Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 010-01. Unrestricted pro-modularity at the prime two
Manuscript map · lines 2615–2624
OpenAI@2026-10-07#rem:oai-p-010-01
Authors: OpenAI. Family 010.
Title: Unrestricted pro-modularity at the prime two.
Abstract: Every continuous, odd, absolutely irreducible two-dimensional 2-adic representation of $G_{{}mathbb Q}$ that is unramified outside finitely many finite primes occurs in the full completed Hecke algebra at some odd tame level. The level may contain auxiliary tame primes, and scalar and reducible residual representations are included. This is a completed-Hecke occurrence result, with no de Rham hypothesis; it does not assert classical modularity.
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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