Zero-Infinity Dimensional Recursion (ZIDR): Resolving High-Redshift Anomalies and Deriving the CMB Power Spectrum Version 6 introduces the formal CMB power spectrum derivation, geometric dispersion modeling, and expanded theoretical components of the Zero-Infinity Dimensional Recursion (ZIDR) framework. This release represents an independent theoretical research contribution intended for open scientific discussion, mathematical development, and future observational comparison. The ZIDR framework describes the universe as a recursive geometric structure defined within an infinite-dimensional Hilbert space (M ∈ ℓ²), converging toward a fundamental zero-dimensional (0D) origin. Observable three-dimensional spacetime is interpreted as a projection of this recursive structure. Within this formulation, gravity is not treated as a fundamental force but as an emergent consequence of dimensional compression, while cosmological redshift is attributed to photon propagation through variations in a continuous Dimensional Density Field (ρD). This work addresses several major observational and conceptual challenges in modern cosmology. The recent discovery of highly evolved galaxies and massive black holes at extreme redshifts by the James Webb Space Telescope (JWST) is interpreted within an eternal framework where observed redshift is not directly equivalent to cosmic age. The model therefore provides an alternative interpretation of early galaxy formation without requiring extremely compressed evolutionary timescales. A central advancement in Version 6 is the derivation and numerical modeling of the ZIDR Cosmic Microwave Background (CMB) structure. In this framework, the CMB is interpreted as an invariant thermal boundary condition of the recursive manifold rather than a remnant radiation field from an initial hot Big Bang state. The model introduces a geometric resonance structure combined with a dispersion operator representing stochastic variations in dimensional density. This mechanism converts discrete recursive resonance states into a continuous angular power spectrum comparable with satellite observations. The resulting numerical simulations reproduce the main structural characteristics of the observed CMB spectrum, including the large-scale Sachs-Wolfe region and the primary resonance locations near multipoles ℓ ≈ 220 and ℓ ≈ 540. Beyond the CMB, this version develops additional theoretical components of the ZIDR framework, including: a geometric derivation of cosmological redshift and Type Ia supernova time dilation; an emergent gravity model based on dimensional compression fields; a non-singular interpretation of black holes as dimensional transition boundaries; a geometric interpretation of quantum correlations through the shared zero-dimensional limit; a recursive explanation of large-scale cosmic structure formation. The manuscript also defines future observational and computational tests required to further evaluate the framework, including complete field-equation development, higher-order CMB multipole predictions, distance-redshift reconstruction, galaxy rotation curve analysis, gravitational lensing comparisons, and black hole thermodynamic modeling. ZIDR is presented as a mathematically structured and falsifiable alternative cosmological framework intended for further theoretical development and comparison with observational astrophysical datasets.

Observations from the James Webb Space Telescope (JWST) have revealed highly evolved galaxies and supermassive black holes at extreme redshifts (z ≈ 7–15), challenging conventional hierarchical structure formation timelines within the standard ΛCDM cosmological model. This paper presents Version 6 of the Zero-Infinity Dimensional Recursion (ZIDR) framework, an alternative cosmological model that replaces metric cosmic expansion with an eternal, static, infinite-dimensional recursive manifold (M ∈ ℓ²) converging toward a zero-dimensional (0D) origin. Within this framework, gravity emerges from dimensional compression, while cosmological redshift is interpreted as a propagation effect produced by gradients in a continuous Dimensional Density Field (ρD). This interpretation decouples observed redshift from a finite cosmic age and provides a geometric explanation for high-redshift structures without requiring an initial singularity. A key development of this work is the formalization of the ZIDR Cosmic Microwave Background (CMB) model. The CMB is modeled as the fundamental thermal boundary structure of the recursive manifold rather than as a relic of a hot Big Bang phase. By introducing a geometric dispersion operator representing stochastic variations in dimensional density, discrete recursive resonance states are transformed into a continuous angular power spectrum. Numerical modeling demonstrates agreement with the principal structural features of the observed CMB spectrum, including the primary resonance regions near multipoles ℓ ≈ 220 and ℓ ≈ 540. The framework also develops geometric descriptions of Type Ia supernova time dilation, emergent gravitational dynamics, non-singular black hole structures, and quantum correlations through the shared zero-dimensional limit of the recursive manifold. ZIDR is presented as a mathematically formulated and observationally testable alternative cosmological framework. Future work will focus on complete field-equation derivation, quantitative comparison with cosmological observations, higher-resolution CMB predictions, and independent tests involving gravitational lensing and large-scale structure.

IMPORTANT NOTICE: This is the official and actively maintained version (Version 6.0, August 2026) of the ZIDR framework. A previous version (10.5281/zenodo.20324184, February–June 2026) represented earlier development of the framework. This Version 6.0 release is the canonical and citable reference moving forward and introduces the formal CMB power spectrum derivation, geometric dispersion modeling, and expanded mathematical development.

Version 6 introduces the formal CMB power spectrum derivation, geometric dispersion modeling, and expanded mathematical development of the Zero-Infinity Dimensional Recursion (ZIDR) framework. This release represents an independent theoretical cosmology model developed for open scientific discussion and future observational testing.