Participatory horizons and the hemispherical power asymmetry: a curl evidence channel

The ΛCDM model provides a thoroughly tested account of the cosmic microwave background, yet persistent large-angle anomalies remain unexplained. Among these is the hemispherical power asymmetry (HPA), an L=1 dipolar modulation reported in Planck at the 2–3σ level. The participatory horizon programme proposes that large-scale CMB anomalies occur because the observer's causal diamond acts as a recording aperture on the realised sky, otherwise retaining ΛCDM. Previous papers derived a three-level scalar recording architecture addressing the geometry of the low-power, cosmic dipole, alignment, and parity anomaly sectors. The current paper extends this work to address the HPA.

We show that every sign-erasing scalar channel constructed in the programme's architecture produces an antipodally even evidence rate whose odd spherical harmonic content vanishes identically, structurally blocking the scalar sector from L=1. The lowest-rank extension of the local stress-energy measurement class that evades this obstruction is a tangent vector evidence current built from the modularly weighted momentum-density component T₀ᵢ. Its curl component on the sky sphere produces a pure L=1 pseudoscalar, χ_H(n̂) = n̂·(v̂ × Qv̂). If the classical evidence register processes the scalar and curl readouts jointly, this pseudoscalar can enter recording completeness at first order while leaving the diagonal C_ℓ unchanged.

As an exploratory full-sky diagnostic, we estimate joint L=1 and L=2 covariance-generator components from the Planck SMICA temperature map. For ℓ=2–64, the recovered L=1 generator  lies 10.0° from the covariance-curl direction d̂⁻_cov = (v̂ × Q_cov v̂) (p=0.014±0.004, exact null, headless-axis test), while the raw temperature quadrupole gives only 36.2° (p=0.188). The relation introduces no additional fitted direction once Q_cov has been estimated.

The curl channel extends the programme's recording hierarchy to the vector sector. In this interpretation, the hemispheric asymmetry is not attributed to a primordial modulation of the sky, but to an observer-linked recording effect — the observer's motion through the universe skewed by the quadrupolar covariance shear of the recorded field. The vector channel's activation is deferred to future work, while the amplitude solution is developed in a forthcoming paper.