dim
plain-language theorem explainer
This definition fixes the spatial dimension of the ledger to the constant D. Researchers assembling the tau-step coefficient or cube-face identities cite it when linking wallpaper symmetry to dimensional factors. It is a direct one-line abbreviation that imports D from the foundational constants without additional computation.
Claim. The spatial dimension of the ledger equals the constant $D$.
background
Recognition Science fixes the spatial dimension at three via the eight-tick octave forcing chain. This module derives the muon-to-tau coefficient from wallpaper groups (seventeen two-dimensional symmetries) coupled to that dimension, yielding the linear correction $C_τ = W + D/2$ that expands exactly to $(2W + 3)/2$. The local setting is the structural account of the lepton generation step, where faces supply the leading term and the half-dimension supplies the spin-weight factor. Upstream results establish the primitive distinction axioms that force three spatial dimensions and the mass-topology definitions that count wallpaper groups on the cube faces.
proof idea
This is a one-line definition that directly sets the spatial dimension to the upstream constant D. No lemmas or tactics are invoked beyond the import of D.
why it matters
The definition supplies the spatial dimension required by the tau-step derivation and is referenced by the DimensionedQuantity structure for all physical constants. It realizes the T8 forcing-chain landmark that sets D equal to three and supports downstream identities such as the cube-face count six equals two times three. It closes the link between two-dimensional wallpaper symmetry and the dimensional coupling term in the lepton mass ladder.
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