The concentric low-variance circle families in the CMB are statistically anomalous — present at significance (reported up to 6σ) incompatible with a standard ΛCDM sky.

Four independent reanalyses converge — under ΛCDM-spectrum nulls the circle abundance is typical, and the strictest (DeAbreu et al.) froze the proponents' own parameters. The surviving proponent arguments (sky-twist, anisotropy) are untested rather than weighed, which is why the claim is contradicted rather than closed.

Four independent reanalyses demonstrated that the 6σ significance only appears when testing against an improper white-noise null. When simulated with the full ΛCDM power spectrum, the features occur at chance abundance, and recent analyses trace the strongest structures to local pixel artifacts inflating the baseline variance. The strongest opposing consideration is the proponents' unverified "sky-twist" test, which supposedly shows the rings collapse when searched for as ellipses, suggesting a genuine spherical geometry.

The claim that the concentric low-variance circle families are anomalous at up to 6σ under ΛCDM is directly and repeatedly contradicted by independent analyses. Wehus & Eriksen, Moss, Scott & Zibin, Hajian, and DeAbreu et al. all find that when simulations include the observed ΛCDM power spectrum and realistic noise, the same kinds and abundance of features appear as in the real sky, rendering the circles fully consistent with ΛCDM. Bodnia et al. further identify a mechanism—few-pixel anomalies inflating the baseline variance—by which the search procedure manufactures concentric low-variance sets, and after removing these pixels they find no significant circles at all. The main counterpoints are the proponents’ sky-twist ellipticity and anisotropy arguments, but these are post-hoc statistics that have not been independently validated under artifact screening and therefore do not overturn the strong ensemble-based nulls.

Four independent reanalyses each find the observed circle abundance fully consistent with ΛCDM-spectrum simulations containing no previous aeon, and Bodnia et al. 2024 show that few-pixel spots manufacture concentric low-variance families under the proponents' criterion, after which no significant circles remain at full resolution. No independent group has reproduced the claimed 6σ significance; that figure appears only against a Gaussian-plus-noise null that lacks the known large-scale correlations of the CMB. The strongest opposing consideration is the proponents' sky-twist ellipticity drop-off and the extreme anisotropy of circle centers, neither of which has been independently run under artifact screening — real gaps in the critical record, but they do not rehabilitate a significance that lives only in the choice of an impoverished null.

Four independent reanalyses — Wehus & Eriksen (CCC-E002), Moss/Scott/Zibin (CCC-E003), Hajian with realistic anisotropic noise (CCC-E004), and DeAbreu et al. using the proponents' own frozen parameters on Planck data (CCC-E008) — each find the observed circle abundance typical of ΛCDM-spectrum skies, and Bodnia et al. 2024 (CCC-E012) identify the mechanism by which few-pixel spots manufacture concentric low-variance circles under the search criterion. The reported 6σ survives only against a Gaussian-plus-noise null that omits the sky's known large-scale correlations; treating that null as inadequate is a methodological norm (the one prior-based input here), and the record documents it independently. The strongest opposing consideration is that the proponents' sky-twist ellipticity test (CCC-E006) has never been independently run and the anisotropy of ring centers (CCC-C504) lacks a specific conventional accounting — genuine gaps, but both are post-hoc proponent constructions, and artifact-driven circles would clump as well. No independent group has ever reproduced the claimed significance.

Four independent groups, using different statistics (χ², matched filters, anisotropic-noise Monte Carlos, and the proponents' own frozen parameters) and two datasets, all find the circle abundance consistent with simulated ΛCDM skies; Hajian specifically closes the anisotropic-noise loophole the proponents raised. Bodnia et al. add a mechanism for the false positives and report no significant low-variance circles at full resolution after artifact screening. No independent group has ever reproduced the 6σ figure. The strongest opposing consideration is the sky-twist result (CCC-C503), which claims the effect prefers circles over ellipses without appeal to simulations and has never been independently checked — a genuine gap, but an a-posteriori statistic introduced in the same paper that reports its success, and one whose behaviour under few-pixel artifacts is unassessed.

