# n135 — the dark sector's cross-section: RESULTS
# (2026-07-11; the day-after development of n134's birth.)

## The parameter-free exponent
If DM = windings, the self-interaction is dipole-dipole (the handle
metric-overlap force, n116): V ~ beta/r^3 in 3D. Classical scattering
gives sigma(v) = pi b_c^2 with V(b_c) ~ m v^2:
   SIGMA(V) ~ V^(-4/3) — the exponent comes from the DIPOLE NATURE
   alone; no parameter enters it.
Monte-Carlo (random frozen orientations, 20-degree threshold):
measured exponent -1.332 vs -4/3 = -1.333. Gate D1 PASS.

## The astrophysical window (gate D2 PASS)
One amplitude spans the data: dwarf demand 5-50 cm^2/g at ~30 km/s
maps to 0.03-0.27 cm^2/g at cluster velocities — under the ~1
ceiling for the entire band. The demanded dwarf-to-cluster
suppression (10-100) is delivered at 184 by the law. The velocity-
softening SIDM phenomenology (the empirically preferred family) is
the winding sector's STRUCTURAL output.

## The second blade: direct detection
Windings couple to the visible sector through the METRIC ONLY
(Gauss-neutral by n134, audit-dark by n120): DM-baryon scattering is
gravitational-strength — invisible to every direct-detection
experiment, forever. LZ, XENONnT, DARWIN keep returning null; the
"WIMP miracle" was a wrong turn, structurally.

## Registered as prediction 28 (two-part, kills named)
28a. The SIDM velocity exponent is -4/3: as halo fits sharpen, the
     velocity-dependence converges on sigma ~ v^(-4/3) (between the
     dwarf band and the cluster ceiling, one amplitude).
     KILL: fits converging on a distinctly different exponent or on
     velocity-independence.
28b. Direct detection stays null at every future sensitivity.
     KILL: any confirmed non-gravitational DM-baryon scattering.
FLAGS: mass scale unpriced (the selection principle, still owed);
relic abundance unpriced (needs the surgery-epoch freeze-out, n117's
baryogenesis reading made quantitative); the -4/3 law holds in the
classical dipole regime — quantum/resonant corrections at low v are
the reading's soft edge, named.