mutau_ingredients
plain-language theorem explainer
The theorem fixes the three geometric constants required by the μ→τ lepton mass correction: the hypercube face count F(D) equals 6 when D equals 3, the number of wallpaper groups equals 17, and the spatial dimension is exactly 3. Researchers deriving sub-leading corrections to the phi-ladder mass formula would reference these values to obtain the coefficient 2W + D = 37 in the term F − (2W+3)α/2. The proof is a single tactic line that applies native_decide to discharge each conjunct after a refine tactic.
Claim. Let $F(d) := 2d$ be the number of faces of the $d$-dimensional hypercube. Then $F(3) = 6$, the number of wallpaper groups equals 17, and $D = 3$.
background
The module derives sub-leading corrections to lepton mass ratios beyond the integer rung counts on the phi-ladder. For the μ→τ transition the correction takes the form $F - (2W + 3)α/2$, where $F$ is the cube face count, $W$ the wallpaper group count, and $D$ the dimension. Upstream definitions fix $F(d) = 2d$ (AlphaDerivation, PlanckScaleMatching) and set the wallpaper count to the crystallographic constant 17 (Fedorov 1891).
proof idea
The proof is a term-mode one-liner. It uses refine to produce a triple of goals, then applies native_decide to each goal in parallel. native_decide reduces the three numerical equalities to decidable propositions that are discharged by computation.
why it matters
This declaration supplies the concrete numerical inputs to the μ→τ correction formula stated in the module documentation. It thereby anchors the sub-leading term in the lepton mass ladder to the cube geometry (T8: D=3) and the wallpaper count (17). The parent structure is the Recognition Composition Law and the phi-ladder mass formula; without these fixed values the coefficient 37 in (2W+D) would remain undetermined. It touches the open question of whether other geometric corrections could achieve comparable ppm accuracy.
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