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Kinematic participatory horizons and the Axis of Evil

O'Grady, Gregory

Abstract

Disclaimer: This Measureverse module is shared solely for conceptual exploration and discussion. It is a preprint and has not undergone peer review.Standard $\Lambda$CDM cosmology provides an excellent fit to the observed Cosmic Microwave Background (CMB) anisotropies across a wide range of angular scales, yet several statistically unusual features persist at the largest scales. Among these, the so called "Axis of Evil" is particularly striking. Analyses of WMAP and Planck temperature maps have reported an anomalously strong mutual alignment between the quadrupole and octopole, defining a preferred axis that is correlated with both the ecliptic geometry and the CMB kinematic dipole. Estimates of the significance of these alignments are commonly regarded in the order of $10^{-2}$ to $10^{-3}$. If taken at face value, the correlation with late time solar system geometry and motion appears in tension with the Copernican principle, and raises a temporal paradox: why should the largest scale modes, usually treated as fixed at last scattering, know about our solar system's peculiar velocity? Motivated by Wheeler's Participatory Universe, operationalised within the Measureverse framework, we treat the CMB not as a passive fossil field but relationally, as a collection of irreversible records actualised within the causal diamond of a specific detector in the present epoch. In earlier work this perspective was actioned by modelling the causal horizon as an effective isotropic information aperture, yielding a simple horizon filter that can suppress large angle temperature correlations while preserving the successful high multipole phenomenology of $\Lambda$CDM. Here we explore the next logical implication. If the observer’s causal diamond functions as a physical information aperture, we may parameterise a minimal dipole aligned anisotropy anchored to the kinematic dipole direction. We therefore model a boosted, dipole aligned aperture as a minimal anisotropic deformation that acts in harmonic space by redistributing variance among $m$ modes at fixed $\ell$ in the kinematic dipole frame, controlled by a single deformation strength $\epsilon$, with per $\ell$ renormalisation enforced, so that the total power at each affected multipole is preserved. Using Gaussian Monte Carlo skies drawn from a Planck $C_\ell$ input spectrum (truncated at $L_{\max}=40$) and deforming only $\ell \in [2,5]$, it is quantified how often Axis of Evil like configurations could arise under this dipole anchored model. For $N=50{,}000$ realisations per $\epsilon$, the one sided tail probability for a scalar alignment score increases from $p_{1} \simeq 2\times 10^{-3}$ at $\epsilon=0$ to $p_{1} \simeq 6.8\times 10^{-2}$ at $\epsilon=0.96$. A cone diagnostic requiring both the quadrupole and octopole axes to lie within $30^\circ$ of the dipole direction rises from $p_{\mathrm{cone}} \simeq 1.7\%$ to $p_{\mathrm{cone}} \simeq 34\%$, while a stricter joint event matching all three observed alignment angles increases from $p_{\mathrm{joint}} \simeq 4\times 10^{-4}$ to $p_{\mathrm{joint}} \simeq 1.5\times 10^{-2}$. Thus, a weakly anisotropic, observer centred information aperture can substantially reduce the apparent extremeness of dipole correlated low $\ell$ alignments. The current implementation therefore serves as a phenomenological proof of principle. If the mechanism operates at the level of primordial scalar perturbations (rather than as a late time temperature only selection effect), correlated low-$\ell$ TE and EE structure is expected. Forthcoming low-$\ell$ polarisation measurements, particularly from LiteBIRD, therefore offer an observational test.

