Struct CountingCert 

pub struct CountingCert {
    pub pigeons: u128,
    pub holes: u128,
}

The pigeonhole counting certificate — the symmetry break taken to its absolute limit. For the complete bipartite instance PHP(pigeons → holes) (every pigeon may use every hole, each hole ≤ 1 pigeon), the full pigeon set has neighborhood = all holes slots, so Hall’s condition fails the instant pigeons > holes. That single inequality IS the refutation — sound, O(1), and scale-free.

This is the indisputable object. PHP(n) over booleans has n·(n−1) variables, and every resolution or CDCL refutation has at least 2^Ω(n) steps (Haken, 1985) — so for n = 2¹²⁸ the shortest possible search proof has more steps than a number with ~10³⁷ digits, beyond any computation this universe could ever run. The counting break decides and certifies the very same fact in one comparison.

Fields

pigeons: u128

holes: u128

Trait Implementations

impl Clone for CountingCert

fn clone(&self) -> CountingCert

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for CountingCert

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for CountingCert

fn eq(&self, other: &CountingCert) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for CountingCert

impl Eq for CountingCert

impl StructuralPartialEq for CountingCert