# Target-paper judge evidence and active merge

This page contains only the `w0JhOFWPJl` entries extracted from the two global judge inputs pinned in [`../evidence/pins.json`](../evidence/pins.json). No unrelated feed entries are retained or summarised.

## Immutable input precedence

Both judge files are pinned at challenge revision `7b5b56aebf3abe590eab9f2c241a796125cab928`. The active merge policy is **anchored overrides legacy**: for this target paper, `claims_anchored.json` is the active source and replaces the legacy `claims.json` entries.

## Legacy input — superseded

1. GLU structure reshapes the NTK spectrum, leading to smaller condition number and more compact eigenvalue distribution.
2. GLU primary benefit lies in accelerating optimization rather than reducing stochastic error.

## Active anchored input

1. GLU achieves quadratically better NTK conditioning than non-GLU structure, with condition number κ(K̃) = O(n/d²) for GLU versus κ(K) = O(n/d) for non-GLU (Theorem 3.1).
2. The GLU NTK can be approximated as a Hadamard-reweighted kernel K̃ ≈ K ⊙ (XX^T/d), producing a more contracted eigenvalue distribution than the non-GLU NTK (Section 3).
3. GLU's largest NTK eigenvalue scales as λ_max(K̃) = O(mn/d²) compared to λ_max(K) = O(mn/d) for non-GLU, while both share λ_min ~ O(m) (Section 3, Theorem 3.1).
4. A loss-crossing phenomenon shows GLU and non-GLU training losses cross during optimization, consistent with the kernel-regime analysis of stage-wise convergence (Proposition 4.1, Corollary 4.2, Figure 6).
5. GLU's primary benefit is accelerating optimization via better spectral conditioning rather than shrinking the generalization gap, as shown by comparing generalization gaps of GLU and non-GLU models (Section 5, Figure 7).
6. Condition numbers of GLU versus non-GLU structures are empirically measured in real architectures including ViT and GPT-2, corroborating the theoretical scaling (Figure 3).

## Release boundary

These are judge inputs, not reproduced release assertions. The release supports only the finite CPU, 50-sample Gaussian empirical-NTK measurement recorded on Claim 1. Claim 2 remains **Unverified.** No active anchored item above is promoted by this package beyond that narrow boundary.