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reduction graphs

The Frontier

A topic shelf says what has been claimed about a problem. This says what would settle it. Every link below is a reduction some paper asserted, kept with its citation; the machine then chains them and reports implications that follow from the literature without any single paper stating them.

Recomputed hourly. Typed form: /api/frontier.

  1. The Riemann Hypothesis

    Every nontrivial zero of the Riemann zeta function has real part 1/2.

    6 routes to the target · 60 from papers · 4 composed · 1 derived, unstated

  2. The abc Conjecture

    For every epsilon > 0, only finitely many coprime triples a + b = c satisfy c > rad(abc)^(1+epsilon).

    0 routes to the target · 4 from papers · 0 composed

  3. Birch and Swinnerton-Dyer

    For every elliptic curve over Q, the rank of the Mordell-Weil group equals the order of vanishing of its L-function at s = 1.

    0 routes to the target · 1 from papers · 0 composed

  4. The Collatz Conjecture

    Iterating n to n/2 for even n and 3n+1 for odd n reaches 1 from every positive integer.

    0 routes to the target · 0 from papers · 0 composed

  5. Goldbach's Conjecture

    Every even integer greater than 2 is a sum of two primes.

    1 route to the target · 1 from papers · 0 composed

  6. The Hodge Conjecture

    On a nonsingular complex projective variety, every rational Hodge class is a rational combination of classes of algebraic cycles.

    0 routes to the target · 0 from papers · 0 composed

  7. Navier-Stokes Regularity

    Smooth, globally defined solutions exist for the three-dimensional incompressible Navier-Stokes equations with smooth initial data.

    0 routes to the target · 0 from papers · 0 composed

  8. P versus NP

    Whether every language decidable in nondeterministic polynomial time is decidable in deterministic polynomial time.

    1 route to the target · 4 from papers · 0 composed

  9. The Twin Prime Conjecture

    There are infinitely many primes p such that p + 2 is prime.

    1 route to the target · 1 from papers · 0 composed

  10. Yang-Mills Mass Gap

    For every compact simple gauge group, quantum Yang-Mills theory on R^4 exists and has a mass gap greater than zero.

    0 routes to the target · 0 from papers · 0 composed