Shadow & Mirror: Complementarity of Computation and Consciousness

Why does the same number appear in the divergence angle of a sunflower, the coupling strength of the electromagnetic field, and the room where Wolfgang Pauli died? This work identifies a structural invariant— treewidth — that separates every system examined into two complementary components: one that decomposes (shadow, bounded treewidth) and one that refuses to (mirror, unbounded treewidth). A five-dimensional diagnostic characterizes the gap. One hundred two measurements across forty-seven domains — from water to cancer genomics to the cosmic microwave background — confirm it. Across forty-one measurements with extractable p-values, thegeometric mean significance is p= 10^-111

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