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The irrationality measure of π is at most 7.101862832357

Published 10 Sep 2026 in math.NT | (2609.11276v1)

Abstract: We introduce two independent numerator exponents into the Zeilberger--Zudilin integral and specialize them to [ A_1=A_2=\frac{1857}{2785}. ] The resulting integer linear forms in $1$ and ππ prove [ μ(π)<7.101862832357. ] This lowers the Zeilberger--Zudilin upper bound 7.1032053341377.103205334137\ldots by more than $0.001342501780$; the difference between the unrounded bounds is 0.00134250178065090.0013425017806509\ldots, approximately 0.01890%0.01890\%. The same parameter point is a strict two-dimensional local minimizer of the explicit auxiliary upper-bound function in its admissible arithmetic chamber. This is a local statement about that function, not a claim that the point is a global optimizer among all constructions.

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