Tax
Every obligation traces a path
International tax law forms a traversable structure. Graph-theoretic methods map jurisdictional relationships and identify the minimum-cost path through the network.
Formal Structure
G = (V, E, w)
The global tax system is represented as a weighted directed graph. The structure encodes the full topology of jurisdictional relationships, making the path optimization problem well-defined.
Jurisdictions, legal entities, and structural positions constitute the node set. Each vertex carries attributes encoding the applicable regulatory regime and treaty participation.
Treaty relationships, cross-border pathways, and inter-entity flows form the directed arc set. Directionality encodes the asymmetric character of jurisdictional relationships.
A scalar-valued function over the arc set quantifying the obligatory cost of each traversal. Weights aggregate along a path to yield total burden for any route through the graph.
Graph Traversal
Shortest path through structured space
Construct
The graph is assembled from jurisdictional nodes, treaty arcs, and the corresponding weight function encoding obligatory cost per arc.
Enumerate
A shortest-path algorithm is applied over the weighted directed graph to enumerate all feasible routes from source to terminal, minimizing cumulative weight.
Screen
Candidate paths are tested against the full regulatory constraint set. Only routes satisfying every binding feasibility condition are admitted.
Emit
The minimum-cost feasible path is emitted as a declarative structural specification defining the precise sequence of nodes and arcs.
Structural Result
Every obligation traces a path.
Graph theory transforms tax analysis from an advisory discipline into a deterministic optimization problem. The minimum-cost path is a property of the graph — not a matter of judgment.
If the graph is defined
the minimum-cost path exists.
If the path exists
it is derivable without discretion.
If it is derivable
it is auditable and reproducible.
Correspondence
Inquiries and discussions
Research inquiries and methodological discussions are welcomed via direct correspondence.