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Kinematic participatory horizons and the Axis of Evil Gregory O’Grady December 16, 2025 Disclaimer: This Measureverse module is shared solely for conceptual exploration and discussion. The analysis and interpretations have not yet been independently reproduced or peer reviewed by domain experts. Portions of the manuscript and the associated computational workflow were produced with assistance from generative AI tools under close human oversight and there may be errors. Abstract Standard ΛCDM cosmology provides an excellent fit to the observed Cosmic Microwave Background (CMB) anisotropies across a wide range of angular scales, yet several statistically unusual features persist at the largest scales. Among these, the so called “Axis of Evil” is particularly striking. Analyses of WMAP and Planck temperature maps have reported an anomalously strong mutual alignment between the quadrupole and octopole, defining a preferred axis that is correlated with both the ecliptic geometry and the CMB kinematic dipole. Estimates of the significance of these alignments vary across analyses and depend on the choice of statistic, sky treatment, and a posteriori selections, but are often quoted at the 10−2to 10−3level. If taken at face value, reported correlations with late time Solar System geometry and the CMB kinematic dipole motivate further scrutiny of systematics and of models that couple the lowest multipoles to properties of the observer’s worldline. Motivated by Wheeler’s Participatory Universe, operationalised within the Measureverse framework, we treat the CMB not as a passive fossil field but relationally, as a collection of irreversible records actualised within the causal diamond of a specific detector in the present epoch. In earlier work this perspective was actioned by modelling the causal horizon as an effective isotropic information aperture, yielding a simple horizon filter that can suppress large angle temperature correlations while preserving the successful high multipole phenomenology of ΛCDM. Here we explore the next logical implication. If the observer’s causal diamond functions as a physical information aperture, we may parameterise a minimal dipole aligned anisotropy anchored to the kinematic dipole direction. We therefore model a a dipole anchored, dipole aligned aperture as a minimal anisotropic deformation that acts in harmonic space by redistributing variance among mmodes at fixed ℓin the kinematic dipole frame, controlled by a single deformation strength ϵ(an effective susceptibility parameter, not assumed to scale with |β|), with per ℓrenormalisation enforced, so that the total power at each affected multipole is preserved. Using Gaussian Monte Carlo skies drawn from a Planck Cℓinput spectrum (truncated at Lmax = 40) and deforming only ℓ∈[2,5], it is quantified how often Axis of Evil like configurations could arise under this dipole anchored model. For N= 50,000 realisations per ϵ, the one sided tail probability for a scalar alignment score increases from p1≃2×10−3at ϵ= 0 to p1≃6.8×10−2at ϵ= 0.96. A cone diagnostic requiring both the quadrupole and octopole axes to lie within 30◦of the dipole direction rises from pcone ≃1.7% to pcone ≃34%, while a stricter joint event matching all three observed alignment angles increases from pjoint ≃4×10−4to pjoint ≃1.5×10−2. Thus, within this restricted toy deformation, a weakly anisotropic, observer centred information aperture can reduce the apparent extremeness of selected 1 dipole correlated low multipole alignment diagnostics, under the adopted preprocessing and thresholds. The current implementation therefore serves as a phenomenological proof of principle. If the mechanism operates at the level of primordial scalar perturbations (rather than as a late time temperature only selection effect), correlated low-ℓTE and EE structure is expected. Forthcoming low-ℓpolarisation measurements, particularly from LiteBIRD, therefore offer an observational test. 1 Introduction The standard ΛCDM cosmology remains an exceptionally successful effective theory of the universe. It gives a precise account of the angular power spectrum over a wide range of multipoles, with only six principal parameters, and is strongly supported by the Planck data [1–3]. Within this framework the CMB sky is modelled as a statistically isotropic, Gaussian realisation of a nearly scale invariant primordial spectrum, with most cosmological tests reinforcing this description. However, a collection of persistent anomalies and tensions continues to raise questions. These include the low power anomaly at large angular scales [3–5], various indications of hemispherical asymmetry and related parity odd features [6, 7], and apparent tensions between the CMB kinematic dipole and matter rest frames inferred from radio source counts [8, 9]. Each individual feature is of modest significance, but their collective persistence hints that some aspect of our standard assumptions may be incomplete. A particularly striking member of this