Four independent reanalyses converge on chance abundance under ΛCDM nulls, including one that froze the proponents' own parameters (CCC-E008), and CCC-E012 identifies the false-positive mechanism. Nothing in CCC-E022 addresses the circle statistics.

Four independent reanalyses converge on chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 supplies the false-positive mechanism with full-resolution nulls. The supporting records (CCC-E006, CCC-E007) are proponent or proponent-adjacent and rest on post-hoc statistics; nothing new addresses the circle statistics.

Four independent reanalyses converge on chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 adds both a false-positive mechanism and full-resolution nulls. The supporting records (CCC-E006, CCC-E007) are proponent or proponent-adjacent and rest on post-hoc statistics; nothing new bears on the circle statistics.

Four independent reanalyses converge on chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 supplies both a false-positive mechanism and full-resolution nulls. Supporting records (CCC-E006, CCC-E007) are proponent or proponent-adjacent and rest on post-hoc statistics; nothing in this run touches the circle statistics.

Four independent reanalyses converge on chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 adds both a false-positive mechanism and full-resolution nulls. Supporting records (CCC-E006, CCC-E007) are proponent or proponent-adjacent and rest on post-hoc statistics; nothing new bears on the circle statistics.

Four independent reanalyses demonstrate that when the CMB data is tested against a properly correlated ΛCDM null ensemble, the concentric low-variance circles are not statistically anomalous. The 2024 Bodnia study further illustrates how few-pixel spots artificially trigger the proponents' low-variance search criteria, manufacturing the circles. The strongest opposing point is the proponents' sky-twist ellipticity test, which purports to show signal collapse under non-circular conditions, but this post-hoc metric cannot overcome the failure against standard cosmological nulls.

Four independent reanalyses using ΛCDM power-spectrum simulations and realistic noise (Wehus & Eriksen; Moss, Scott & Zibin; Hajian; DeAbreu et al.) all find that the abundance of low-variance circle families in WMAP and Planck is fully consistent with standard ΛCDM skies. Bodnia et al. further identify a concrete artifact mechanism whereby few-pixel hotspots or coldspots generate spurious concentric low-variance circles under the proponents' own criterion, and show that after removing such spots no statistically significant excess remains. The main opposing consideration is the proponents’ sky-twist ellipticity test and reported anisotropy of centers, which have not yet been independently repeated under artifact screening; however, these secondary structural claims cannot restore a 6σ anomaly that disappears under corrected nulls and artifact control.

Four independent reanalyses (Wehus and Eriksen 2011; Moss, Scott and Zibin 2011; Hajian 2011; DeAbreu et al. 2015) each found the observed circle abundance consistent with ΛCDM-spectrum simulations containing no previous aeon, and Bodnia et al. 2024 showed that few-pixel spots manufacture concentric low-variance families under the proponents' own criterion. The reported 6σ lives only against a pure-Gaussian-plus-noise null that omits the known CMB correlations. The strongest opposing consideration is the unreplicated sky-twist ellipticity drop-off and the extreme reported anisotropy of circle centers, neither of which has been independently run under artifact screening.

Four independent reanalyses — Wehus & Eriksen, Moss/Scott/Zibin, Hajian, and DeAbreu et al. — each find the observed circle abundance fully typical of simulated ΛCDM skies, with Hajian closing the anisotropic-noise loophole and DeAbreu freezing the proponents' own published parameters, a de facto prespecification (CCC-E002 through CCC-E008). The 6σ figure arises only against the Gaussian-plus-noise null that omits the measured large-scale correlations of the real sky. The 2024 artifact diagnosis (CCC-E012) then supplies the generating mechanism for false positives, which is the difference between a statistical quibble and a contradiction. The strongest opposing consideration is the sky-twist ellipticity drop-off (CCC-C503), a simulation-free comparison no independent group has ever run; it is a genuine gap, but it is also an a-posteriori statistic introduced after the critiques, so it cannot presently outweigh four concordant independent nulls.

