DOI: 10.5281/zenodo.17648033
title: Rotation Field of the Cosmic Microwave Background — Boundary Standing-Wave & Phase-Structure Analysis (v2.11)

description: Summary

This release (v2.11) completes the boundary-analysis branch of the 22 Blue project by studying the standing-wave structure, phase behavior, symbolic patterns, and residual grammar encoded along the dual-domain boundary discovered in earlier versions. The investigation is entirely map-free: all analysis is performed only on the locked 272-element boundary sequence inherited from v2.9 and v2.10. No recomputation or modification of earlier inputs occurs. The goal is to determine whether the boundary itself carries an interpretable physical signal.

Versions v2.8 through v2.10 revealed that the sky contains a stable two-domain structure. The interface between these domains traces a closed loop around the sky. When alpha(n_hat) is sampled along this loop in the correct geometric order, the resulting sequence behaves like a one-dimensional measurement of the global Delta-ell ~ 109 standing wave. Version 2.10 established that the boundary sequence is not random: it contains repeating motifs, mirror patterns, and phase-linked structure.

Version 2.11 takes the next step: treat the boundary sequence as a physical signal, similar to measuring displacement along a vibrating ring. The aim is to find out which structures are intrinsic to the chain and which collapse under null tests, shuffles, or synthetic replacements. This is the first release to bring all sequence-level tests into a single framework.

MethodsThe chain x[i] is normalized and analyzed using several complementary approaches.

(1) Global Fourier standing-wave test.The chain is expanded as a discrete Fourier series. The fraction of total power in the k = 1 mode,P1 = A1^2 / sum(Ak^2),is used to measure whether the boundary behaves like a dominant standing wave.

(2) Mirror-structure scan.Sliding windows of length 2*m are split into left and right halves. The right half is reversed and compared to the left. The mismatch fraction is compared to a null ensemble of shuffled chains.

(3) Harmonic finite-difference test.This test checks whether the chain behaves like a discrete harmonic function. Correlations between x, the negative first difference, and the leading eigenmode of the second-difference operator provide a strong check.

(4) Local phase coherence.A sliding-window FFT extracts the local k = 1 phase. Phase dispersion is compared to null sequences.

(5) Scramble robustness.Three types of controlled shuffles are tested: block permutations, local pixel shuffles, and full randomization. The goal is to separate geometric effects from global-order effects.

(6) Pure k = 1 surrogate comparison.A synthetic cosine mode is fitted and analyzed to determine which features of the real chain cannot be explained by a single standing wave.

(7) Residual structure.After subtracting the k = 1 mode, r[i] = x[i] - k1[i], the residuals are symbolized and tested for memory using entropy and null ensembles.

(8) Phase–symbol locking.The Fourier phase is binned and compared to symbol categories. Mutual information measures whether symbol patterns encode phase.

FindingsThe chain exhibits a dominant standing wave.P1 = 0.8334, with amplitude A1 = 5.961e-20.Correlation between the chain and the pure k = 1 mode is 0.9129.This confirms the Delta-ell ~ 109 standing wave is directly expressed along the boundary.

Mirror structure is unusually strong.Perfect mirrors occur in long windows, with null comparisons reaching ~6.7 sigma.

Finite-difference tests show harmonic-string behavior.Differences between real and null ensembles reach very high significance (for example, z ~ -36).

Local phase coherence is real but spatially variable.Average windowed power is about half the global value. Phase coherence is weak but significantly above random.

Scramble tests show the structure is geometric.Local shuffles preserve the mode and mirror patterns, but global shuffles destroy them.

The pure k = 1 surrogate does not reproduce the chain.Mismatch ~0.26 and failures in symbolic grammar show additional structure is present.

Residuals are highly structured.Entropy differs from null by roughly 92 sigma, indicating organized substructure beyond the global standing wave.

Phase–symbol locking is extremely strong.Mutual information = 1.42 bits, compared to a null of about 0.13 bits.

Scientific InterpretationThe domain boundary in the CMB rotation field is not a passive or noisy object. It carries a coherent standing-wave signature, strong mirror symmetry, symbolic structure, and multiple layers of harmonic and residual behavior. The Delta-ell ~ 109 harmonic is directly expressed along the boundary, not only globally but as a structured, rule-governed boundary signal. The boundary acts as the geometric locus where the global harmonic becomes locally measurable.

InstructionsAll analysis runs solely on the locked boundary sequence. Reproduction requires the NSIDE=16 domain maps from v2.9, the boundary sequence from v2.10, and the v2.11 analysis code. All random seeds are stored in the JSON files.

CitationCondit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Boundary Standing-Wave and Phase-Structure Analysis (v2.11). 22 Blue – The Heartbeat of the Universe. https://doi.org/10.5281/zenodo.17648033

Derived FromCondit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Boundary Sequence Structure on the Dual-Domain Loop (v2.10). https://doi.org/10.5281/zenodo.17635811Condit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Dual-Domain Coherence and Boundary Geometry (v2.9). https://doi.org/10.5281/zenodo.17621871Condit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Topology of the Delta ell approx 109 Boundary Network (v2.8). https://doi.org/10.5281/zenodo.17620605Condit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Angular Locality of the Delta ell approx 109 Standing Wave (v2.6). https://doi.org/10.5281/zenodo.17613348Condit, Amy (2025). Rotation Field of the Cosmic Microwave Background – Spectral Surgery on the Delta ell approx 109 Harmonic (v2.5). https://doi.org/10.5281/zenodo.17604982

Version HistorySep 20 2025 – Harmonic phase alignments discoveredv1.0 Oct 10 – First quantitative detectionv1.1 Oct 20 – Statistical validationv1.2 Oct 21 – Two-harmonic extensionv1.3 Oct 28 – Robustness testsDataverse Oct 29 – DOI 10.7910/DVN/PTDG20v1.4 Nov 1 – MASTER calibrated spectrav1.41 to 1.44 – SMICA/NILC splits and parity testsv1.5 Nov 9 – Model selectionv1.6 Nov 9 – Interpretationv1.7 Nov 9 – Forward predictionv1.8 Nov 9 – Persistence testsv2.0 Nov 10 – Intrinsic Delta-ell ~ 108 discoveredv2.1 Nov 10 – xi(theta) physicsv2.2 Nov 11 – Universe model evaluationv2.3 Nov 12 – Domain geometry inferencev2.4 Nov 13 – Real-space confirmationv2.5 Nov 13 – Spectral surgeryv2.6 Nov 14 – Angular localityv2.7 Nov 15 – Sky localityv2.8 Nov 15 – Domain topologyv2.9 Nov 16 – Field coherencev2.10 Nov 17 – Boundary sequence structurev2.11 Nov 19 – Boundary standing-wave and phase structure

22 Blue – The Heartbeat of the UniverseTwitter/X: @Project22Blue