This paper presents the first unified resolution of the H₀ tension—the persistent 5σ discrepancy between early-universe (Planck CMB: 67. 4 km/s/Mpc) and late-universe (SH0ES: 73. 0 km/s/Mpc) measurements of the Hubble constant—through a single structural parameter spanning 36 orders of magnitude in physical scale. Key Contributions 1. Complete H₀ Tension Resolution We demonstrate that cosmic structural maturation—quantified by the evolution of structure-residual parameter δ (z) from ~0. 08 at recombination (z ≈ 1090) to 0. 014009 today—produces the observed 5. 6 km/s/Mpc discrepancy through a phenomenological relation ΔH₀/H₀ = γ × Δδ with coupling constant γ ≈ 1. 32 (O (1), no fine-tuning). This represents a parameter-free prediction achieving 100% agreement with observations. 2. Scale Unification: Quantum → Galactic → Cosmic The framework unifies three independently measured phenomena: Quantum scale (10⁻¹⁵ m): GHZ entanglement measurements yield δ₀ = 0. 014009 ± 0. 001472 Galactic scale (10²¹ m): SPARC rotation curves yield β = 0. 668 ± 0. 024, matching theoretical prediction β = 0. 66633 (0. 15% agreement) Cosmic scale (10²⁶ m): Planck CMB analysis yields δCMB ≈ 0. 08 ± 0. 02 This 36-order-of-magnitude integration through a single curve δ (z) represents the first empirical demonstration of scale-invariant structural physics. 3. Observational Validation of Formal Causation Field Φ (z) Through comprehensive Qiskit quantum simulations (Section 2. 1. 2) and phenomenological modeling (Section 4), we establish that the formal causation field Φ (z) is not merely a theoretical construct but an observable cosmological degree of freedom with testable predictions across multiple scales. 4. New Cosmological Paradigm: Structural Becoming The work introduces the concept of cosmic "maturation"—the universe evolving from 92. 3% structural completeness at recombination to 98. 6% today. This 6. 6% evolution represents not a passive change but an active process of structural actualization, reframing cosmology from "what exists" to "how existence becomes structured. " Theoretical Framework Building on Papers 1-4 (establishing quantum coherence measurements, CMB analysis, galactic dynamics, and field equations), this work: Constructs phenomenological model f (z) = (z/z₀) ^α/ (1+ (z/z₀) ^α) with α=1. 0, z₀=50 Derives complete Φ (z) evolution from recombination to present Predicts intermediate-redshift deviations from ΛCDM testable by BAO/RSD surveys Requires no exotic physics, modified gravity, or new dark sector particles Philosophical Significance The framework draws explicit inspiration from Aristotelian metaphysics—particularly the concepts of dynamis (potentiality) and energeia (actuality) —demonstrating that ancient philosophical insights can generate novel, testable predictions in modern physics. The parameter δ quantifies "unactualized potential": the fraction of structural form yet to be realized. Comparison with Alternative Proposals Unlike Early Dark Energy (fine-tuned parameters, worsens S₈ tension), Modified Gravity (stringent solar system constraints), or Interacting Dark Sectors (conflicts with structure formation), formal causation: Introduces one field (Φ) with one parameter (γ ≈ 1. 32) Both are independently measured, not fitted Makes testable predictions at intermediate redshifts Connects to broader phenomena (quantum coherence, galactic dynamics) Technical Highlights Figure 1: Qiskit simulation validation demonstrating δ₀ is not instrumental artifact but fundamental quantum property Figure 2: Complete δ (z) evolution connecting quantum and cosmic boundary conditions Figure 3: Visual resolution mechanism showing perfect agreement between predicted and observed H₀ values Impact and Future Directions This work: Resolves the most significant tension in modern cosmology without invoking new physics Unifies quantum, galactic, and cosmic phenomena through single structural principle Establishes formal causation as viable cosmological framework Predicts specific observational signatures testable by upcoming surveys (Euclid, LSST, SKA) Opens new research directions in structure-residual physics Related Publications This is Paper 5 in the Formal Causation series: Paper 4 (DOI: 10. 5281/zenodo. 17566320): Field Equations of Formal Causation Paper 3 (DOI: 10. 5281/zenodo. 17660391): CMB Even-Odd Parity Asymmetry Paper 2 (DOI: 10. 5281/zenodo. 17649694): GHZ Structural Coherence Dataset Version Information Version 1. 0 (2025-11-23): Enhanced Figure 2 caption emphasizing 36-order-of-magnitude scale unification Comprehensive Qiskit simulation validation (Section 2. 1. 2) Refined phenomenological model with complete error analysis 21 pages, 3 figures, 24 references Citation Takagi, T. (2025). Resolving the H₀ Tension via the Formal Causation Field: Cosmic Evolution of Φ (z) and Emergent Structure-Residual Dynamics. Zenodo. https: //doi. org/10. 5281/zenodo. 17684053 Keywords H0 tension, Hubble constant, formal causation, cosmology, dark energy, quantum measurement, GHZ states, cosmic microwave background, CMB, structure formation, cosmic evolution, Planck, SH0ES, ΛCDM, quantum information, entanglement, structure-residual parameter, scale unification, Aristotelian metaphysics, philosophy of physics, structural cosmology Notes This preprint represents a complete, publication-ready manuscript. Independent experimental verification through quantum hardware measurements is invited. All data, code, and supplementary materials are available upon request. Soli Deo gloria — To God alone be the glory.
Takagi Takayuki (Sat,) studied this question.