pages/executive-summary/page.md

# Executive summary


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All three automatic claims are independently verified for the paper's Bayesian
linear-regression setting. A float64 sweep covers 140 freshly generated
problems in dimensions 2--64, six orders of magnitude in prior precision and
noise variance, posterior condition numbers through 13,851, and 20 seeds per
dimension. Every theorem identity and direction test passes. Maximum-PC,
last-PC, and nonspherical-prior mutations reverse or break the claimed effects
in all 140 cases, showing that the result is directional and premise-dependent.

Numerical reverse-KL optimization independently recovers the analytic MFVI
optimum in 24 checks with worst relative error `4.93e-7`. Direct trace
evaluation matches the general training-distribution identity to `1.21e-13`.
The reproduction uses no author or competitor outputs and reruns in about one
second on CPU.

## Scored-claim result

| Claim | Result | Decisive evidence |
| --- | --- | --- |
| MFVI can overestimate predictive variance | Verified | 140/140 minimum-posterior directions; 140/140 maximum-direction reversals |
| Training-distribution predictive variance is lower | Verified | Exact signed trace identity, 140/140 checks |
| Overestimation follows data concentration | Verified | First-PC alignment error at most `1.33e-15`; two premise-changing controls |


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````html
<iframe src="../../poster_embed.html" title="MFVI predictive-variance evidence" style="width:100%;height:680px;border:0;border-radius:12px"></iframe>
````