family is the so-called ‘Axis of Evil’ (AoE), in which the quadrupole and octopole exhibit an anomalous mutual alignment and an apparently nontrivial correlation with the geometry and motion of the solar system, reportedly including the ecliptic plane and the CMB dipole direction [7, 10, 11]. Depending on the approach, the probability that such an alignment would arise in an exactly statistically isotropic Gaussian sky has been estimated in the order of 10−2to 10−3[3, 7, 11]. The reasonable and conservative response has been to treat the Axis of Evil, together with the low power and related anomalies, as statistical flukes, compounded by a posteriori statistics, residual systematics and the inevitable ambiguities of Galactic foreground removal. This view is articulated in a range of careful analyses which stress both the modest formal significance of individual anomalies and the dangers of over-interpreting them [3, 12, 13]. This position is justified by current standard model physics, because if the ‘Axis of Evil’ reflects a genuine cosmological feature, it would seem to both violate the Copernican principle, while posing a profound temporal paradox: how could the decoupling surface of CMB photons, at redshift z∼103, have known about the detailed kinematic state of observers who would only emerge billions of years later in the ‘here and now’?[7, 14] Most concrete attempts to address the AoE anomalies have therefore looked for purely physical mechanisms, located in the early universe, that might imprint preferred directions or suppress power on the largest scales. Proposals include models with an explicit cutoff or suppression of primordial power on super horizon scales [4, 5, 15, 16], anisotropic or shear dominated cosmologies represented through Bianchi templates [7, 17], and scenarios in which pre-inflationary relics or anisotropic initial conditions leave a residual imprint on the low multipoles [15, 18]. Several of these constructions can reduce particular diagnostics and provide useful feasibility models of how global departures from isotropy might appear in the CMB. However, they typically require tuned parameters, introduce tensions with other data, or treat the preferred axes as arbitrary unexplained features of the early universe itself. In line with previous enquiries [14, 19], this paper takes a different approach inspired by John Archibald Wheeler’s ‘Participatory Universe’ [20]. Wheeler envisaged the universe as a self-excited circuit in which acts of observation, understood as irreversible amplification 2 into classical records, play a constitutive role in the emergence of a definite reality [21–23]. The ‘Measureverse’ framework, of which the current paper is a consequence, proposes to operationalise this vision and apply it to current problems in the foundations of physics [14]. Fundamentally, in the Measureverse perspective, the boundary between any ‘observer’ and ‘system’ is treated as the defining structural pivot of our physical description of reality. Quantum decoherence theory has clarified how environmental entanglement can give rise to effectively classical pointer states [24]. However, Wheeler’s view was that “no elementary phenomenon is a phenomenon until it is a registered phenomenon (record). . . brought to a close by an irreversible act of amplification” [21]. Treating this principle strictly, the Measureverse approach is to treat the CMB not as a passive detector of a fossil record, but as the locus at which quantum possibilities are coarse grained into the finite collection of macroscopic facts that define the observed sky [19]. In an initial application to the low power anomaly, the Measureverse was instantiated by modelling the observer’s causal diamond as a finite information aperture [19]. This isotropic participatory horizon was shown in an initial phenomenological model to plausibly act as a scale-dependent window function that successfully suppresses the largest angle correlations (S1/2statistic) towards their observed values, without disturbing the successful ΛCDM fit on smaller scales [19], providing the first concrete demonstration of how Wheeler-style participatory ideas can be translated into testable, minimal modifications of the standard cosmological inference pipeline. The Axis of Evil presents an immediately suggestive next challenge, given it singles out the observer’s kinematic state [14]. This paper aims to articulate this conjecture in a quantitative manner. 