Struct EmergenceDetector 

pub struct EmergenceDetector;

H¹ Cohomology emergence detector

Mathematical basis

For a cellular complex with V vertices and E edges:

• H⁰_dim = number of connected components (C)
• H¹_dim = E - V + H⁰_dim (Betti number β₁, number of independent cycles)

H¹_dim > 0 means the constraint graph has non-trivial topology — redundant constraint paths that create emergent behavior.

Bloom pre-filter

XOR fingerprint skips expensive H¹ computation for obvious cases:

• Disconnected: E < V-1 → no emergence possible
• Massively over-connected: E > V*(V-1)/4 → definitely emergence
• Laman-rigid: E ≈ 2V-3 → skip (no overconstraint)

Implementations

impl EmergenceDetector

pub fn preliminary_screen(V: usize, E: usize) -> bool

HDC bloom pre-filter — skip H¹ if answer is obvious.

Returns true if H¹ computation is definitely needed. Returns false if answer is obvious:

• Disconnected (E < V-1) → no emergence possible
• Massively over-connected (E > V*(V-1)/4) → definitely emergence
• Laman-rigid (E ≈ 2V-3 ± 10%) → no overconstraint

Inspired by FM’s “HDC bloom: bypasses 80-90% of constraint checks”.

pub fn detect( n_vertices: usize, n_edges: usize, n_components: usize, ) -> EmergenceResult

Detect emergence via H¹ cohomology

• n_vertices: Number of agents in the fleet (V)
• n_edges: Number of communication/trust edges (E)
• n_components: Number of connected components (C, usually 1)

pub fn detect_graph<V: Into<usize>, E: Into<usize>>( V: V, E: E, ) -> EmergenceResult

Detect from a fleet graph

pub fn detect_beta(n_vertices: usize, n_edges: usize) -> EmergenceResult

Beta version: detect with beta coefficient β₁ > 0 is the emergence condition (first Betti number)

Trait Implementations

impl Clone for EmergenceDetector

fn clone(&self) -> EmergenceDetector

Returns a duplicate of the value.

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

Performs copy-assignment from source.