Record the margins of one rounded LU perturbation

[jwr404]

Summary

• With the stated factor caps, the product perturbation stays strictly below 200 p^3 eta and the perturbed inverse stays at most 64p.
• The grown factor stays at most 66 p^2, and amplifying the two residuals by that cap stays below 530 p^2 eta, which is strictly below one.
• The comparisons hold for every positive precision and were checked directly for precisions 1 through 200. The selected κ is unchanged.

Test plan

• python3.12 -B research/factor-perturbation-margin/verify.py
• python3.12 -B research/factor-perturbation-margin/test_verify.py
• python3.12 scripts/research_package.py --package research/factor-perturbation-margin
• Maintainer replay from the pinned base commit

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Made with Cursor