delta_derived_not_calibrated
plain-language theorem explainer
The theorem shows that for three dimensions the structural correction from cube geometry equals 3/2, the axis-additive correction from exclusivity also equals 3/2, the two expressions coincide, and the face-to-vertex ratio equals 3/2. Researchers deriving lepton mass steps in Recognition Science cite it to establish that the mu-to-tau correction is fixed by geometry alone. The proof is a term-mode wrapper that assembles three prior D=3 lemmas and reduces the final ratio by simplification and numeric evaluation.
Claim. For spatial dimension three the structural correction satisfies $Δ(3)=3/2$, the axis-additive correction satisfies $Δ(3)=3/2$, the two corrections agree, and the ratio of the number of faces to the number of vertices per face equals $3/2$.
background
The module derives the dimension-dependent correction $Δ(D)=D/2$ directly from the geometry of the D-dimensional cube without reference to measured masses. The structural formula counts faces and vertices per face; the axis-additive formula follows from the exclusivity property of the recognition lattice. Upstream, the vertex count of the D-cube is defined by $V(D)=2^D$, and the inflaton potential is given by $V(φ_inf)=J(1+φ_inf)$ where $J$ is the recognition cost function. The local setting is the first-principles derivation of the mu-to-tau step as a facet-mediated process whose differential contribution is the reciprocal of the discrete vertex measure per facet.
proof idea
The term proof refines the four-part conjunction by supplying the three specialized lemmas deltaStructural_D3, deltaAxisAdditive_D3 and delta_D3_derived. The remaining conjunct is discharged by rewriting with the definitions of faceCount and faceVertexCount followed by numeric normalization.
why it matters
The result closes the geometric derivation of the tau-step correction inside the lepton-generations module and confirms that no external calibration is required at D=3. It supplies the concrete value used by downstream mass-ladder constructions and aligns with the forcing-chain step that fixes three spatial dimensions. The parent theorems are the D=3 specializations of the structural and axis-additive formulas already established in the same file.
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