Analysis of 34 real networks shows real interaction strengths organize functional memory at greater hierarchical depth than random weights, collapsing onto four recurrent dynamical organizations with weight geometry as the primary driver.
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Pre-registered multilayer network tests across seven substrates show betweenness-based hub persistence recovers expert-described logic structures better than degree, with confirmed correlations in ISCAS85 and Lean mathlib4.
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Weight geometry governs functional memory in complex systems
Analysis of 34 real networks shows real interaction strengths organize functional memory at greater hierarchical depth than random weights, collapsing onto four recurrent dynamical organizations with weight geometry as the primary driver.
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Topology as Logic: Structural Role Geometry Across Formal, Software, Biological, and Prebiotic Systems
Pre-registered multilayer network tests across seven substrates show betweenness-based hub persistence recovers expert-described logic structures better than degree, with confirmed correlations in ISCAS85 and Lean mathlib4.
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