# n138 — the no-freedom cross-check: the SIDM blade dies by arithmetic
# (2026-07-11. The computation with no parameter left, fired as
#  promised. HEADSTONE 33.)

## The arithmetic (all inputs already fixed elsewhere)
sigma/m for dipole scattering = pi (2 beta)^(2/3) / (m^(5/3) v^(4/3)),
beta = hbar*gamma (6 l_s)^3 (the handle's size and energy under the
anchor), m = 1.9-13.5 keV (n137), l_s < 4.3e-27 m (the card's GRB
dispersion bound), v = 30 km/s (dwarfs).
Required l_s for the dwarf band (20 cm^2/g): 1-5e-20 m —
VIOLATES THE GRB BOUND BY 6-7 ORDERS. At the allowed l_s:
   sigma/m <= 3e-12 cm^2/g. Thirteen orders below the dwarf demand.
No O(1) generosity bridges thirteen orders.

## HEADSTONE 33 — the SIDM reading of the dark sector
Two organs die as one (they were one claim in two dialects):
- Prediction 28a (the v^-4/3 SIDM amplitude in the dwarf band),
  registered three days ago: dead by its own no-freedom arithmetic.
  The v^-4/3 SHAPE survives as the form of a 1e-13 cm^2/g
  interaction — true and irrelevant.
- Prediction 10's SIDM rider ("necessarily self-interacting through
  the r^-3.5 residual"), registered in the EM-residual era: dead
  with it. Its kill condition ("DM shown exactly collisionless")
  fired INWARD — our own candidate is the collisionless DM it
  warned against.

## The flip (the surviving structure, sharpened)
THE WINDING DARK MATTER IS EFFECTIVELY COLLISIONLESS - cold-born
(KZ), keV-band, topologically stable, gravitationally coupled only.
Consequences, registered:
- Dwarf cores must be BARYONIC-FEEDBACK artifacts, not new physics.
  (The framework now sides with vanilla CDM on collisionlessness,
  against the SIDM literature it endorsed last week — because its
  own arithmetic said so.)
- Prediction 10 amended: the core claim survives (DM is real,
  parity-neutral matter — cannot be faked); the SIDM rider is
  retired. NEW KILL: any CONFIRMED DM self-interaction at
  sigma/m >= 1e-3 cm^2/g kills the winding sector (13 orders of
  safety margin — a clean, wide-open falsification window).
- Predictions 28b (no direct detection, ever) and 28c (no decay
  line, ever) are UNTOUCHED - they never needed the amplitude.

## What the dark sector looks like after its own firing squad
keV-band, born cold, collisionless, invisible underground, never
decaying, self-interacting only in principle (1e-13). Distinguishable
from vanilla CDM by: the mass band (structure formation cutoff at
the keV-cold-defect scale - free-streaming absent but the FORMATION
correlation scale xi_f may imprint; unpriced), the no-detection
forever bets, and the topological conservation law. The sector
survived its execution leaner and harder to vary.