Four independent reanalyses reached the same conclusion by different routes: ΛCDM simulations yield substantially larger annular variance than the proponents assumed (Wehus & Eriksen), properly simulated Gaussian skies contain the same variations (Moss/Scott/Zibin), realistic anisotropic WMAP noise leaves all three claimed families consistent at 3σ (Hajian), and the proponents' own frozen parameters applied to Planck give chance-level abundance (DeAbreu et al.). Bodnia et al. 2024 added the generating mechanism for false positives and reported no significant circles after artifact removal. No independent group has ever reproduced the 6σ figure. The strongest opposing consideration is the sky-twist ellipticity result (CCC-E006), which needs no simulated ensemble and has never been independently tested — but it is an a-posteriori statistic whose null behaviour was characterized in the same paper that reported its success, and Bodnia's few-pixel mechanism could plausibly interact with it in unassessed ways.

Four independent reanalyses find chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 adds both full-resolution nulls and a false-positive mechanism. The supporting records (CCC-E006, CCC-E007) come from proponent or proponent-adjacent groups using post-hoc statistics; no new material bears on this.

Four independent reanalyses demonstrated that the concentric low-variance circles are not statistically anomalous when evaluated against a standard LCDM null ensemble. Furthermore, high-resolution analyses reveal that the search criterion generates these circles as artifacts around few-pixel anomalies. The strongest opposing argument is the proponents' "sky-twist" test showing a drop-off for elliptical searches, but this does not overcome the failure to survive proper LCDM simulation comparisons.

Four independent reanalyses using ΛCDM-spectrum simulations and realistic noise (Wehus & Eriksen, Moss/Scott/Zibin, Hajian, DeAbreu/Contreras/Scott; CCC-E002–E004, E008) all find that the abundance of concentric low-variance circles is fully consistent with standard ΛCDM skies, directly contradicting the claimed multi-sigma anomaly. Bodnia et al. further show that the proponents’ own search criterion manufactures concentric families around few-pixel bright/dark spots and that, once these are removed, no significant circle population remains at full resolution (CCC-E012). The main opposing consideration is the unreplicated sky-twist ellipticity test and anisotropy of centers (CCC-E006, C503, C504), which could, if independently confirmed under artifact screening, signal non-generic structure, but presently rest on post-hoc statistics lacking null calibration.

Four independent reanalyses that simulate skies from the observed ΛCDM power spectrum find the claimed circle families at chance abundance, and DeAbreu et al. obtain that null after freezing the proponents' own published search parameters and extending the test to Planck. Bodnia et al. further show that screening a handful of freak pixels eliminates statistically significant circles at full resolution, which identifies a concrete false-positive mechanism under the original criterion. The strongest opposing consideration is the unreplicated sky-twist ellipticity drop-off and the reported anisotropy of circle centers, which sidestep the ensemble dispute and have not been independently run under artifact screening.

Four independent reanalyses simulating skies with the ΛCDM power spectrum (CCC-E002, CCC-E003, CCC-E004, CCC-E008) each found the observed circle abundance fully consistent with the standard sky; the 6σ lives entirely in the pure-Gaussian-plus-noise null, as the proponents' own response note confirms (CCC-E005). Bodnia et al. then supplied the generating mechanism for false positives under the proponents' criterion (CCC-E012), and DeAbreu et al. obtained the null using the proponents' own published parameters. No independent group has reproduced the claimed significance. Strongest opposing consideration: the proponents' sky-twist ellipticity result (CCC-E006) has never been independently replicated under artifact screening, leaving one structural discriminator untested — but it is a different, post-hoc statistic and does not rehabilitate the specific 6σ anomaly claimed here.

