Mark Erdős Problem 260 as solved

A complete Lean 4 proof of the exact right-hand side of
`FormalConjectures/ErdosProblems/260.lean` is available in an external
repository:

- Permanent proof: https://github.com/Hanziwww/erdos260/blob/1f2baf4547f2c2805cdd160611b0b983f43941aa/Erdos260/DeepMind.lean#L92-L132
- Proof repository: https://github.com/Hanziwww/erdos260
- Successful verification run: https://github.com/Hanziwww/erdos260/actions/runs/29516048968
- Associated paper: https://arxiv.org/abs/2606.24972

The external theorem proves the exact RHS currently used in Formal
Conjectures, including `a : ℕ → ℤ`, the original `n = 0` division, integer
exponentiation in `2 ^ a n`, `StrictMono`, `Tendsto`, `HasSum`, and the
conclusion `Irrational s`.

The pinned proof repository builds without `sorry`, project-specific axioms,
or `opaque` proof stand-ins. Its successful CI run includes the ordinary Lean
build and axiom audit at trust level zero, serial Leanchecker replay, and an
independent Nanoda kernel check.

I propose the following small update:

1. Change `@[category research open]` to `@[category research solved]`.
2. Replace `answer(sorry)` with `answer(True)`.
3. Add a `formal_proof using lean4` attribute pointing to the permanent proof
above.

The full proof will remain in the external repository, following the
contribution guideline for proofs longer than approximately 25--50 lines.

Related: #457 and #1629.

Open FormalConjectures/ErdosProblems/260.lean and compare the right-hand side with Erdos260/DeepMind.lean lines 92-132 from the pinned proof repository. Apply the requested solved category, answer(True), and formal_proof using lean4 attribute, then run the repository's Lean build to confirm the theorem and metadata compile.

Written by the indexing model from the issue text.