Scientific Computing Verification Stack

Abstract

Documentation-only R3 addendum to Scientific Computing Verification Stack R2 (https://doi.org/10.5281/zenodo.22861401). The new PDF walks through four distinct questions in the finite R15 Maxwell sequence: measured source-problem refinement, the separately reported conforming R5 spectral comparator, failure of the historical hybrid pencil at β = 4, and the still-open physical-cluster equivalence of the revised β = 24 pencil. It derives the Schur reduction under an explicit invertibility assumption, computes the final-pair observed curl-error rate 0.973607357390671 from the reported mesh widths and errors, and explains why 323 negative finite modes at β = 4 cannot be erased by a local zero-negative-mode result for a changed operator. Local R7/R8 archive and bounded rerun checks are described with their limitations: the original R6 checkout was not authenticated and the R5 oracle was not rerun. This note does not claim a continuum theorem, spectral equivalence, physical Maxwell validation, or independent third-party review. This version deposits one original explanatory PDF only; it contains no solver code, source archive, or copied third-party figure. CC BY 4.0 applies only to that PDF. Earlier files and rights remain unchanged. Riccardo Giudici acts as an independent systems orchestrator and discloses computational and AI assistance; no institutional endorsement is claimed.