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We study the behaviour of Newton polygons attached to monic polynomial families over valuation rings under specialization. Using valuation-theoretic Newton polygon stratifications together with filtered coefficient modules and admissible filtered free resolutions, we introduce a derived Newton defect measuring the failure of exactness after passage to associated graded Newton data. We prove that, under Henselianity, residual coprimality, torsion-control, and bounded filtered-resolution hypotheses, constancy of the derived Newton defect along a specialization implies stability of lifted slope-block factorization type. The resulting framework provides a filtered-homological refinement of classical Newton polygon methods and Henselian factorization theory for deformation families over valuation rings.
Kundnani R. T., Marimuthu V., Alam K., Kant Sh. 2026. Filtered Homological Newton Stratifications and Factorization Stability over Valuation Rings. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115525
