

[All results, charts and papers](https://spin-forge.com/proof)

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