Spectral Graph Laplacian & Fiedler Slicer
Visualizing codebase topology as an algebraic graph matrix. When cognitive burden or line count exceeds safety invariants, 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 ($v_2$)
The eigenvector corresponding to the second-smallest eigenvalue ($\lambda_2$) of the Graph Laplacian is known as the Fiedler vector. It provides a continuous 1D geometric embedding where the sign cut ($v_2[i] \ge 0$ vs. $v_2[i] < 0$) 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 Senior SE Discipline 2: instead of deleting code, the engine invokes spectral graph partitioning to cleave the monolith into coherent sibling modules (e.g. *_helpers.go).