{
  "id": "the-gaussian-moat-problem",
  "title": "The Gaussian moat problem",
  "description": "Walks through Gaussian primes with bounded steps. The arithmetic of split primes and the reduction of the uniform component bound to a finite periodic sieve; Shannon entropy, Pinsker's inequality, short lists of candidates and averages over random coordinates; Hoeffding's inequality and the isoperimetry of the discrete cube; many differences of a walk stretch and their separation by randomly signed products of Gaussian primes; entropy enrichment by sampling differences; coverage transferred backwards with shared continuations; a common sampling schedule; and the information cost of avoiding zero classes. Together they prove that for every step bound the connected components of the Gaussian-prime graph have bounded size, so that one cannot walk to infinity on Gaussian primes with bounded steps.",
  "units": [
    {
      "id": "walks-through-gaussian-primes",
      "title": "Walks through Gaussian primes",
      "reader": "walks-through-gaussian-primes.html",
      "source": "src/walks-through-gaussian-primes.md",
      "source_sha256": "05a969fd7c27e8bebd715e61c0e7e52de0a7b1250e776461fef2a774954c0081",
      "status": "author_self_checked"
    },
    {
      "id": "entropy-of-finite-random-variables",
      "title": "Entropy of finite random variables",
      "reader": "entropy-of-finite-random-variables.html",
      "source": "src/entropy-of-finite-random-variables.md",
      "source_sha256": "6a0bc7c02affb83b8c0025a4ad36b8c8d40891297641c7d5628ce68af109bdf2",
      "status": "author_self_checked"
    },
    {
      "id": "concentration-and-the-discrete-cube",
      "title": "Concentration and the discrete cube",
      "reader": "concentration-and-the-discrete-cube.html",
      "source": "src/concentration-and-the-discrete-cube.md",
      "source_sha256": "bb1740929ac5d34d1630dd1d7695f3415d3509b27dc2416967af7e494aa8ea76",
      "status": "author_self_checked"
    },
    {
      "id": "differences-of-a-walk-and-separating-products",
      "title": "Differences of a walk and separating products",
      "reader": "differences-of-a-walk-and-separating-products.html",
      "source": "src/differences-of-a-walk-and-separating-products.md",
      "source_sha256": "5f997cacb277439a5cc0f513776cbe1b14a9f0084e0347aacbb03e9e41271261",
      "status": "author_self_checked"
    },
    {
      "id": "entropy-enrichment",
      "title": "Entropy enrichment",
      "reader": "entropy-enrichment.html",
      "source": "src/entropy-enrichment.md",
      "source_sha256": "cd863394001c0dde0efcca596a174368631e22926d7b5c52813339360dd723f2",
      "status": "author_self_checked"
    },
    {
      "id": "coverage-from-shared-continuations",
      "title": "Coverage from shared continuations",
      "reader": "coverage-from-shared-continuations.html",
      "source": "src/coverage-from-shared-continuations.md",
      "source_sha256": "3ed0698b0686fe02ac06597447ae89e4890dca07a93b44c1872a813e4686fd20",
      "status": "author_self_checked"
    },
    {
      "id": "a-common-sampling-schedule",
      "title": "A common sampling schedule",
      "reader": "a-common-sampling-schedule.html",
      "source": "src/a-common-sampling-schedule.md",
      "source_sha256": "e3f4f551180a74e739bb6a3d3eba646f029327dd358442400a64cbe212e9e28e",
      "status": "author_self_checked"
    },
    {
      "id": "zero-avoidance-and-the-finite-sieve",
      "title": "Zero avoidance and the finite sieve",
      "reader": "zero-avoidance-and-the-finite-sieve.html",
      "source": "src/zero-avoidance-and-the-finite-sieve.md",
      "source_sha256": "1adacb60c3e4134c323efbae20da96dac047a6d901be874b829a00821b35774f",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "Core course C40 (Euclidean domains, unique factorization)",
    "Core course B90 (finite probability)",
    "Core course D60, Lecture 30 (Brouwer's fixed-point theorem)",
    "NT-ZETA lesson on Chebyshev's bounds",
    "NT-DIRL lesson on the prime number theorem for arithmetic progressions"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}