Disconfirming Edge 5: Branching vs Scale Invariance
C16 (Branching) contradicts C10 (Scale Invariance)
Tension: If branching networks are optimal transport solutions (C16), they should be engineering-optimal — not necessarily fractal. If they are fractal (C10, scale-invariant), they must follow power-law scaling — but engineering optimality often produces exponential, not power-law, scaling.
Resolution status: PARTIALLY RESOLVED
What would settle it: A definitive proof that Murray’s Law (r^3) follows from fractal geometry rather than viscous dissipation optimization; OR demonstration that optimal transport under realistic biological constraints necessarily produces fractal, not exponential, scaling.
Current state: Bejan’s constructal law claims to derive branching from optimization, but the derivation assumes a fractal Ansatz. WBE (1997) derive the 3/4 scaling exponent from network geometry plus minimization, suggesting both nodes are partially right.
Honest assessment: The tension is more apparent than real — both branching and fractality emerge from the same physical constraints (space-filling + minimum cost). But the rival frames of each node are in genuine tension: one says geometry is primary, the other says optimization is primary.
Summary Table: Disconfirming Edges
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Corpus map
- C16 (Branching): C16 in the Encyclopedia · C16 in the Catalogue
- C10 (Scale Invariance): C10 in the Encyclopedia · C10 in the Catalogue
- Disconfirming edges: 1 · 2 · 3 · 4 · 5
- Catalogue hub: Convergence Catalogue — Public Article · The Schema