Rotation Field of the Cosmic Microwave Background - Boundary Sequence Structure on the Dual-Domain Loop (v2.10)

Summary Version 2.10 of the 22 Blue project analyzes the ordered sequence of alpha(n) values along the dual-domain boundary discovered in earlier versions. This version does not reconstruct alpha, does not refit any harmonic scales, and does not use alm or smoothing. All work uses the locked NSIDE=16 maps released in v2.6 through v2.9. Purpose:Earlier versions showed that the Delta ell approx 109 standing wave is theta-local, sky-local, and supported by two antipodal domains. Version 2.10 asks whether the values of alpha along the physical boundary carry a non-random sequence structure when arranged in true geometric adjacency order. Methods:1. Extract the boundary pixels belonging to the two largest domains from v2.9.2. Build a single ordered boundary chain using the NSIDE=16 neighbor graph.3. Quantize the chain into 16 symbols and construct a null ensemble by random permutations that preserve the histogram but destroy order.4. Measure entropy, compression ratio, and Lempel Ziv complexity on the real chain and null chains.5. Re-quantize into 4 symbols and test for mirror symmetry blocks.6. Compute mutual information and correlation at lags 1 through 20.7. Compute conditional entropy for Markov orders 1 through 4.8. Compute the discrete Fourier spectrum of the raw alpha chain. NSIDE=16 Analysis Note For geometric investigations presented in this release, the reconstructed rotation field was represented using a locked NSIDE=16 HEALPix grid. This representation emphasizes the largest angular-scale features of the field while reducing sensitivity to small-scale fluctuations, allowing coherent domains, boundaries, and large-scale geometric structure to be studied directly. Findings:1. The real boundary chain is far more compressible than null permutations with the same histogram. Order, not symbol counts, carries the structure.2. The first part of the chain has unusually low complexity and entropy, consistent with a short ordered prefix.3. In the 4 symbol representation, the first twenty four positions form an exact mirrored block not seen in any null chain.4. Mutual information and correlation remain high out to lag twenty, showing long range ordering that does not appear in null chains.5. Conditional entropies are much lower than in the null ensemble, showing that a short context predicts the next symbol well.6. The raw alpha chain is dominated by a k=1 standing wave around the dual-domain boundary, with most power in modes k <= 4. Null chains do not show this pattern. Conclusion:Version 2.10 finds that the boundary values of alpha(n) form a strongly ordered sequence when arranged along the physical dual-domain loop. The structure appears through reduced complexity, ordered prefixes, mirrored blocks, long range statistical dependence, and a dominant k=1 Fourier mode. These results describe the geometric organization of the boundary sequence and require no new reconstruction of alpha(n). Instructions:All inputs are locked products from v2.6 through v2.9. No harmonic fitting, no alm transforms, and no smoothing should be rerun. All results are reproducible from the included chain file and analysis metadata. Citation:Condit, Amy (2025). Rotation Field of the Cosmic Microwave Background - Boundary Sequence Structure on the Dual-Domain Loop (v2.10). 22 Blue - The Heartbeat of the Universe. https://doi.org/10.5281/zenodo.17635811 Derived From:Condit, 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 PUBLICATION RECORD PREDECESSOR PUBLICATION (separate record)1. Sep 20, 2025 (v1.0) -- Harmonic Phase Alignments in Planck 2018 CMB -- DOI:10.5281/zenodo.17167268 MAIN RESEARCH SERIESConcept DOI:10.5281/zenodo.173173972. Oct 10, 2025 (v1.0) -- Scale-Dependent Anisotropic Birefringence: Initial Detection -- DOI:10.5281/zenodo.173173983. Oct 20, 2025 (v1.1) -- Scale-Dependent Anisotropic Birefringence: Validation Dataset -- DOI:10.5281/zenodo.173964284. Oct 21, 2025 (v1.2) -- Two-Harmonic Extension -- DOI:10.5281/zenodo.174107645. Oct 28, 2025 (v1.3) -- Two-Harmonic Dipole Verification -- DOI:10.5281/zenodo.174689886. Nov 1, 2025 (v1.4) -- MASTER-Calibrated Dipole -- DOI:10.5281/zenodo.175007917. Nov 1, 2025 (v1.41) -- Extended MASTER Calibration and Robustness -- DOI:10.5281/zenodo.175089088. Nov 7, 2025 (v1.42) -- Dependence-Aware Joint Validation -- DOI:10.5281/zenodo.175538299. Nov 8, 2025 (v1.43) -- Phase Model Validation -- DOI:10.5281/zenodo.1756131310. Nov 8, 2025 (v1.44) -- Axis + Frequency + Half-Mission Validation -- DOI:10.5281/zenodo.1756176811. Nov 9, 2025 (v1.5) -- Multipole Structure and Model Selection -- DOI:10.5281/zenodo.1756296512. Nov 9, 2025 (v1.6) -- Phenomenology and Physical Interpretation -- DOI:10.5281/zenodo.1756619713. Nov 9, 2025 (v1.7) -- Prediction and Experiment Overlays -- DOI:10.5281/zenodo.1756687014. Nov 9, 2025 (v1.8) -- Model Rejection and Delta-l Persistence -- DOI:10.5281/zenodo.1756724115. Nov 10, 2025 (v2.0) -- Intrinsic Periodicity in l-space -- DOI:10.5281/zenodo.1757404816. Nov 10, 2025 (v2.1) -- Physical Origin of Delta-l Modulation -- DOI:10.5281/zenodo.1757708617. Nov 11, 2025 (v2.2) -- Universe-Model Evaluation -- DOI:10.5281/zenodo.1758541918. Nov 12, 2025 (v2.3) -- Domain Geometry and Topological Inference -- DOI:10.5281/zenodo.1759415719. Nov 13, 2025 (v2.4) -- Real-Space Correlation of Birefringence Field -- DOI:10.5281/zenodo.1759753720. Nov 13, 2025 (v2.5) -- Spectral Surgery on Delta-l ~109 Harmonic -- DOI:10.5281/zenodo.1760498221. Nov 14, 2025 (v2.6) -- Angular Locality of Delta-l = 109 Standing Wave -- DOI:10.5281/zenodo.1761334822. Nov 15, 2025 (v2.7) -- Sky-Local Origin of Delta-l ~109 Standing Wave -- DOI:10.5281/zenodo.1762002923. Nov 15, 2025 (v2.8) -- Domain Topology of Delta-l ~109 Standing Wave -- DOI:10.5281/zenodo.1762060524. Nov 16, 2025 (v2.9) -- Dual-Domain Coherence and Boundary Geometry -- DOI:10.5281/zenodo.1762187125. Nov 17, 2025 (v2.10) -- Boundary Sequence Structure on Dual-Domain Loop -- DOI:10.5281/zenodo.1763581126. Nov 19, 2025 (v2.11) -- Boundary Standing-Wave and Phase-Structure Analysis -- DOI:10.5281/zenodo.1764803327. Nov 21, 2025 (v2.12) -- Boundary Universality and Standing-Wave Fingerprints -- DOI:10.5281/zenodo.1767637728. Nov 23, 2025 (v2.13) -- Interior Propagation and Boundary-Driven Structure -- DOI:10.5281/zenodo.17693540 Contact email: [e-mail] 22 Blue - The Heartbeat of the Universe