Void Theorem

OVERVIEW

Void Theorem is an interactive art system that maps formal proof structure into a navigable, emissive hypergraph. Axiom, lemma, and theorem nodes inhabit a deep procedural void; each selection propagates inference through directed hyperedges, revealing hidden theorem reachability as coherent light cascades across the graph.

ARCHITECTURE

The piece combines a typed state model for nodes and hyperedges with deterministic propagation rules and GPU-oriented rendering. Core simulation stages include topological closure, wavefront expansion, coherence/energy interpolation, and flow updates over premise-to-conclusion edges. Rendering targets instanced node geometry, flow-driven edge tubes, and an atmosphere layer that adapts to global coherence with device-tier quality controls.

FUNCTIONALITY

• Directed hypergraph core with premise sets and conclusion nodes for each inference edge
• Selection-triggered closure and BFS-style propagation front for deduction cascades
• Coherence state progression from superposition shimmer to collapsed certainty
• Energy decay and activation rules that create visible proof storm and dead-end dimming behaviour
• Flow-weighted edge styling where brightness and radius encode proof-path throughput
• Frame-rate-safe animation loop using capped delta-time updates
• Force-directed 3D layout with damping and theorem-centrality bias
• Responsive rendering tiers for desktop/tablet/mobile with explicit degradation strategy

HOW IT WORKS

Selecting a node marks it as visited and seeds a propagation front from topological reachability. On each frame, active nodes lerp toward collapsed coherence while unvisited regions oscillate in low-coherence shimmer. Hyperedges activate once premises are satisfied, then update flow intensity based on selected proof-path pressure. Camera orbit and dolly controls expose structure at macro and micro scales while preserving deterministic update order.

OUTCOMES

• Turns abstract logic and proof dependency into an explorable spatial narrative
• Lets visitors see how one selected axiom can illuminate theorem reachability across a larger structure
• Makes proof progress legible through cascading light, coherence, and highlighted paths
• Adds a high-concept mathematical artwork that connects formal reasoning with interaction
• Gives the portfolio a distinctive visual proof-space rather than another static project card