The Recursion Unit: Seconds at the Electron Scale

The Cohesion UFT series expresses its timing in recursion units. The torsion slope of
the electromagnetic recursion is g = 6κ
6
Ī
3/2 = 0.0041775 per unit with the recursion
rate normalised to ω = 1, the slip cadence is tcoh = 2/g = 478.75 units, and the restart
rate is g²/ω; every quantity of the fine-structure chain is a ratio and needs no unit, but
attaching seconds to the cadence does, and the record has carried the unit's value as
open, fixed only by dimensional analysis through the Compton frequency and left
between two readings, 2/ωC
 = 2.58 × 10−21 s and 2/(gωC
) = 6.17 × 10−19 s. This note
closes the row from two closures already in the record. The electron closure of E = pr
fixes the recursion length at the reduced Compton length λC
 with unit coefficient; the
trapping condition fixes the rest energy at ħωC
; and the medium's rate c relates the
two, ωC
 = c/λ
C
. The recursion unit at the electron scale is the time in which a rotation
of radius λC
 advances one radian at the medium's rate: u
e
 = λC
/c = ħ/(me
c²) = 1.2881
× 10−21 s. The two readings are then not two values of one quantity but two counts of
one unit, and the record has already chosen between them: the two-unit count is the
superseded 2/ω form of the cadence, and the 2/g count is the coherence interval of
the recursion whose slope g is. The cadence of the fine-structure chain is therefore
6.1667 × 10−19 s, a recursion rate of 1.622 × 1018 per second, 76.2 turns of the
recursion per slip, with the restart rate 1.052 × 1037 rad/s². The rule the
identification instances — the recursion unit of a scale is its coherence length over its
propagation rate — returns at the graphene lattice the clock the record identified
there independently, a/vF
. The slip energy of the toggle's form, 2ħg at the electron's
rate, becomes a number, 2g·me
c² = Δθ·me
c² = 4.27 keV, stated as the release of the
recursion's own gear-shift with no measurement attached, and not as the switching
energy of a device. Standing: the unit identified from two closures of the record; what
remains open is the absolute scale of either, the electron mass from the axiom.