The Question
Multiple structural hypotheses exist for hierarchical reasoning: specific graph topologies (600-cell), golden-ratio frequency scaling, spectral preconditioning, cross-layer coupling. Which ones actually drive performance?
This study systematically isolates each factor through seven controlled experiments.
Seven Experiments
- Frequency hierarchy analysis — does hierarchical frequency structure exist?
- Emergent ratio analysis — does φ-like scaling emerge from the geometry?
- Regime performance comparison — polytope regime vs dyadic baseline
- Coupling suppression dose-response — is coupling causally linked to performance?
- Topology comparison — does graph structure matter under matched dynamics?
- Full-stack feature ablation — which individual features drive performance?
- Spectrum sensitivity — does the specific distribution of learning rates matter?
The Dominant Factors
Learning-rate scale is the dominant factor. Removing eigenvalue-scaled rates degraded quality by 15.45% ± 1.2% — approximately 50× larger than any other individually ablated feature.
Cross-layer coupling is causally beneficial (r = 0.96, p < 0.01, monotonic dose-response across seven suppression levels).
What Didn't Matter
| Feature | Ablation Effect | Verdict |
|---|---|---|
| Learning-rate scale | 15.45% | Dominant |
| Cross-layer coupling | 0.29% (but r=0.96 in dose-response) | Causally important |
| Shell structure | 0.02% | Negligible |
| One-way crystallisation | 0.00% | No effect |
| Ico/dod populations | −2.25% | Negative |
Topology comparison: the complete graph performed comparably or better than the 600-cell under matched dynamics. Six different spectral distributions produced performance within 0.13% of each other.
The Role of the 600-Cell
The 600-cell provided one principled route into a productive rate regime — its eigenvalue spectrum yields learning rates in the right range — but other rate distributions in the same range performed comparably.
The benefit comes from operating in the correct regime, not from the specific geometry.
Scope of Claims
- No claim about biological neural systems
- No claim that φ is necessary for intelligence or reasoning
- No claim that the 600-cell is a required computational substrate
- No validation of broader physics theory
- System-specific conclusions only — one system, synthetic tasks
Performance was dominated by learning-rate scale and cross-layer coupling. What the system is built from mattered less than how it was tuned.