# g142: Trust-Weighted Frechet Mean on Beta Manifold

## Extension of g140
Add trust scores to agents, weighting their contribution to Frechet cost.

## Setup
| Agent | stv | Trust |
|-------|-----------|-------|
| A | (0.9,0.8) | 1.0 |
| B | (0.3,0.6) | 0.3 |
| C | (0.7,0.5) | 0.8 |

Cost: sum(trust_i * rao(mean, agent_i)^2)

## Results
| Method | f | c | df vs uniform | dc vs uniform |
|--------|--------|--------|---------------|---------------|
| Uniform Frechet | 0.6416 | 0.4970 | — | — |
| Trust-weighted | 0.7466 | 0.5648 | +0.1050 | +0.0678 |
| NAL revision | 0.7308 | 0.8667 | +0.0892 | +0.3697 |

## Key Insight
Trust-weighting shifts the geometric mean TOWARD trusted agents.
Distruted agent B's negative belief is downweighted, raising f.
Unlike NAL revision, confidence stays conservative (0.56 vs 0.87).