2 Conceptual framework: a dipole-anchored participatory aperture 2.1 From Wheeler’s circuit to observer-dependent records Wheeler’s “Participatory Universe” begins from the claim that the universe is not a prewritten script but a self-excited circuit in which acts of measurement help to bring particular features of the world into definite being [21]. He stated “no phenomenon is a phenomenon until it is an observed phenomenon”. On the usual reading this remains a suggestive slogan confined to the microscopic domain. Here we take Wheeler’s proposal literally and ask what it would mean to treat cosmological observables as outcomes of concrete, observer-located measurement chains. The starting point is a strict Bohr–Wheeler notion of measurement as irreversible amplification into a classical record. In this view, “measurement” is not ubiquitous environmental decoherence [24], which may occur without any durable registration, but the production of macroscopic, effectively permanent records. In earlier conceptual work we used the term “Measureverse Theory” for an ontology that takes this perspective seriously and operationalises Wheeler’s participatory principles to address real problems in the foundations of physics [14]. The proposal is to regard the large-scale structure of the observed universe as relational and informational [19]: the universe does not supply a fully determinate catalogue of pre-existing facts. Instead, a given observer inhabits a finite informational situation: a causal diamond with a finite entropy budget [25–27]. Within that diamond, only a limited set of potential correlations are ever actualised into irreversible records. The effective boundary of this domain, viewed on large scales, is what has been called an information aperture [19]. Its geometry and capacity are determined both by the cosmological background and by the worldline and measurement practices of the observer. In this framing the observer is not an extraneous ‘eye’ added to a completed spacetime. 3 Rather, the observer’s causal structure and measurement activity supply boundary conditions for which modes and correlations of the primordial field become part of the realised record. We use ‘observer’ in Wheeler’s minimal sense, as ‘anything that can preserve a record’[14]. 2.2 The participatory horizon in isotropic form A first concrete implementation of this idea was developed in a companion analysis of the low power anomaly in large-angle CMB temperature correlations. There, the information aperture was modelled as a statistically isotropic, horizon-scale window [19]. The basic ansatz was that the primordial curvature perturbations are filtered by a soft cutoff at a comoving scale set by a single parameter αthat rescales the effective horizon, while the underlying ΛCDM background remains unchanged. In practice this was realised by introducing a smooth, spherically symmetric window function and propagating its effect through the angular power spectrum using standard Boltzmann codes. Within that framework it was shown that a modest change in the effective horizon scale, with αof order unity, can reduce both the low multipole power and the S1/2statistic toward the values inferred from Planck maps, while leaving the acoustic peak structure for ℓ≳50 essentially intact [19]. The information aperture is therefore not only a metaphor but a phenomenological degree of freedom that can be tuned and tested against data. In that work the statistics remain rotationally invariant by construction: the horizon is treated as finite and participatory, but spherical. From the Measureverse perspective this was a deliberate first step. It asked whether a finite participatory aperture is even compatible with the observed large-angle suppression and with the success of ΛCDM on smaller scales, before entertaining structured departures from isotropy. The present paper extends that construction to the Axis of Evil. 2.3 Why the Axis of Evil motivates a dipole-anchored anisotropy The Axis of Evil (AoE) refers to the empirical observation that the quadrupole and octopole exhibit an anomalous degree of mutual alignment and a non-trivial correlation with Solarsystem axes, including the CMB kinematic dipole direction [7, 10, 11]. Depending on statistic and masking, the probability of such alignments in statistically isotropic Gaussian ΛCDM simulations is typically quoted at the percent level or below [3, 4, 12, 13]. While the quantitative significance remains debated, the qualitative puzzle is profound: why do the lowest multipoles appear to ‘know’ about the observer’s late-time kinematic state? However, if cosmological observables are constrained by a finite information aperture tied to an observer’s causal diamond, then the relevant question is not only what the early universe ‘imprinted’, but also what patterns of low-ℓstructure are preferentially realised as records for a given worldline. The AoE then motivates a minimal structural upgrade of the isotropic aperture as follows: allow the aperture to be anchored to the observer’s kinematic dipole direction, ˆ β, thereby breaking statistical isotropy in a controlled and testable way. It is important to be explicit about what is and is not claimed. A purely kinematic boost of magnitude βinduces well known Doppler and aberration effects and a small, symmetryconstrained pattern of mode coupling [3]. Those effects are tiny at the level of β≃1.23×10−3 and do not by themselves explain the observed low-ℓphase correlations. In the present work we therefore use the kinematic dipole primarily as a symmetry axis for a phenomenological deformation, not as a sufficient dynamical explanation of its amplitude. 