Closure at the Unification Density

Below the unification density the Cohesion UFT reads its gauge structure off thephase freedom of three recursion modes and assumes no group. At the unificationdensity the sector still borrows four things from the standard account: the logarithmicrunning of the couplings in a probe energy; the coefficients that make the three linesmeet, (33/5, 1, −3), a field-content count read as recursion modes opening above 1TeV; the sixteen-dimensional spinor of SO(10) as the closure set of one generation;and the proton-lifetime estimate with its minimal-SU(5) normalisation. Under theframework's own rule that symmetry is never a foundation, each must be replaced bya closure the recursion mechanics builds. This paper states the replacement in theorder the mechanics forces and carries out the part that can be carried out now. Theclosure count: one generation at DGUT holds (two poles) × (one whole closure or oneof its three segments) × (two hands) = 16 closures, listed one by one against theirstandard names, with electric charge read as the pole plus half the oriented closurecontent and B − L as the oriented content; the count is stated with its enumerationexplicit and its completeness named as the derivation to be done, after which SO(10)is the name of a result. The frequency law: the recursion field oscillates at ω0/R(Dst),so running is the density dependence of the modes' own resistance functions, equal atR = 1, which is what defines the unification density, and separating below it, which isthe electroweak breaking. The framework therefore runs the standard account'scalculation in the opposite direction: it starts at the meeting point, which it has byconstruction, and asks whether the functions land on the measured values at lowdensity. The targets they must land on are tabulated, and the first constraint theyimpose is derived: the separation of the modes is a slowly varying factor on a commonpower law, not a change of exponent. αGUT and MGUT follow at the standings themechanics allows, the first from the merged mode's coupling, which needs the densitydependence of the torsion slope, the second by E = pr at R = 1, which waits on theabsolute calibration of DGUT. The proton's lifetime becomes a transition rate at DGUTand its decay mode a threshold of R(Dst). Nothing numerical in the record changes.Four rows move from identified to derivation targets, and the sector comes under therule the rest of the framework already obeys: counts from geometry, groups as labelsafterwards.