Low-multipole E-B chirality bounds in Planck PR4 with an exact-arithmetic pipeline

Abstract

Methods-and-bounds paper. No detection is claimed. The low-multipole (ℓ=2..8) polarization of the Planck PR4 (NPIPE) 100 and 143 GHz maps is analysed with an end-to-end exact-arithmetic pipeline (dyadic–triadic rationals, integer mantissa; ingestion of all 604,127,232 map values exactly reversible — zero rounding error). Three contributions: (1) EE/BB/EB cross-spectra with error bars from crossed half-mission arms, noise-bias-free by construction; the measured EB at ℓ=2,3 lies 26.7 and 75.9 bars from zero and is demonstrated to be foreground plus window mixing, not cosmology. (2) The window-parity selection rule (a mirror-symmetric window cannot couple E→B at the same ℓ) is re-derived in closed form — the leakage of a sharp cut is a pure boundary term, the Wronskian of the two multipoles at the cut edge — and demonstrated directly on data: symmetrizing the mask collapses same-ℓ leakage by factors 22–45, except at ℓ=2 (factor 3.5), where the residual is the twinless equatorial ring of any odd-ring pixelization: an irreducible geometric leakage floor, measured here for the first time. (3) An axial statistic with a planted null (400 synthetic skies per sky cut): no cell of 21 exceeds 3σ; a naive ℓ=3 'Galactic alignment' is re-identified as the mask-induced displacement of the null (p=0.68). The seam region (5.7% of the sky) carries 20–92% of the B-power; the EB does not originate there. The resulting chirality bound, |β| ≲ 1.3°–208° per cell, is one to three orders above current isotropic-birefringence measurements, as expected for frequency maps at low ℓ without component separation: the bound bounds; the method remains. [ES] Paper de método y cotas. Sin detección. Regla de paridad de la ventana demostrada con el dato; fuga irreducible del anillo ecuatorial sin gemelo medida por primera vez; estadístico de eje con nulo plantado; cotas con barra propia. Integrity: PDF SHA-256 c511c2d3ffb6ea3d8fe9591101a760a3dcba0d6d990ccf7b4bedfda432fb7e07 · source SHA-256 10334e2cf1e5411b7221780719717677f0569a5faffeb7177e753dc4cd5dc6c9; OpenTimestamps-anchored before deposit.