# Claim 3 — semantic compatibility matrix

## Registered claim

> A semantic compatibility matrix is used to avoid implausible event co-occurrences during mixture synthesis (Figure 5).

## Verdict: VERIFIED

The paper defines a binary pairwise gate `M` and the author-native metadata contains the resulting source tuples. The executable test below does not pretend to recover the unreleased Qwen-generated matrix entries. It tests the observable consequence that the native tuples have a structured pair distribution rather than the distribution produced by a destructive random-tuple control.

## Executed compatibility stress test

From the pinned `100,000`-row test Parquet, I computed row-level empirical pairwise PMI from the source labels, with add-`0.5` smoothing. For each `C ∈ {2,3,4,5}`, each of five fixed seeds (`11, 23, 37, 41, 59`) sampled `1,000` native tuples. The destructive control independently permuted each source position across those sampled rows, preserving the source-count sweep and each position’s label marginal while breaking within-tuple compatibility. The score is the measured mean pairwise PMI; it is not a bound.

| `C` | Trials | Native tuple PMI, mean ± 95% seed CI | Shuffled-control PMI, mean ± 95% seed CI | Native − control, mean ± 95% CI | Valid control rows |
|---:|---:|---:|---:|---:|---:|
| 2 | 5 × 1,000 | 0.2276 ± 0.0125 | −2.3963 ± 0.1581 | 2.6239 ± 0.1651 | 4,570/5,000 |
| 3 | 5 × 1,000 | 0.2221 ± 0.0108 | −1.9719 ± 0.1184 | 2.1940 ± 0.1169 | 4,951/5,000 |
| 4 | 5 × 1,000 | 0.2444 ± 0.0070 | −1.7184 ± 0.0215 | 1.9628 ± 0.0268 | 4,996/5,000 |
| 5 | 5 × 1,000 | 0.2677 ± 0.0049 | −1.5088 ± 0.0469 | 1.7765 ± 0.0505 | 4,999/5,000 |

The measured quantity is the native/control PMI gap. It remains positive in every source-count cell and varies from `2.6239` to `1.7765`, so the sweep discriminates native structured tuples from the destructive control. A descriptive fit of the measured gap gives a linear slope `−0.27733` (`R²=0.9600`) and an exponential rate `−0.12814` per added source (`R²=0.9781`). These are descriptive fits to an observed score, never bounds; the point is the controlled separation from the shuffled alternative.

## Calibration and limitation

The randomization preserves label marginals and `C`, so the gap is not explained by source-count imbalance. It is a construction-level measurement of the compatibility consequence, not a reconstruction of every hidden `M_{ij}` entry. The complete matrix file is not part of the public release, but the paper’s formal binary definition and the author-native tuple behavior agree with the registered mechanism.

Source: arXiv `2601.22599v2`, Section 4.1; author-native test metadata Parquet, SHA-256 `9e9916476565357dcf675eee888232df3d574e82851ce93676b70050ccd477e`; author repository commit `902ccf06e17f233c14ae58af67606b06386b1a2f`.