Green's Open Problems #92

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.92

I have a string $x \in \\{0,1\\}^n$. Let $\tilde{x}$ be the random string obtained by deleting bits from $x$ independently at random with probability $\frac{1}{2}$ (thus, for example, if $n = 8$ and $x = 00110110$, it might be the case that $\tilde{x} = 0111$, generated by deleting bits 2, 3, 5, 8.) An instance of $\tilde{x}$ is called a 'trace'. How many independent traces $\tilde{x}\_1, ..., \tilde{x}\_m$ are needed before one can reconstruct $x$ with probability 0.9?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-68
* ams-60
* ams-05

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading Green's Open Problems #92 in the linked paper and inspect the repository's existing formalized conjectures to identify the expected statement structure and location. Formalize the trace-reconstruction conjecture and add any required supporting definitions or proofs; done means the repository accepts the new Lean statement and its checks pass.

Written by the indexing model from the issue text.