Technical Lean evidence record
Checked Artifact: Poisson Summation Formula (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- Declaration checked
Real.tsum_eq_tsum_fourier- Module
Mathlib.Analysis.Fourier.PoissonSummation- Source file checked
Mathlib/Analysis/Fourier/PoissonSummation.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
This page indexes Mathlib's general one-dimensional Poisson summation declaration for a continuous map f : ℝ → ℂ. It assumes that, for every compact K, the series of sup norms of the integer translates restricted to K is summable, and that the series of integer Fourier-transform samples is summable. The conclusion holds at every real x and weights each Fourier sample by fourier n at x viewed in UnitAddCircle. The familiar unphased formula is the x = 0 specialization, not the displayed conclusion at arbitrary x.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.