Every substrate, read through every graph invariant, across the Shadow, Equilibrium, and Mirror regimes.
One thesis, 75 profiles. Each crosses a substrate with a graph metric and a structural regime, computes its boundary condition, and prices the simulation with Ross’s Law: cost ≈ exp(Θ(tw(G))). The Shadow and Mirror profiles of each pairing are counterparts — the gap between them is treewidth itself.
Contracting a tensor network means summing over its internal indices, and the largest intermediate tensor you must hold is exponential in the contraction's treewidth. · Classical Simulation Limits
A retrieval-augmented index is a similarity graph; the cost of coherent multi-hop retrieval tracks the treewidth of the activated subgraph, not its raw size. · Context-Window Degradation
A neural-network ansatz represents a quantum state's correlations; its classical tractability is set by the entanglement — and therefore the treewidth — it is forced to carry. · Quantum-Advantage Thresholds
A connectome's information-integration cost is bounded by its treewidth; low width means modular, locally-reducible dynamics. · Phase-Transition Modeling
Community detection and influence inference on a social graph are parameterized by its treewidth; dense overlapping cliques drive it up. · NP-Hard Complexity Scaling