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  "path": "/abs/2603.01393v1",
  "publishedAt": "2026-03-03T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Taisei Otsuji",
    "Peter Fulla",
    "Takuro Fukunaga"
  ],
  "textContent": "**Authors:** Taisei Otsuji, Peter Fulla, Takuro Fukunaga\n\nHotaru Beam is a logic puzzle which objective is to connect circles placed on a grid by drawing only lines with specified starting points and numbers of bends. A zero-knowledge proof is a communication protocol that allows one player to persuade the other that they are in possession of a certain piece of information without actually revealing it. We show that Hotaru Beam is NP-complete and present a physical zero-knowledge proof (i.e. implementable using physical items) for proving that one knows a solution to the puzzle.",
  "title": "NP-Completeness and Physical Zero-Knowledge Proof of Hotaru Beam"
}