Why it matters

Hamiltonian reduction is classic gadget proof. Understanding shapes technique.

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The architecture

Chain gadgets per variable + clause.

Hamiltonian path corresponds to satisfying assignment.

Hamiltonian reductionVariable gadgetschainsClause gadgetsconnectorsHamiltonian pathiff satisfying assignmentGadget technique standard; also proves TSP NP-hard via chain
Hamiltonian reduction.
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How it works end to end

Complex gadgets.

Correctness carefully proven.

Chain to TSP via distance encoding.