Alphabeta Math
CounterexampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07
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An unordered infinite zero sum is not an explicit formula

Statement refuted

For x>1, the bare unordered expression ∑ρxρ/ρ is a defined quantity equal to the sharp explicit-formula zero contribution.

Counterexample

Given: the sharp and smoothed explicit formulas.

1.1

The sharp formula asserts only finite sums ∑∣ℑρ∣<T and specifies an error before any limit is taken.

givenalgebra
2.1

The smoothed formula supplies a different convergence mechanism through its Mellin decay. Neither result assigns a value to the displayed unordered bare sum, so the asserted equality has no defined left side.

step 1.1contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources