The Three Gates — A Rooted-Operator Approach to Weil Positivity

Version 3 of The Three Gates: A Rooted-Operator Approach to Weil Positivity.This revision makes the final dependency structure of the Gate-II argument explicit. In particular, it establishes the strict positivity of the folded pre-scalar pivot before the sequential Schur ledger, makes the P2/P3 bookkeeping explicit, and derives the Green-root condition a posteriori from MASTER coercivity rather than using it as an independent induction hypothesis. The main theorem and the underlying rooted-operator strategy are otherwise unchanged.The accompanying supplementary computational material has been updated in parallel and contains the corresponding reproducibility and verification ledgers, together with the exact-rational certification material.