2.4 Minimal phenomenological implementation: anisotropy at fixed Cℓ Guided by these considerations, we introduce a dipole-anchored participatory aperture as a oneparameter deformation of the low-ℓensemble. The construction is intentionally conservative 4 in two respects. First, the deformation is applied only over a small “alignment band” of multipoles (here ℓ= 2 ...5), so that higher multipoles remain consistent with standard ΛCDM by construction. Second, the deformation is renormalised within each ℓso that the total power Cℓat that multipole is unchanged. The model therefore targets the distribution of power among m modes and the resulting low-ℓgeometry and phase correlations, rather than explaining the AoE by simply injecting additional quadrupole or octopole power. Operationally, we work in the dipole frame, treat ˆ βas the polar axis, and introduce an axisymmetric quadrupolar preference controlled by a single dimensionless parameter ϵ. In the Monte Carlo ensemble, ϵacts as an effective measure of the sensitivity (or susceptibility) of the information aperture to the dipole anchored anisotropy. Importantly, ϵis an effective susceptibility parameter, not a velocity expansion parameter, and it is not assumed to scale with |β|. Values ϵ→0 recover the isotropic participatory horizon model, while larger ϵ increasingly biases the low-ℓmorphology toward AoE-like configurations. This formulation is deliberately phenomenological. It provides a concrete map from a symmetry-constrained deformation to measurable changes in low-ℓalignment statistics. The point of the present paper is not to claim that ϵis derived from first principles, but to show that within the Measureverse stance an observer centred, dipole anchored aperture can bias the distribution toward AoE like alignments without altering the high ℓphenomenology of ΛCDM. 2.5 Conceptual summary The conceptual framework can be summarised as follows. 1. The observer occupies a finite causal diamond with a finite entropy budget [25–27]. The effective boundary of this domain is treated as an information aperture that constrains which correlations become realised as irreversible records. 2. In isotropic form, this aperture can be modelled as a spherical, horizon-scale filter that suppresses large-angle correlations while preserving the high-ℓacoustic structure [19]. 3. The AoE motivates an upgrade in which the aperture is allowed to be dipole anchored: it becomes axisymmetric about the observer’s kinematic dipole direction ˆ β. 4. We implement this as a minimal, one-parameter deformation of the low-ℓensemble, controlled by ϵ, applied only over a narrow alignment band. 5. A key safeguard is per-ℓrenormalisation: the deformation preserves Cℓat each ℓand therefore targets morphology and phase correlations rather than power injection. 6. The resulting model is directly testable through Monte Carlo distributions of AoE alignment statistics computed in the dipole frame, and can be extended to include standard aberration and polarisation predictions in a fully developed version. Figure 1 provides the conceptual schematic of a dipole-anchored aperture, while Figure 2 explains how the implemented m-reweighting biases low multipoles in the dipole frame. 5 Figure 1: A timelike worldline defines a causal diamond that can be interpreted as an effective information aperture [19]. For an observer moving with respect to the CMB rest frame, projecting the boundary of this domain onto the last scattering sphere motivates parameterising a minimal, dipole aligned anisotropy, with symmetry axis ˆ β(the kinematic dipole direction). In this work the anisotropy is implemented as a dipole aligned, axisymmetric quadrupolar reweighting of the lowest multipoles (ℓ∈[2,5]), which increases the probability that the inferred quadrupole and octopole axes (for example ˆ n2and ˆ n3) cluster around ˆ β. Figure 2: Why the dipole anchored deformation biases low multipoles in the dipole frame. Panels (a) and (b) illustrate axial and planar limiting morphologies about the velocity axis ˆ β. Panel (c) shows the variance rescaling factor 1 + ϵQℓm versus |m|for representative ℓ. Panels (d) to (f) provide a schematic intuition for how weighting redistributes power among mmodes at fixed ℓ. 6 3 Phenomenological model and numerical methods This work tests a minimal, dipole anchored phenomenological deformation of the low multipoles. The construction is intentionally conservative. It keeps the usual Gaussian Monte Carlo sky generation from an input temperature spectrum Cℓ, and introduces a single parameter ϵthat redistributes variance among mmodes within a restricted multipole band, while preserving the total power at each affected ℓ. The kinematic dipole direction is used only to define the symmetry axis (the zaxis) of the deformation, after rotating both the observed sky and the simulations into the same dipole frame. Because the key operation acts directly on the (ℓ, m) coefficients, it is helpful to visualise what the deformation does in the dipole frame. Figure 2 