`Challenge.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 981 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Pinned Carleson blueprint

3 declarations, 3 contain sorry, 0 declared as axioms

Challenge file for using comparator

Imports (1)

Carleson.Defs

theorem classical_carleson' Carleson's theorem asserting a.e. convergence of the partial Fourier sums for continous functions sorry line 10 source
Source comment
Carleson's theorem asserting a.e. convergence of the partial Fourier sums for continous functions

depends on sorry what this means
Statement uses: ClassicalCarleson
Proof uses: Real, Complex, sorryAx, Lean.Name, Continuous, Function.Periodic, HMul.hMul, OfNat.ofNat, Real.pi, Filter.Eventually, Filter.Tendsto, Nat, partialFourierSum, Filter.atTop, nhds, MeasureTheory.ae, MeasureTheory.Measure, MeasureTheory.MeasureSpace.volume, Bool.false, Lean.Name.num and 2 more
20 instances, coercions and auxiliary constants left out.

Distinct definitions of this name: Solution.lean:11 (same statement text; different proof or body). Qualify references as classical_carleson'@path.
```
theorem classical_carleson' : ClassicalCarleson := sorry
```
Mentions: ClassicalCarleson
theorem metric_carleson'' sorry line 12 source
depends on sorry what this means
Statement uses: MetricSpaceCarleson
Proof uses: Nat, MetricSpace, NNReal, Set, Complex, KernelProofData, IsCancellative, defaultA, defaultτ, sorryAx, Lean.Name, Membership.mem, Set.Ioc, OfNat.ofNat, NNReal.HolderConjugate, MeasurableSet, Measurable, LE.le, Real, Norm.norm and 18 more
59 instances, coercions and auxiliary constants left out.

Distinct definitions of this name: Solution.lean:13 (same statement text; different proof or body). Qualify references as metric_carleson''@path.
theorem linearized_metric_carleson' sorry line 14 source
depends on sorry what this means
Statement uses: LinearizedMetricCarleson
Proof uses: Nat, MetricSpace, NNReal, Set, Complex, KernelProofData, MeasureTheory.SimpleFunc, defaultA, FunctionDistances.Θ, Real, IsCancellative, defaultτ, sorryAx, Lean.Name, Membership.mem, Set.Ioc, OfNat.ofNat, NNReal.HolderConjugate, MeasurableSet, Measurable and 20 more
62 instances, coercions and auxiliary constants left out.

Distinct definitions of this name: Solution.lean:15 (same statement text; different proof or body). Qualify references as linearized_metric_carleson'@path.