Every independent reanalysis in the ledger finds the observed circle abundance consistent with correctly simulated ΛCDM skies: Wehus & Eriksen obtain substantially larger simulation variance than the proponents, Moss/Scott/Zibin find the variations "entirely expected", Hajian closes the anisotropic-noise loophole, and DeAbreu et al. reach the same verdict while frozen to the proponents' own published parameters — a de facto prespecification that makes their null the heaviest single item here. CCC-E012 then supplies a mechanism for how the criterion manufactures concentric families around anomalous pixels, and reports no significant low-variance circles at full resolution after screening. The strongest opposing consideration is CCC-E006's sky-twist result: an ellipticity dependence measured against distorted copies of the real sky needs no simulation ensemble, and no critic has ever run it. But the statistic and its null behaviour were introduced in the same paper that reported its success, and Bodnia's artifact channel could plausibly interact with it, so it cannot currently carry the 6σ claim.

Four independent reanalyses find chance abundance under ΛCDM nulls (CCC-E002, CCC-E003, CCC-E004, CCC-E008), and CCC-E012 adds full-resolution nulls plus a false-positive mechanism. CCC-E023 adds that the 6σ figure, like every other headline number here, rested on a searcher-supplied signal model that reanalysis varied away.

Four independent reanalyses (Wehus & Eriksen; Moss, Scott & Zibin; Hajian; DeAbreu, Contreras & Scott) each found the observed circle abundance fully consistent with properly simulated ΛCDM skies, and the 2024 Bodnia et al. high-resolution study additionally identified the mechanism by which the search criterion manufactures concentric low-variance circles around few-pixel spots. No independent group has reproduced the claimed significance. The proponents' counter-arguments (ensemble choice, ellipticity tests, anisotropic center distribution) are recorded at CCC-C003 and in the evidence ledger.

Five independent reanalyses using diverse statistical techniques confirm that concentric low-variance rings appear at the same frequency in simulated ΛCDM skies as in the observed WMAP and Planck maps. The original 6σ significance claimed by Gurzadyan & Penrose was an artifact of comparing the real sky against a featureless white-noise null rather than a structured CMB spectrum. When evaluated against appropriate cosmological nulls, the circles exhibit no statistical anomaly. Strongest opposing consideration: Proponents argue that using a power spectrum derived from the data bakes in non-Gaussian structures that bias the null against true pre-Big-Bang signatures.

Wehus & Eriksen, Moss/Scott/Zibin, and Hajian independently reproduce the features and find them consistent with a Gaussian ΛCDM sky even with realistic anisotropic WMAP noise; DeAbreu extends this to Planck using the proponents' own parameters, Bielewicz extends it to the full 0–90° radius range, and Bodnia shows the proponents' criterion manufactures concentric circles around anomalous few-pixel spots. The strongest opposing consideration is the proponents' argument that ΛCDM-spectrum simulations are the wrong null because most of the CMB signal is not random — but that conflates the theory with the standard of chance, and Hajian's noise-realistic route answers the one technical objection the proponents' first response raised.

Several independent analyses recover the searched structures but find them typical of skies drawn from the full ΛCDM angular power spectrum. The result persists with realistic anisotropic WMAP noise, Planck data, the proponents' published search parameters, and ring radii extending to 90 degrees. CCC-E012 supplies an additional artifact mechanism rather than merely another null result. The strongest opposing evidence is CCC-E006's sky-twist circularity result and the weaker 99.7% same-harmonic-content comparison in CCC-E007.

Five-plus independent groups using ΛCDM angular-power-spectrum simulations find the low-variance concentric families unremarkable; Bodnia et al. further show few-pixel spots manufacture the families under the original criterion. The founding 6σ used an inadequate pure-Gaussian- plus-noise null. Strongest opposing consideration remains the proponents’ assertion that ΛCDM simulations are the wrong standard because most of the CMB is “not random,” which is a methodological preference rather than a demonstrated excess under the cosmology fitted by the same maps.

Wehus & Eriksen reproduce the procedure but obtain substantially larger simulated variance, finding the maps fully consistent with ΛCDM; Moss/Scott/Zibin, Hajian (with realistic anisotropic noise), DeAbreu et al. (proponents' own parameters, extended to Planck), Bielewicz et al. (radii 0–90°) and Bodnia et al. (maximum resolution, artifact screening) all concur. The 6σ figure rests on a pure-Gaussian-plus-noise null that the proponents themselves acknowledge differs from every reanalysis (CCC-E005), and the founding paper was never refereed. Opposing consideration: whether the ΛCDM-spectrum ensemble is the right null is a genuine methodological question (CCC-C003) — but the claim as stated asserts incompatibility with a ΛCDM sky, and that is what the reanalyses test and reject.

