Polynomial Index
Abstract
A Hasse derivative lowers a polynomial’s weighted index by at most its derivative weight.
Theorem 1.1 (Polynomial Index).
Lean statement: D5/S3/Arith/DiophantineApproximation/PolynomialIndex.index_le_hasseDeriv_add
Proof. Machine-checked in Lean as D5/S3/Arith/DiophantineApproximation/PolynomialIndex.index_le_hasseDeriv_add (✓ std3). ∎
Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.
Commentary.
A Hasse derivative lowers a polynomial’s weighted index by at most its derivative weight.