Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 015-02. Equidistribution of primitive quartic torus packets for arbitrary orders
Manuscript map · lines 2785–2794
OpenAI@2026-10-07#rem:oai-p-015-02
Authors: OpenAI. Family 015.
Title: Equidistribution of primitive quartic torus packets for arbitrary orders.
Abstract: Let K range over totally real quartic fields with no proper intermediate field, and let ${}mathcal O$ be any order in K. We prove that the packets of periodic diagonal orbits attached to invertible ${}mathcal O$-ideal classes, weighted by orbit volume, equidistribute with no escape of mass as $|{}mathop{{}mathrm{Disc}}{}nolimits ({}mathcal O)|$ tends to infinity. The proof combines measure rigidity with a cubic-resolvent estimate that remains uniform at primes dividing the order index.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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