provides an intuitive explanation: axisymmetry about ˆ βimplies an mdependent redistribution at fixed ℓ, and the per ℓrenormalisation ensures the change is morphological rather than a change in Cℓ. 3.1 Data, resolution, and dipole frame Observed map. We use the Planck 2018 SMICA temperature map [3]. For computational efficiency the map is downgraded to Nside = 32 and expanded to aℓm up to Lmax = 40 using healpy’s map2alm (three iterations). This unmasked, low resolution treatment is adopted for computational simplicity in a proof of principle study. Because low multipole alignment diagnostics can be sensitive to masking and residual foregrounds, all reported frequencies should be interpreted as conditional on these preprocessing choices. Dipole frame rotation. Let ˆ βdenote the unit vector of the CMB kinematic dipole. We adopt the Planck dipole direction in Galactic coordinates, (ℓ, b) = (264.021◦,48.253◦) [3]. We rotate the observed map so that ˆ βis mapped to the Cartesian ˆ zaxis. Operationally, we construct a rotation matrix Rsatisfying Rˆ β=ˆ z, and apply it by evaluating the original map at the inverse rotated directions with bilinear interpolation on the sphere. All alignment statistics are then computed in this dipole frame, where ˆ zis the dipole axis. Low multipole cleaning. After transforming the observed map to aℓm, we set the monopole and dipole to zero by explicitly forcing all ℓ= 0,1 coefficients to vanish. This ensures that the subsequent low multipole axis estimators are not contaminated by the residual dipole. 3.2 Reference Monte Carlo ensemble Input spectrum. The simulation ensemble is generated from a fiducial temperature power spectrum Cℓread from the Planck 2018 TT file [3]. The file is provided as Dℓ≡ℓ(ℓ+1)Cℓ/(2π); we convert to Cℓvia Cℓ=     0, ℓ = 0,1, 2π ℓ(ℓ+ 1) Dℓ, ℓ ≥2,(1) and truncate at Lmax = 40. Gaussian skies. For each realisation we draw complex Gaussian coefficients aℓm with variance Cℓusing healpy’s synalm, enforcing reality through the standard constraint aℓ,−m= (−1)ma∗ ℓm. As for the observed sky, we set ℓ= 0,1 to zero for every simulated realisation. 7 3.3 Dipole anchored anisotropic aperture in harmonic space Restricted alignment band. The deformation is applied only over the multipole interval ℓ∈[ℓmin, ℓalign max ], ℓmin = 2, ℓalign max = 5,(2) and all higher multipoles are left unchanged. This ensures that the modification targets only the morphology of the quadrupole and octopole and their immediate neighbourhood. Planar weighting template. Working in the dipole frame, where ˆ z=ˆ β, we apply an axisymmetric quadrupolar weighting to each affected (ℓ, m). Define Qℓm ≡3m2−ℓ(ℓ+ 1) ℓ(ℓ+ 1) .(3) In the “planar” mode used in this study, the amplitude of aℓm is rescaled as aℓm →aℓm p1+ϵ Qℓm, ℓmin ≤ℓ≤ℓalign max ,(4) with ϵa dimensionless deformation parameter. Since Qℓm is negative for small |m|and positive for large |m|, this choice enhances high |m|modes relative to m= 0, producing more planar low multipole morphology about the ˆ zaxis. We apply the rescaling only to the stored m≥0 coefficients, and reconstruct the full −ℓ≤m≤ℓvector using the reality constraint when needed for axis estimation. Figure 2 provides a schematic intuition for how this redistribution translates into axial versus planar morphology about the dipole axis. Positivity safeguard. To prevent numerical pathologies when 1+ϵQℓm becomes small, we impose a floor on the variance factor: 1+ϵQℓm ≥fmin, fmin = 10−10,(5) and record the number of clipped coefficients as a diagnostic. In planar mode we additionally restrict to ϵ < 1 in the parameter scans reported here. Per ℓrenormalisation. A key safeguard is that we preserve the total power at each affected ℓ. Let Pℓ≡ ℓ X m=−ℓ |aℓm|2.(6) After applying the weighting (4) at fixed ℓ, we rescale all mat that ℓby a common factor aℓm →sℓaℓm, sℓ=sPbefore ℓ Pafter ℓ .(7) Because sℓrescales all mat fixed ℓby a common factor, it does not affect the inferred multipole axes; it is included only to preserve the total power at each affected multipole within each realisation. This ensures that the deformation changes the distribution of power among mmodes (hence the geometry and phase structure), rather than injecting or removing total variance at a given multipole. 8 3.4 Multipole axis estimator: dispersion axis To define a robust axis for each multipole we use the angular momentum dispersion axis. For a given ℓ, construct the full coefficient vector a(ℓ)of dimension 2ℓ+1, ordered by m=−ℓ, . . . , ℓ. Let Libe the usual spin ℓangular momentum generators in this basis. We form the symmetric 3×3 matrix A(ℓ) ij ≡ ℜa(ℓ)†LiLj+LjLi 2a(ℓ),(8) and define the dispersion axis ˆ nℓas the unit eigenvector corresponding to the largest eigenvalue of A(ℓ) ij . We compute ˆ n2and ˆ n3for the quadrupole and octopole for both the observed sky and each simulated realisation. 