NomosSpectral Graph Laplacian & Fiedler Slicer
Visualizing codebase topology as an algebraic graph matrix. When cognitive burden or line count exceeds safety invariants (≤ 400 LOC), the automated Graph Laplacian ($L = D - A$) and Fiedler eigenvector ($v_2$) partition monolithic packages along their minimal algebraic cut, enforcing Nomos Axiom 4 without destructive AST truncation.
ALGEBRAIC CONNECTIVITY (λ₂)
Second-smallest eigenvalue of the Graph Laplacian. Measures the structural robustness of code coupling. Values < 0.08 indicate emergent modular cleavage opportunities; values > 0.20 indicate a tightly entangled circular knot.
MINIMAL-CUT COUPLING METRICS
Severing these 0 cross-cutting edges along the Fiedler boundary yields two independent Single-Responsibility units satisfying Senior SE Discipline 2.
FIEDLER EIGENVECTOR (v₂) PARTITION
1. The Graph Laplacian (L = D - A)
Every Go codebase can be modeled as an undirected graph where functions/files are vertices and afferent/efferent imports are edges. The Laplacian matrix combines the diagonal degree matrix D and adjacency matrix A. The spectrum of L encodes the global connectivity and clustering topology of the system.
2. The Fiedler Vector (v₂)
The eigenvector corresponding to the second-smallest eigenvalue (λ₂) of the Graph Laplacian is known as the Fiedler vector. It provides a continuous 1D geometric embedding where the sign cut (v₂[i] ≥ 0 vs. v₂[i] < 0) solves the NP-hard graph partitioning problem along its minimal edge cut.
3. Axiom 4: Topological Slicing
In traditional AI development, models tasked with editing monolithic files suffer from attention drift and destructive truncation. Nomos enforces topological slicing: instead of deleting code, engineers cleave monoliths into coherent sibling modules (e.g. *_helpers.go) within the 400-LOC ceiling.