# External Lattice Comparison

Generated: 2026-04-30T07:31:24.024Z

## Method

The current CATALYST/HDC simulator extracts a single scalar gap, so the only defensible first-pass external comparison is against the lightest scalar SU(3) glueball channel, commonly denoted `0++`.

Default HDC parameters:

- Dimension: 10000
- Coupling: 0.8
- Steps: 100
- Seed: 314159
- Extracted HDC gap: 0.324283
- Log-fit R2: 0.999979

## Results

| Calibration | Prediction | Reference | HDC predicted | Error |
| --- | --- | ---: | ---: | ---: |
| Michael & Teper 1989 m_0++ / sqrt(sigma) | Morningstar & Peardon 1999 m_0++ MeV | 1730 +/- 80 MeV | 1540.000 MeV | -10.983% (-2.38 sigma) |
| Morningstar & Peardon 1999 m_0++ MeV | Michael & Teper 1989 m_0++ / sqrt(sigma) | 3.5 +/- 0.2 m/sqrt(sigma) | 3.932 m/sqrt(sigma) | 12.338% (2.16 sigma) |

## Cross-Scale Sanity Check

- Ratio calibration mapped to MeV with sqrt(sigma) = 0.44 GeV gives 1540.0 MeV.
- MeV calibration mapped back to m/sqrt(sigma) gives 3.932.

## Interpretation

This comparison is intentionally conservative. Matching a single scalar mass after calibration is not strong validation. The next real test is spectrum shape: add HDC operators for `2++`, `0-+`, `1+-`, and `2+-`, then compare dimensionless mass ratios against lattice references.