The Recursion Unit: Seconds at the Electron Scale

The Cohesion UFT series expresses its timing in recursion units. The torsion slope ofthe electromagnetic recursion is g = 6κ6Ī3/2 = 0.0041775 per unit with the recursionrate normalised to ω = 1, the slip cadence is tcoh = 2/g = 478.75 units, and the restartrate is g²/ω; every quantity of the fine-structure chain is a ratio and needs no unit, butattaching seconds to the cadence does, and the record has carried the unit's value asopen, fixed only by dimensional analysis through the Compton frequency and leftbetween two readings, 2/ωC = 2.58 × 10−21 s and 2/(gωC) = 6.17 × 10−19 s. This notecloses the row from two closures already in the record. The electron closure of E = prfixes the recursion length at the reduced Compton length λC with unit coefficient; thetrapping condition fixes the rest energy at ħωC; and the medium's rate c relates thetwo, ωC = c/λC. The recursion unit at the electron scale is the time in which a rotationof radius λC advances one radian at the medium's rate: ue = λC/c = ħ/(mec²) = 1.2881× 10−21 s. The two readings are then not two values of one quantity but two counts ofone unit, and the record has already chosen between them: the two-unit count is thesuperseded 2/ω form of the cadence, and the 2/g count is the coherence interval ofthe recursion whose slope g is. The cadence of the fine-structure chain is therefore6.1667 × 10−19 s, a recursion rate of 1.622 × 1018 per second, 76.2 turns of therecursion per slip, with the restart rate 1.052 × 1037 rad/s². The rule theidentification instances — the recursion unit of a scale is its coherence length over itspropagation rate — returns at the graphene lattice the clock the record identifiedthere independently, a/vF. The slip energy of the toggle's form, 2ħg at the electron'srate, becomes a number, 2g·mec² = Δθ·mec² = 4.27 keV, stated as the release of therecursion's own gear-shift with no measurement attached, and not as the switchingenergy of a device. Standing: the unit identified from two closures of the record; whatremains open is the absolute scale of either, the electron mass from the axiom.