Localized Weil Positivity and Rooted-Operator Induction for the Riemann Hypothesis

This edition presents the strongest internally audited proof chain currently assembled in the project. The finite certificates have been replayed in the supplied working environment; the form-level closure, quantitative Schur transfer, endpoint induction, and all-support compression have been assembled at theorem level. Independent referee-level validation has not yet occurred. Accordingly, this record presents an authorial proof claim and proof submission, not a claim of prior community acceptance of the Riemann Hypothesis. The manuscript develops a localized rooted-operator approach to the restricted odd Weil criterion. The framework includes a canonical prime-free analytic base at a₂ = 1/2 log 2 with an exact rational coercive bound, an all-k structural induction for k ≥ 2, refined endpoint bookkeeping, corrected common-cut and no-double-spend identities, an explicit closed-form Schur transfer, and a self-contained finite verification package. The manuscript also records its provenance, relation to prior work, reproducibility protocol, verification ledger, and AI disclosure.