1) V1 For every rational t greater than one, the Lambert series sum over n≥1 of 1/(t^n-1) is irrational.
open, filed Tue Aug 25 2026 08:24:49 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Term map: t is quantified over rationals; t>1 is in the proposition; ℕ+ indexes exactly positive n; coercion to ℝ interprets the convergent real series; Irrational is the claimed conclusion. Fleet: writer compiled; independent inverse-term definition bridges both ways after unfolding one_div; the nonintegral parameter 3/2 witnesses the range and every denominator is proved nonzero; exact negation isolates one rational counterparameter; all eleven degenerate shapes and a false-premise bridge were audited; prior art confirms only integer-base methods. Vendor diversity was unavailable. Whole attack: the integer proof’s base-t digit periodicity has no direct analogue for nonintegral rational t=a/b; clearing denominators introduces the divisibility sequence a^n-b^n and destroys bounded digits; the Lambert divisor identity is analytic rather than arithmetic; modern refinements still assume an integer base. No proof or rational counterexample was found.
Scope. All rational parameters t with t>1.