Struct QuantumCapability 

pub struct QuantumCapability<const P: usize, const Q: usize, const R: usize> {
    pub capability: Capability,
    pub k_class: QuantumKClass<P, Q, R>,
}

A capability enhanced with quantum K-theory data

While a standard Capability uses a Schubert class (cohomological), a QuantumCapability additionally carries a K-theory class representing the “sheaf of sections” of the capability bundle over the Grassmannian.

This enables:

• Quantum corrections: Capabilities that interact through rational curve contributions (analogous to quantum entanglement in the namespace lattice)
• Euler characteristic counting: chi(E) gives a refined count of valid configurations weighted by sheaf cohomology
• Adams operations: psi^k acts on capabilities, modeling “k-fold amplification” of access rights

Contract

invariant: self.capability.schubert_class == classical limit of self.k_class

Fields

capability: Capability

Classical capability (Schubert class)

k_class: QuantumKClass<P, Q, R>

Quantum K-theory class (sheaf data)

Implementations

impl<const P: usize, const Q: usize, const R: usize> QuantumCapability<P, Q, R>

pub fn from_classical(capability: Capability) -> Self

Create a quantum capability from a classical one

The K-theory class defaults to the structure sheaf of the Schubert variety.

pub fn new(capability: Capability, k_class: QuantumKClass<P, Q, R>) -> Self

Create with explicit K-theory data

pub fn quantum_entangle( &self, other: &Self, ) -> EnumerativeResult<QuantumKClass<P, Q, R>>

Quantum product of two capabilities

Returns the entangled capability with quantum corrections from rational curves connecting the two Schubert varieties.

Contract

ensures: result.q_power >= self.k_class.q_power + other.k_class.q_power

pub fn euler_characteristic(&self, ambient_dimension: usize) -> Rational64

Euler characteristic: refined configuration count

While the classical count_configurations gives the intersection number, this gives chi(E) = integral ch(E) * td(X), which accounts for higher cohomology.

Contract

ensures: result == self.k_class.euler_characteristic(ambient_dimension)

pub fn amplify(&self, k: i32) -> Self

Adams amplification: psi^k acts on the capability

Models “k-fold amplification” of the access right. psi^k preserves the underlying Schubert class but modifies the K-theoretic refinement.

Contract

ensures: result.capability == self.capability  (Schubert class unchanged)
ensures: result.k_class == psi^k(self.k_class)

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize> Clone for QuantumCapability<P, Q, R>

fn clone(&self) -> QuantumCapability<P, Q, R>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: usize, const Q: usize, const R: usize> Debug for QuantumCapability<P, Q, R>

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

Formats the value using the given formatter.