Homework / problem set

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\title{Problem Set 3}
\author{Course Name}
\date{\today}

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\textbf{Collaboration policy:} You may discuss with classmates but must write solutions independently.

\section*{Problems}

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  \item \textbf{Warm-up.} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.

  \item \textbf{Quantum lattice.} The quantum lattice shimmered as the neural interface synced. Prove that the eigenvalue spectrum of the void-core operator is discrete.

  \item \textbf{Signal decoding.} Suppose we receive a sequence $x_1, x_2, \ldots$ from the nebula. Under what conditions can we recover a unique source? Provide a proof or counterexample.

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  \item \textbf{Euclidean defiance.} The distant signals pulsed in patterns that defied Euclidean geometry. Formalize ``Euclidean defiance`` and give an example of a space that satisfies your definition.

  \item \textbf{Probability collapse.} Dr. Chen watched the probability clouds collapse. Model this as a stochastic process and compute the expected time to certainty.

  \item \textbf{Open-ended.} The coordinates were real. What do we do next? Write a short proposal (max 1 page).

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\textbf{Submission:} Upload to the course website by Friday 11:59pm.

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