https://w3id.org/np/RAozJpyEwyicimaEY95izkeFeUw7OzJZtlZWiGgrdwFrs
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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dc:description "Bravais's Theorem XLVI is the classic crystallographic restriction theorem—a pure mathematical deduction following from the requirement that a discrete 3D translational lattice be invariant under rotation. Because it is proved deductively from the definition of a periodic point lattice rather than tested by empirical sampling, it receives low operationalizability under the dataset-resolvability rubric and is classified as not empirically resolvable.";
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<http://www.w3.org/2000/01/rdf-schema#comment> "Proposed test with existing data: This is a pure mathematical theorem (the crystallographic restriction theorem for 3D discrete translation lattices): for any rotation matrix R preserving a 3D lattice L, tr(R) = 1 + 2 cos(θ) must be an integer, restricting rotational orders to n ∈ {1, 2, 3, 4, 6}. An empirical companion check would query periodic crystal structure databases for rotational symmetry orders, but the claim as stated is a deductive property of mathematical point lattices.";
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