pith. sign in
theorem

F_quarter_admissible

proved
show as:
module
IndisputableMonolith.Physics.LeptonGenerations.TauStepExclusivity
domain
Physics
line
188 · github
papers citing
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plain-language theorem explainer

F/4 satisfies the admissible correction criteria because it coincides exactly with D/2. Researchers deriving lepton generation steps from hypercube geometry cite this result to equate face-based and axis-based corrections in the tau coefficient. The argument reduces the claim to the already-proved D/2 case via functional equality and transport of the admissibility property.

Claim. The function $f : ℕ → ℝ$ given by $f(D) = F(D)/4$ is axis-additive and satisfies $f(3) = 3/2$.

background

AdmissibleCorrection is the structure requiring a map $f : ℕ → ℝ$ to be axis-additive (i.e., $f(0)=0$ and $f(a+b)=f(a)+f(b)$) together with the calibration $f(3)=3/2$. The module establishes that the tau generation step coefficient must be of the form $W + D/2$ once this admissibility class is imposed. F is the face count of the D-cube (satisfying $F=2D$), so the F/4 form is algebraically identical to D/2. Upstream results supply the edge count E and the axis-additivity predicate used to define the admissible class.

proof idea

One-line wrapper that applies functional extensionality to obtain correction_F_quarter = correction_D_half from F_quarter_eq_D_half, then rewrites the goal and invokes D_half_admissible.

why it matters

The result closes the algebraically equivalent alternatives (Category 1) in the tau-step exclusivity argument, confirming that only the axis-additive D/2 form survives. It feeds the parent claim that (W + D/2) is forced once admissibility is required. The construction aligns with the Recognition framework's T8 (D=3) and the axis-additivity principle stated in the module.

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