Wehus & Eriksen, Moss/Scott/Zibin, Hajian, Bielewicz et al. and DeAbreu et al. (CCC-E002, E003, E004, E037, E008) all reproduce the circles and find them at chance abundance against ΛCDM ensembles, the last with the proponents' own frozen parameters and Planck data; Bodnia et al. (CCC-E012) find no significant circles at full resolution after removing few-pixel spots and identify how they are manufactured; Bielewicz et al. (CCC-E056, E057) supply a positive mechanism for the large-radius deficit. The supporting records (CCC-E001, E006, E007) compute significance against a pure Gaussian null or with statistics introduced post hoc (CCC-E023). Rests on the ensemble question (CCC-C003), which the proponents contest but have never quantified.

While Gurzadyan and Penrose initially reported circle families at up to 6σ, independent evaluations by Wehus & Eriksen (2011), Moss et al. (2011), Hajian (2011), Bielewicz et al. (2013), and DeAbreu et al. (2015) proved that standard ΛCDM skies exhibit equivalent ring-variance distributions at up to 3σ consistency. The apparent anomaly vanished as soon as the comparison null incorporated the known CMB angular power spectrum rather than a flat Gaussian baseline. The strongest opposing consideration is Gurzadyan and Penrose's (2013) sky-twist test claiming a sharp drop in ring counts when searching for ellipses rather than circles.

The 6σ figure was computed against a pure-Gaussian-plus-noise ensemble, and every independent reanalysis using the full ΛCDM spectrum — Wehus & Eriksen, Moss/Scott/Zibin, Hajian with realistic anisotropic noise, DeAbreu with the proponents' own parameters, Bielewicz over the full radius range — finds the circles fully consistent with a standard sky. Bodnia et al. additionally show few-pixel spots manufacture the signatures under the GP criterion. The strongest opposing consideration is that the proponents' sky-twist test has never been independently replicated with an appropriate null, so the ellipse branch of the claim is untested rather than refuted.

Several independent analyses reproduce the rings but find them typical of skies drawn from the ΛCDM power spectrum, including analyses with realistic WMAP noise, Planck data, proponents' search settings, and the full 0–90-degree radius range. CCC-E012 also identifies a mechanism by which a few extreme pixels generate apparent concentric sets. The strongest opposing consideration is CCC-E006's simulation-independent sky-twist result, but that post-hoc statistic has not been independently replicated and does not sustain the stated incompatibility with ΛCDM.

Five independent reanalyses using ΛCDM-spectrum nulls (Wehus & Eriksen 2011, Moss/Scott/Zibin 2011, Hajian 2011, DeAbreu et al. 2015, Bielewicz et al. 2013) and the later full-resolution Bodnia et al. 2024 search all find the observed low-variance concentric families to be typical once the correct ensemble is used; the original 6σ figure was obtained only against pure-Gaussian-plus-noise simulations. Bodnia additionally shows that few-pixel temperature spots manufacture the apparent concentric sets under the published criteria. The strongest opposing consideration remains the sky-twist ellipticity dependence reported by the proponents, which has not been independently stress-tested.

Five independent reanalyses using different statistics, different noise models, different datasets, and in one case the proponents' own frozen parameters all place the observed ring variances inside the ΛCDM range (CCC-E002, CCC-E003, CCC-E004, CCC-E008, CCC-E037), and CCC-E012 identifies a generating mechanism for the apparent excess. The 6σ figure rests on a pure-Gaussian-plus-noise ensemble that the proponents themselves acknowledge differs from the critics' (CCC-E005), and the proponents' own 2011 note concedes circles arise at similar frequency under the WMAP-derived spectrum. Strongest opposing consideration: if the ΛCDM-spectrum ensemble is the wrong notion of "chance," as CCC-C003 records the proponents arguing, the reanalyses lose their force — but no quantitative defence of that position against the data has been published.

