# n176 — C2 done: the dark doublet is helicity ±2
# (2026-07-11. The second of the six constructions.)

## Half 1 — exact algebra
Under a rotation by theta about the propagation axis, the dark
doublet transforms as [[cos2theta, sin2theta], [-sin2theta,
cos2theta]] - AN EXACT ROTATION BY 2-THETA (elements match to 1e-12;
the orientation is a basis convention). The complex combinations
h_(+-) = (+) -/+ i(x) pick up e^(-/+ 2 i theta): HELICITY +-2 BY
DEFINITION. (The harness first flagged the orientation as a failure;
the determinant-1 matrix with |elements| exact settled it - recorded
per the suite discipline.)

## Half 2 — measured covariance
The four-budget dark space at OFF-AXIS momenta equals the rotated TT
pair with overlap 1.0000 at every tested direction ((0,0,1), (1,0,2),
(1,1,1)) and magnitude. CAVEAT, declared: the derived rows used the
leading-order (continuum-form) momentum structure (q.d)(d_i), which
is exactly covariant by construction; the full lattice rows
(1 - e^{-iq.d} phases) would show O(q^2) anisotropy - the emergent-
isotropy statement at the lattice level remains an IR limit, like
everything else on the lattice.

## The little group's other half
The null-rotation ("translation") part of ISO(2) acts on massless
states as gauge: here those directions are the sym-grad-u modes
(the substrate relabelings), already identified as the gauge quotient
(n165). Physical content: the two helicity-+-2 states, nothing else.

## C-list status
C1 propagator (bubble level): DONE - positive norm, no tachyon.
C2 helicity +-2: DONE - exact algebra + measured covariance.
C3 source coupling and G: NEXT. C4 factor four: LARES-2 judges.
C5 quadrupole amplitude: the double pulsar judges. C6 Weinberg-Deser:
after C3-C5, legitimately.