Struct StabilityCondition 

pub struct StabilityCondition {
    pub grassmannian: (usize, usize),
    pub trust_level: f64,
}

A Bridgeland-type stability condition parameterized by trust level.

The central charge is:

Z_t(σ_λ) = -codim(σ_λ) + i · t · dim(σ_λ)

A Schubert class is stable at trust level t if its phase φ = (1/π)·arg(Z_t) ∈ (0, 1).

Fields

grassmannian: (usize, usize)

Grassmannian parameters

trust_level: f64

Trust level parameter

Implementations

impl StabilityCondition

pub fn standard(grassmannian: (usize, usize), trust_level: f64) -> Self

Create the standard stability condition for a Grassmannian.

Contract

requires: trust_level > 0
ensures: result.is_stable(σ_λ) depends on codim/dim ratio

pub fn central_charge(&self, class: &SchubertClass) -> (f64, f64)

Compute the central charge Z_t(σ_λ).

Returns (real_part, imaginary_part).

Contract

ensures: result.0 == -codim(class)
ensures: result.1 == trust_level * dim(class)

pub fn phase(&self, class: &SchubertClass) -> f64

Compute the phase φ = (1/π) · arg(Z_t(σ_λ)).

Phase in (0, 1) means the class is stable. Phase = 0 or 1 means semistable (on a wall).

Contract

ensures: 0.0 <= result <= 1.0

pub fn is_stable(&self, capability: &Capability) -> bool

Check if a capability is stable at this trust level.

Contract

ensures: result == (0 < phase(class) < 1)

pub fn stable_capabilities<'a>( &self, namespace: &'a Namespace, ) -> Vec<&'a Capability>

Find all stable capabilities in a namespace at this trust level.

Contract

ensures: forall cap in result. self.is_stable(cap) == true
ensures: result.len() <= namespace.capabilities.len()

pub fn stable_count(&self, namespace: &Namespace) -> usize

Count stable capabilities.

Contract

ensures: result == self.stable_capabilities(namespace).len()

Trait Implementations

impl Clone for StabilityCondition

fn clone(&self) -> StabilityCondition

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for StabilityCondition

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

Formats the value using the given formatter.