Research reading guide¶

Initial search and review: 31 October 2026. Map/transfer-method additions checked 2-4 November 2026. This is a focused evidence map, not an exhaustive systematic review. Primary papers and official data documentation were searched for Planck large-angle correlation, quadrupole, parity, covariance, foregrounds, and selection effects. Full-text methodological sections were examined where marked; other entries were checked at abstract/documentation level. No claim is made to have read every paper cited by these sources.

Core observational and methodological literature¶

Source	Reading depth	Relevance to this project
Planck 2018 VII: Isotropy and Statistics, published 2020	Selected full-text methods and results	Establishes the official anomaly context, including map and mask dependence. Our defined spectral and map experiments do not reproduce all of its tests or end-to-end simulations.
Planck 2018 V: Power spectra and likelihoods, 2020	Abstract and archive documentation	Explains the hybrid low/high multipole likelihood. Motivates the explicit distinction between released point estimates and an actual sampling likelihood.
Planck 2018 IV: Diffuse component separation, 2020	Abstract and map documentation	Describes the Commander, NILC, SEVEM and SMICA products and limitations in noise/systematics modelling. Supports the provenance of our measured SMICA input.
Planck 2018 VI: Cosmological parameters, 2020	Abstract	Supplies context for using the best-fit base-LCDM theory. We hold that theory fixed rather than refitting cosmological parameters.
Muir, Adhikari & Huterer: Covariance of CMB anomalies, 2018	Full-text statistics definitions and estimator comparison	Direct prior art for joint anomaly studies. Demonstrates that full-sky and cut-sky S1/2 probabilities differ. Our conditional and covariance work must not be presented as the first such investigation.
Efstathiou, Ma & Hanson: Large-Angle Correlations, 2010	Selected full text	Develops the estimator/reconstruction perspective and cautions against interpreting an a-posteriori correlation statistic in isolation.
Copi et al.: Lack of large-angle TT correlations persists, 2015	Abstract and journal methods excerpt	Argues for the robustness of low cut-sky correlations across WMAP and Planck. Provides a substantive contrasting perspective to reconstruction-based interpretations.
Schwarz, Copi, Huterer & Starkman: CMB Anomalies after Planck, 2016	Abstract	Organizes the wider anomaly landscape. Motivates a limited first project rather than treating every reported feature as one solved problem.
Copi et al.: Large-angle anomalies in the CMB, 2010	Abstract and journal excerpts	Historical background and discussion of the differences between full-sky and cut-sky correlation.
Copi et al.: Large-scale alignments from WMAP and Planck, 2015	Abstract and journal excerpt	Illustrates phase-dependent alignment questions. Our hemisphere search is also phase sensitive but does not measure quadrupole-octopole alignment.

Later results and live disagreements¶

Planck intermediate LVII: NPIPE, 2020. Abstract checked. Describes joint LFI/HFI reprocessing and end-to-end simulations. It is the basis for extending the project beyond PR3; a new processing release is a systematic cross-check of the same sky, not an independent cosmic realization.

Jung et al.: Revisiting large-scale anomalies and local SZ contributions, 2024. Selected full-text methods and results examined. Uses PR4 and constrained local-Universe simulations; the modeled local thermal and kinetic SZ contributions have negligible impact on the tested large-angle anomalies. This does not exclude every conceivable foreground mechanism.

Hogan et al.: Dipole-independent measurements of nearly-zero correlation, 2025. Abstract and publication status checked. Investigates even-parity angular correlations and proposes a causal-coherence interpretation. The interpretation is a theoretical proposal, not an established explanation, and this repository does not reproduce its specialized statistic.

Jones, Copi, Starkman & Akrami: Strong Evidence Against a Statistically Isotropic Universe, revised March 2026. Selected full text, tail-statistics and discussion examined. The authors emphasize joint tail rarity for four map-based anomaly classes and argue for a physical explanation. Their four statistics are not our four spectral diagnostics. The arXiv record describes preparation for resubmission; this guide does not presume final peer-review status.

Guth & Namjoo: Statistical isotropy and the look-elsewhere effect, February 2026. Selected full text examined. Challenges combined-anomaly interpretation on two grounds: some statistics test a particular spectrum rather than isotropy, and selecting anomalies from a larger test set changes significance. The unknown historical search space remains difficult to quantify. We implement a transparent finite-family correction rather than assert either side has settled the issue.

Numerical and archive references¶

Gorski et al.: HEALPix, 2005. Abstract and package documentation checked. Equal-area spherical pixelization used to display the measured and simulated skies. healpy documentation explains map ordering, transforms, and degradation caveats. Pixel averaging here is visualization only.

IRSA PR3 ancillary products and IRSA PR3 CMB maps were inspected directly. Exact product URLs and downloaded hashes appear in data/manifest.json.

Synthesis¶

The existence of unusual low-order summary statistics is well studied. Their physical cause and overall evidential weight are unsettled. A useful contribution needs explicit estimators, selection rules, observational uncertainty, and a prediction that can fail. This project supplies reproducible experiments with quantified numerical checks and stated observational limits. Conditional tests, anomaly covariance, and look-elsewhere corrections all have prior art; none is claimed as newly invented here.

Version 0.2.0 extends the numerical study to measured-sky estimators and a CAMB primordial-power hypothesis. Version 0.3.0 adds conditional harmonic morphology, random orientation, simultaneous envelopes and injected-signal recovery. A novelty claim would require a dedicated search and independent review; these additions use established mathematical tools and are presented as an independently reproducible study.

Added for conditional morphology and sensitivity¶

Primary source	Reading depth	Role and boundary
Akrami et al.: Power asymmetry using a local variance estimator, 2014	Sections 1–3, including the modulation definition and sensitivity experiment	Motivation for injecting known anisotropy to measure detector power. Our 24-axis hemisphere search and post-smoothing modulation do not reproduce their local-disc estimator, end-to-end simulations or reported significance.

Efstathiou, Ma and Hanson's large-angle correlation paper, already listed above, was revisited for estimator/sky-cut dependence. The new method notes derive the actual conditional samplers, document reading depth and explicitly distinguish fixed-power from globally rotated ensembles. The healpy Wigner-rotation API documentation was checked. These implementations do not establish a new physical explanation.

Added for the measured-sky and transfer calculations¶

Primary source	Reading depth	Role and boundary
Lewis, Challinor & Lasenby: Efficient computation of CMB anisotropies, 2000	Abstract and current CAMB API documentation	Credit for CAMB; transfer calculation from a specified primordial spectrum. The code uses a flat background, not the paper's closed-universe example as a claimed fit.
Contaldi, Peloso, Kofman & Linde: Suppressing the lower multipoles, 2003	Abstract and inference discussion in the abstract	Prior art for primordial low-power hypotheses; motivates checking parameter-search cost. Our smooth test spectrum is not a reproduction of their inflaton dynamics or WMAP likelihood.
Hivon et al.: MASTER, 2002	Abstract and method context	Establishes pseudo-spectrum masking methodology. Our finite-band correlation division is not a MASTER coupling-matrix inversion.
Probing foreground residuals in cleaned CMB temperature maps from Planck, 2025	Selected full-text data/preprocessing sections	Documents 5 arcmin PR3 SMICA beam, harmonic beam/pixel transformation and confidence mask. Our CMB-only null does not reproduce their foreground study.

Software documentation checked: CAMB result units and transfer reuse, primordial spectrum interpolation, healpy equal-area transforms, harmonic smoothing, and SciencePlots style registration. These are implementation references, not evidence for an anomaly's physical cause.