# Executive summary


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All twenty-two gates pass. The sole pinned arXiv revision supports the five
live claims with explicit upper-bound, lower-construction, optimizer, and
same-feature-space scopes. Nontrivial finite projections satisfy residual
orthogonality and the BCE/KL identity to displayed numerical zero; all 48
cyclic logit paths satisfy coverage, monotonicity, and the source bound. The
probability-passing control is worse in every panel, and 56 Gauss-Hermite hard-
instance cells keep excess BCE times `D/k` between `0.04908` and `0.09975`.
The former complete-coverage limitation in Claim 1 is closed by 100 additional
correlated-support cells: all satisfy `M`-coverage and the full-information
`B_p* B_X M/sqrt(D)` upper-bound certificate, with positive excess in 79 cells.

| Item | Value |
| --- | --- |
| GPU / compute | None; deterministic CPU-only NumPy/Matplotlib |
| Registered claims | 5/5 exact literal strings retained |
| Primary source | arXiv 2605.01082v1 PDF and TeX SHA-256 pinned |

Links: [OpenReview](https://openreview.net/forum?id=mrtg4NmvAe),
[arXiv v1](https://arxiv.org/abs/2605.01082v1), and the reserved future
[Space target](https://huggingface.co/spaces/ProCreations/repro-networked-information-aggregation-for-binary-classification).


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````html
<iframe src="poster_embed.html" title="Networked BCE reproduction poster" style="width:100%;height:900px;border:0"></iframe>
````