Gourevitch.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 7190 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, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Gourevitch's series identity

References:

About a New Kind of Ramanujan-Type Series by Jesús Guillera
[G2003] Guillera, Jesús. "About a new kind of Ramanujan-type series." Experimental Mathematics 12.4 (2003): 507-510.
[A2025] Au, Kam Cheong. "Wilf-Zeilberger seeds and non-trivial hypergeometric identities." Journal of Symbolic Computation 130 (2025): 102421. arXiv:2312.14051

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100SolvedSet1.lean

theorem Gourevitch.gourevitch_series_identity The Gourevitch series identity: The following identity holds sorry line 40 source
Source documentation
The Gourevitch series identity: The following identity holds: $\sum_{n=0}^{\infty} \frac{1 + 14 n + 76 n^2 + 168 n^3}{2^{20 n}} \binom{2n}{n}^7 = \frac{32}{\pi^3}.$ This was originally conjectured in [G2003] by Guillera and proven in [A2025] by Au.

depends on sorry what this means
Statement uses: Eq, Real, tsum, Nat, HMul.hMul, HDiv.hDiv, HAdd.hAdd, OfNat.ofNat, HPow.hPow, Nat.centralBinom, SummationFilter.unconditional, Real.pi
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
48 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem gourevitch_series_identity :
    ∑' n : ℕ, ((1 + 14 * n + 76 * n ^ 2 + 168 * n ^ 3) / (2 ^ (20 * n)) : ℝ)
      * Nat.centralBinom n ^ 7 = 32 / (Real.pi ^ 3) := by
…
```