Administrative correction only - no new mathematical content

Abstract

Correction and provenance notice (5 August 2026). This version was created in error while attempting to add a metadata correction notice to the historical record. It contains no new mathematical content. Its files, creators, DOI, and version history are retained unchanged for provenance. The maintained correction collection is identified by the stable all-versions DOI 10.5281/zenodo.17010427. This record is obsoleted and corrected by 10.5281/zenodo.17010427. Correction notice. The original PDF and authorship are preserved unchanged in this successor. The common-half-arc selection equality used in the sharp L1 Poincaré–Wirtinger proof line is false: an exact rational example has levelwise optimum 4/5 and best common-half-arc cost 9/10. DOI 10.5281/zenodo.17010427 gives a different coarea and nested-core proof of the sharp coefficient 1/4, with exact verification files. This correction does not audit the wider automorphic, motivic, Collatz, p-adic, entropy, or spectral bridges. They are not carried forward by the maintained correction record and require independent proofs. Correction audit: The Clankers, 5 August 2026.