Remark. DGG monitors update geometry, not evaluation safety [ftip-0082]

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The identities in Theorem [ftip-007Z]--Theorem [ftip-0081] concern gradients, importance ratios, activations, and occurrence-specific logit Jacobians. The intermediate bound controls a local contribution; a shared-weight bound needs control over all contributing occurrences. None of their hypotheses mentions the fixed independent-evaluation functional \(J_{\rm ev}\) of Definition [ftip-005E]. They therefore cannot imply that accepting an update preserves \(J_{\rm ev}\), or that rejecting one would have prevented a decrease.

DGG adds an empirical policy on top of those identities: it monitors the increment in head-gradient energy, standardizes that increment against a trailing window, and rejects some reused updates before the optimizer step [miao2026when, Section 5 and Algorithm 1]. Its reported experiments relate that policy to observed training stability. They do not turn the Z-score into a calibrated test of independent-evaluation safety.