Independent reanalyses by Wehus & Eriksen (2011), Moss et al. (2011), Hajian (2011), Bielewicz et al. (2013), and DeAbreu et al. (2015) consistently demonstrate that low-variance concentric circles appear at the same frequency in standard ΛCDM simulations as in the actual sky, completely refuting the claim of up to 6σ statistical anomaly. Gurzadyan and Penrose obtained inflated significance by comparing the data to a pure Gaussian white-noise null that ignored the cosmic microwave background's actual angular power spectrum. The strongest opposing consideration is Gurzadyan and Penrose's 2013 report that ring prevalence drops sharply when testing for ellipses rather than circles.

Four independent groups (Wehus & Eriksen, Moss/Scott/Zibin, Hajian, DeAbreu) plus Bielewicz et al. reproduce the features but find them typical of ΛCDM simulations, with Hajian closing the anisotropic-noise loophole and Bodnia identifying few-pixel spots as a false-positive generator under the proponents' own criteria. The strongest opposing consideration is the proponents' argument that ΛCDM-spectrum simulations presuppose exactly the randomness CCC denies (CCC-E005) — but that is a philosophical objection to the null, not a demonstration that the features exceed it, and the five-way convergence under different statistics is what the evidence weighs.

Several independent reanalyses recover the circle structures but find them compatible with skies drawn from the ΛCDM power spectrum, including analyses with realistic noise, Planck data, the proponents' parameters, and radii extending to 90 degrees. This directly contradicts the claim that the families are incompatible with standard ΛCDM. The strongest opposing evidence is CCC-E006's simulation-free sky-twist result and CCC-E007's 99.7% report, but both use statistics developed after inspection and neither overturns the replicated null-ensemble findings.

Five independent reanalyses (Wehus & Eriksen, Moss/Scott/Zibin, Hajian, DeAbreu, Bielewicz) plus Bodnia et al. demonstrate that the low-variance concentric families appear at comparable abundance in ΛCDM-spectrum simulations; the original 6σ figure was computed against an inadequate pure-Gaussian-plus-noise null. The strongest opposing consideration is the proponents’ sky-twist claim that circularity preference cannot be a random effect, which has not been tested under an ellipse-specific null.

Six analyses from five groups independent of the proponents find the circle families at the abundance a ΛCDM sky produces, by different routes: χ² statistics and matched filters (E002), properly simulated Gaussian skies (E003), realistic anisotropic WMAP noise (E004), the proponents' own frozen parameters extended to Planck (E008), a fast-convolution estimator over radii 0–90° (E037), and a full-resolution search with few-pixel artifact screening (E012). The 6σ figure (E001) was computed against a pure-Gaussian-plus-noise null rather than skies with the ΛCDM power spectrum, in a preprint never refereed in that form. The sky-twist test (E006) compares the sky only with distorted versions of itself, so whatever it shows, it cannot establish incompatibility with ΛCDM, which is what this claim asserts. Strongest opposing consideration: the Warsaw group's 99.7% (E007) was computed against maps of the same harmonic content, a null that already concedes the power-spectrum point, and no primary reanalysis of that statistic is on the ledger — though it is proponent-adjacent and its statistic and threshold were chosen post hoc.

Five independent reanalyses reproduce the rings and find them at chance abundance against standard-model skies: - Wehus & Eriksen (CCC-E002); - Moss, Scott & Zibin (CCC-E003); - Hajian, with realistic noise (CCC-E004); - Bielewicz et al., over 0–90° (CCC-E037); - DeAbreu et al., with the proponents' own parameters on Planck (CCC-E008). Bodnia et al. show few-pixel spots generate concentric sets (CCC-E012). The supporting records (CCC-E001, CCC-E006, CCC-E007) rest on disputed or post-hoc comparisons, and CCC-E023 shows neither side preregistered.