torsion_overlap
plain-language theorem explainer
The torsion overlap quantity is defined as the golden ratio raised to the power of negative three. Researchers deriving CKM matrix elements from cubic voxel constraints cite it to isolate the first-generation geometric factor subtracted by radiative corrections. The definition consists of a direct exponentiation with no intermediate lemmas or reductions.
Claim. Let $φ$ denote the golden ratio. The torsion overlap is defined to be $φ^{-3}$.
background
The module formalizes cubic voxel topology constraints that force CKM and PMNS mixing parameters. The torsion overlap captures the 3-generation torsion on the cubic ledger and corresponds to delocalization of the first generation across three spatial dimensions. Upstream results include the gap function $F(Z) = ln(1 + Z/φ)/ln(φ)$ from the anchor derivations and the step operation that applies a local rule to produce a successor tape in the cellular automata setting.
proof idea
The declaration is a direct definition that evaluates the golden ratio to the integer power negative three.
why it matters
It supplies the $φ^{-3}$ factor used in V_us predictions and Jarlskog invariant calculations. Downstream results such as V_us_match and jarlskog_witness_pos rely on it to obtain numerical agreement with experiment. The quantity connects to the three-dimensional forcing chain and the phi-ladder structure in the mass formula.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.