Struct MetastabilityBound 

pub struct MetastabilityBound {
    pub name: String,
    pub bound_table: Vec<Vec<u64>>,
    pub is_tight: bool,
}

Encodes Tao’s metastability bound Φ(ε, k) for a convergent sequence.

A sequence (a_n) is metastable with rate Φ if for every ε > 0 and k, there exists n ≤ Φ(ε, k) such that |a_n - a_{n+1}| < ε for all indices in [n, n + k].

Fields

name: String

Name of the theorem/sequence this bound applies to.

bound_table: Vec<Vec<u64>>

The bound function Φ: (epsilon_inv, steps) → index bound. We represent ε as its inverse (a natural number).

is_tight: bool

Whether the bound is tight (matches known lower bounds).

Implementations

impl MetastabilityBound

pub fn constant(name: impl Into<String>, c: u64) -> Self

Create a metastability bound with a constant Φ(ε_inv, k) = c.

pub fn evaluate(&self, epsilon_inv: usize, k: usize) -> u64

Evaluate Φ(epsilon_inv, k): look up the bound table, clamped.

pub fn is_finite(&self) -> bool

Returns true if the bound is finite for all inputs.

Trait Implementations

impl Clone for MetastabilityBound

fn clone(&self) -> MetastabilityBound

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MetastabilityBound

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

Formats the value using the given formatter.