Dspatial
plain-language theorem explainer
Dspatial fixes the spatial dimension at three inside the Recognition Science cardinality spectrum. Analysts verifying cross-domain decompositions cite it when confirming that spectrum entries arise from multiplications and powers of the cube generators together with this dimension. The declaration is a direct constant assignment with no computation or lemmas required.
Claim. $D_ {spatial} := 3$
background
The module shows that cardinalities across the RS stack form the structured spectrum {2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 16, 45, 70, 125, 216, 256, 3125, ...}. Each entry decomposes via the cube-generators {2, 3}, the configuration dimension 5, and gap45. Dspatial supplies the spatial dimension fixed at three, which appears in the eight-tick octave and the three-dimensional spatial setting of the framework.
proof idea
The declaration is a direct definition that assigns the natural number 3 to Dspatial. No lemmas are applied and no tactics are used.
why it matters
Dspatial anchors the spatial dimension for the entire cardinality spectrum. It is referenced inside CardinalitySpectrumCert by the field Dspatial_is_3 and supplies the base value for downstream definitions such as eightTick = 2^Dspatial and cubeFaces = 2 * Dspatial. In the Recognition Science framework it realizes the T8 step that sets D = 3 spatial dimensions, enabling the eight-tick octave and the gap45 decomposition.
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