# n136 — the relic: RESULTS
# (2026-07-11; the abundance mechanism of the winding dark sector.)

## R1/R2 — Kibble-Zurek verified in the framework's own compact layer
2D XY quench (L = 128, overdamped Langevin, T ramped to zero over
tau_Q), frozen vortex density:
   n(tau_Q) ~ tau_Q^(-0.615), log residual 0.034 over 1.5 decades
   (73 -> 9 vortices per sweep; exponent inside the declared KZ
   family (0.1, 0.7); the value carries BKT log corrections and is
   recorded, not targeted.)
THE MECHANISM EXISTS IN-HOUSE: a quenched crystallization of the
compact layer freezes windings at a density set by the quench rate.
The dark sector's abundance is a KIBBLE-ZUREK RELIC of
geometrogenesis.

## R3 — the no-inflation lock (the structural headline)
GUT cosmology's monopole problem: topological relics of a hot
transition OVERCLOSE the universe; inflation was invented (in part)
to dilute them away. This framework CANNOT dilute them — it has no
inflaton (prediction 24) — and it does not want to:
   THE MONOPOLE PROBLEM IS THE DARK-MATTER BUDGET.
The two commitments lock: inflation's homogeneity job was already
done pre-geometrically (n117: adjacency before distance), and
inflation's relic-killing job must NOT be done, because the relics
are the dark matter. One mechanism (crystallization), two of
cosmology's items (homogeneity, DM) — and prediction 24 and
prediction 28 become one structure that dies together: detect the
inflationary B-modes and BOTH halves collapse.

## The honest ledger of the abundance
Omega_DM is NOT predicted tonight. The relation is:
   rho_DM = m_w * n_KZ(tau_Q) — two substrate unknowns (the winding
   mass scale = the selection principle's debt; the quench rate =
   the cooling history, unbuilt FRW sector) against one observable.
What IS new: the abundance question is now MECHANIZED (a defined
computation in a defined model class), the exponent p = 0.615 is
measured in-house, and the framework's two boldest cosmological
bets are revealed to be one bet.