Void Theorem
Interactive hypergraph space where selected axioms trigger light-based propagation pathways via a living void-light topology.
Interactive demo
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Interactive hypergraph space where selected axioms trigger light-based propagation pathways via a living void-light topology.
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.
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.
┌────────────────────────────────────────────────────────────────────────────┐
│ AXIOM SELECTION · ORBIT / DOLLY · RENDERER CONTROLS │
└────────────────────────────────────────────────────────────────────────────┘
│
▼
┌────────────────────────────────────────────────────────────────────────────┐
│ PROOF-SPACE ENGINE (deterministic core) │
├────────────────────────────────────────────────────────────────────────────┤
│ │
│ ┌────────────────────────────────────────────────────────────────────┐ │
│ │ HYPERGRAPH MODEL │ │
│ │ Axiom · lemma · theorem nodes · premise-set to conclusion │ │
│ └────────────────────────────────────────────────────────────────────┘ │
│ │ │
│ ▼ │
│ ┌────────────────────────────────────────────────────────────────────┐ │
│ │ CLOSURE + WAVEFRONT PROPAGATION │ │
│ │ Topological reachability · BFS deduction front · activation │ │
│ └────────────────────────────────────────────────────────────────────┘ │
│ │ │
│ ▼ │
│ ┌────────────────────────────────────────────────────────────────────┐ │
│ │ COHERENCE + ENERGY INTEGRATION │ │
│ │ ┌──────────────────────────┐ ┌─────────────────────────────┐ │ │
│ │ │ Superposition to collapse│ │ Energy decay · dead-end dim │ │ │
│ │ │ lerp · capped delta-time │ │ flow-weighted edge styling │ │ │
│ │ └──────────────────────────┘ └─────────────────────────────┘ │ │
│ └────────────────────────────────────────────────────────────────────┘ │
│ │ │
│ ▼ │
│ ┌────────────────────────────────────────────────────────────────────┐ │
│ │ GPU RENDER + DEVICE-TIER QUALITY │ │
│ │ Instanced nodes · flow-driven edge tubes · coherent atmosphere │ │
│ └────────────────────────────────────────────────────────────────────┘ │
│ │
└────────────────────────────────────────────────────────────────────────────┘
│
▼
┌────────────────────────────────────────────────────────────────────────────┐
│ ILLUMINATED PROOF PATHS + THEOREM REACHABILITY │
└────────────────────────────────────────────────────────────────────────────┘Selecting a node marks it as visited and seeds a propagation front from topological reachability. On each frame, active nodes lerp towards 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.