DIRECTIONAL CMB PARITY ASYMMETRY AND THE MTN-G WINDOWED POWER SPECTRUM A Pre-Registered Spherical-Cap Patch-Scan Analysis of Planck 2018 PR3 Data

Abstract We present a pre-registered, falsification-oriented analysis of the Planck 2018 low-multipole anomalies against a two-level phenomenological model: (i) an isotropic k²-suppressed primordial power spectrum below a critical scale kcrit (the D5 windowed template), and (ii) a directional extension in which the suppression is localised within a sky island of amplitude ε, angular radius θTL, and direction n̂₀ (Temporal Layering, TL). The theoretical interpretation — spacetime as an emergent phase of a Type III₁ von Neumann algebraic substrate undergoing Exceptional-Point coalescence (MTN-G) — motivates the templates but is not assumed by the statistical tests: every hypothesis below is decidable against the templates alone. One structural fact governs the analysis and is stated first: the directional hypothesis is undecidable from angular power spectra — band-power statistics carry no directional information — so it is decidable only by the map-level likelihood specified herein. Three results are established. First, an internal-consistency analysis of the low-ℓ TT fit shows that the achievable Bayesian preference of D5 over ΛCDM from ℓ = 2–20 band-powers is bounded — anchored to the anomaly’s own 2. 5–3σ significance — at ln B ≈ 1. 6–3. 0 (BIC-corrected): a modest, quadrupole-dominated preference whose lower edge approaches zero under pure cosmic-variance weighting (Table 2a), so that even the sign of the isotropic preference is settled only by the exact non-Gaussian low-ℓ likelihood. Second, a validated nested-sampling calibration (null mocks: ln B = −0. 25 ± 0. 30; injected-signal mocks: direction posterior equal to prior) demonstrates that band-power statistics carry no directional information — the island parameters enter only through the sky-averaged factor s = 1 − ε (1 − cos θTL) /2 — so the directional hypothesis H3 is decidable only at map level, where the anisotropic pixel covariance breaks the degeneracy exactly. Third, a theoretical audit of the third-order prediction H5 proves that a deterministic variance modulation of a Gaussian field generates no three-point signal at leading order (verified numerically at the 10⁻³ level) ; the genuine second-order-in-ε observable is the fourth-order structure of the harmonic covariance, and H5 is accordingly revised, before any map-level data examination, to a BipoSH/kurtosis-based statistic H5′ with a derived expected amplitude. Against published Planck 2018 statistics, H1 satisfies its pre-registered per-cap threshold (3. 5σ localised TT suppression) but corresponds to a look-elsewhere-corrected global significance of 0. 86σ — local consistency, not global evidence; H2 (E/B parity asymmetry, 2. 1σ, foreground-bounded to < 0. 3σ) is a suggestive consistency signal awaiting map-level validation. H3 is INCONCLUSIVE. H4 (T-E suppression in the island, derived range RTE ≈ 0. 40–0. 67 depending on measurement aperture, threshold RTE < 0. 80) and H5′ remain open, genuinely independent falsification channels on existing data. Fisher forecasts show the map-level analysis is well powered — σ (ε) ≈ 0. 08–0. 30 and island localisation to 2–10° depending on the modulation’s ℓ-support — and H5′ is predicted in shape as well as amplitude: mask-decoupled BipoSH power concentrated at L = 1–3 with peak at L = 2. Appendix D establishes that the k² exponent is decisively separable from k¹ on current data (Δχ² ≈ 17) while separation from the memoryless k³ limit requires polarisation. The complete map-level pipeline — priors, likelihood, degeneracy-breaking covariance, mock validation, and falsification criteria — is specified for independent execution, with analysis code and machine-readable results released alongside this article. Key words: CMB low-ℓ anomalies · quadrupole suppression · primordial power spectrum · k²-suppression · statistical anisotropy · E/B parity asymmetry · spherical-cap patch scan · Bayesian model comparison · nested sampling · look-elsewhere correction · BipoSH · Planck 2018 PR3 · Exceptional Point · Type III₁ von Neumann algebra · emergent spacetime · MTN-G · Temporal Layering · pre-registration · falsifiability