3.5 Alignment statistics and Monte Carlo probabilities Angles in the dipole frame. In the dipole frame, with ˆ z=ˆ β, we define three absolute angles: θ23 ≡arccos(|ˆ n2·ˆ n3|),(9) θ2β≡arccos(|ˆ n2·ˆ z|),(10) θ3β≡arccos(|ˆ n3·ˆ z|),(11) reported in degrees. The absolute value identifies axes up to a sign, as is standard for multipole directions. Scalar alignment score. We also define a single summary statistic Salign ≡|ˆ n2·ˆ n3|+|ˆ n2·ˆ z|+|ˆ n3·ˆ z| 3.(12) Larger Salign corresponds to stronger mutual alignment and stronger correlation with the dipole axis. Observed reference values. The observed values θobs 23 ,θobs 2β,θobs 3β, and Sobs align are computed from the rotated SMICA map using the same dispersion axis estimator and definitions above. These are the thresholds used to define tail probabilities in the simulation ensemble. Monte Carlo probabilities. For each ϵwe generate Nrealisations and estimate three probabilities: 1. A one sided tail probability for the scalar score, p1(ϵ)≡PrSalign ≥Sobs align.(13) 2. A cone probability that both low multipole axes fall within a half angle Θ of the dipole axis, pcone(ϵ; Θ) ≡Pr(θ2β<Θ and θ3β<Θ) ,Θ = 30◦.(14) 3. A joint angle probability requiring each of the three angles to be at least as extreme as observed, pjoint(ϵ)≡Prθ23 ≤θobs 23 and θ2β≤θobs 2βand θ3β≤θobs 3β.(15) Uncertainties are reported as binomial standard errors, σp=pp(1 −p)/N. 9 In the low power case, an isotropic participatory horizon with a soft cutoff was sufficient to suppress large-angle correlations without disturbing the acoustic peak structure. Here, the same horizon is allowed to acquire a mild kinematic anisotropy, so that modes aligned with the observer’s velocity are preferentially recorded. The two analyses therefore probe complementary aspects of the same hypothesis, namely that some of the largest-scale features inferred from the CMB reflect participatory boundary conditions rather than primordial dynamics alone. A natural concern is that such a construction appears to single out the Solar system as a physically special location, in tension with the Copernican principle. On a naive reading, the quadrupole and octopole would then be genuinely aligned with the ecliptic plane and the Sun’s motion through space. The participatory horizon picture, however, specifically avoids this conclusion. The information aperture is tied, by construction, to the causal diamond of the observer. Under this framework, an astronomer in the Andromeda galaxy, equipped with an equivalent instrument and analysing her own CMB sky, would couple to a different worldline and a differently oriented causal diamond. In the strong participatory regime she would therefore infer low multipoles biased toward her own motion, not ours. The apparent specialness of the Solar system is then purely perspectival, not a violation of Copernican principles. Two familiar objections are often raised against Wheeler-style participatory models. The first is that environmental decoherence already accounts for the emergence of classicality, rendering any appeal to measurement superfluous [24]. The second is that any role for late-time observation risks introducing retrocausal influences on the early universe. Both issues were discussed in the analysis of the low power anomaly [19], and are summarised here. Decoherence theory explains how entanglement with environmental degrees of freedom suppresses interference and selects robust pointer states, but it does not by itself identify which records are actually realised, nor which subsystems count as observers. The Measureverse framework does not challenge decoherence, but complements it by treating irreversible amplification into concrete records, in Wheeler’s sense, as a primitive ingredient for classical reality. The participatory horizon is a bookkeeping device for where such records can be formed, not a replacement for decoherence dynamics. With respect to retrocausality, the present model does not posit signals propagating backwards in time. Instead it treats the low-ℓCMB pattern and the pattern of records within an observer’s causal diamond as parts of a single globally constrained history. From a practical perspective, several extensions suggest themselves. The most immediate would be to advance this initial phenomenological approach to more sophisticated analyses. But a further implication of the relational picture is its relevance to existing tensions between rest frames inferred from different cosmological observables. In particular, discrepancies between the CMB dipole and the matter rest frame inferred from radio source counts [8, 9] may admit a natural interpretation if the effective cosmic rest frame is not absolute but weakly observer-dependent at the largest scales. Conceptually, the most direct test of the Measureverse hypothesis would be to repeat the CMB experiment along genuinely distinct worldlines. In practice we are confined to a small region of the Solar system, and the difference between terrestrial and near-planetary vantage points is miniscule compared with the size of the causal horizon. Even so, future CMB measurements from different orbital platforms might yet be probed to provide cross-checks. 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