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TheTomandClaude Opus 4.7 80fc2f4c84 [paper] Appendix A: document geometric-mean algebraic relation
Adds a short paragraph in Appendix A documenting the algebraic identity
sqrt(S_unb * S_bias) = ||x||/||c||, which coincides with the matched-norm
scale. Frames it as an algebraic interpolation between the two
EDEN-derived forms, notes it is not derived in DRIVE, EDEN, or the
TurboQuant/EDEN note paper (arXiv:2604.18555), and does not correspond
to an optimization objective in those works.

The empirical head-to-head numbers in the table directly above the new
paragraph already show that each form attains the optimum of its own
objective and only its own; matched-norm behaves as a distinct operating
point, not as a tuning of either EDEN scale.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-04 16:31:51 -05:00
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