The Dipole-Cold Spot Double Repeller etc. Fit Geier's Fibonacci-Lucas-Φ Programme very well (>98%) by Stefan Geier et al., Gerhart-Hauptmann-Straße 6, 83071 Haidholzen

The Dipole-Cold Spot Double Repeller etc. Fit Geier's Fibonacci-Lucas-Φ Programme very well (>98%) - A first look
by Stefan Geier et al., Gerhart-Hauptmann-Straße 6, 83071 Haidholzen

Main result. In the normalized cosmographic coordinate r₁₀₀ = V_CMB/(100 km s⁻¹), the Cosmicflows-3 Dipole and Cold Spot repellers and the Cosmicflows-4 ungrouped merged basin take the values 140, 230 and 197.95. They align with F₁₂ = 144, F₁₃ = 233 and L₁₁ = 199 ≈ Φ¹¹ = 199.005, respectively, with 98.469% mean bounded proximity.

Question and analytical framework

In standard ΛCDM cosmography, a repeller is an underdense region associated with outward peculiar flow, not an object exerting exotic antigravity. Cosmicflows-3 (CF3) reconstructed two basins of repulsion - the Dipole Repeller at approximately 14,000 km s⁻¹ and the Cold Spot Repeller at approximately 23,000 km s⁻¹ - whereas Cosmicflows-4 (CF4) later represented them as one enormous extended basin.[1-3] The present test asks whether these data-fixed radial coordinates are descriptively compatible with the Φ, Φⁿ, Fibonacci and Lucas structure proposed in Geier's programme.[4]

Φ = (1 + √5)/2 = 1.6180339…     F_n ≈ Φⁿ/√5     L_n ≈ Φⁿ

The bounded proximity score is P(x,t) = 100 min(x,t)/max(x,t). Exact equality gives 100%. This score is a transparent similarity measure, not a probability, confidence level or statistical significance.

Principal numerical result

The two CF3 endpoints map to consecutive Fibonacci numbers: 140 ≈ F₁₂ = 144 and 230 ≈ F₁₃ = 233. Their dimensionless ratio 230/140 = 1.642857 has 98.489% proximity to Φ (relative deviation +1.534%). The radial difference 90 is close to F₁₁ = 89, yielding (90, 140, 230) ≈ (F₁₁, F₁₂, F₁₃); however, 90 is derived from the two radii and is not an independent observation. The CF4 ungrouped centre, 197.95, is especially close to L₁₁ = 199 and Φ¹¹ = 199.005 (99.47%). The central triplet thus occupies the local mixed lattice F₁₂ - L₁₁ - F₁₃.

Figure 1. Observed cosmographic coordinates (circles) and Fibonacci-Lucas targets (squares). The first three entries form the primary F₁₂ - L₁₁ - F₁₃ triplet (mean proximity 98.469%); the grouped CF4 reconstruction is retained as the principal robustness warning.

 

Results at a glance

Table 1. Direct comparison of the selected astronomical quantities with the fixed Φ-Fibonacci-Lucas targets.

Astronomical quantity	Observed	Fixed target	Proximity	Scientific reading
CF3 Dipole Repeller radius	140	F₁₂ = 144 ≈ Φ¹²/√5	97.222%	Supportive central-value fit; relative deviation -2.778%.
CF4 merged basin, individual galaxies	197.95	L₁₁ = 199 ≈ Φ¹¹	99.472%	Closest match and the Lucas/Φⁿ branch of the triplet.
CF3 Cold Spot Repeller radius	230	F₁₃ = 233 ≈ Φ¹³/√5	98.712%	Supportive, but the published distance is only a rough lower limit.
CF3 radial ratio, 230/140	1.642857	Φ = 1.618034	98.489%	Unit-independent relation; relative deviation +1.534%.
CF4 merged basin, grouped galaxies	177.64	L₁₁ = 199	89.266%	Major robustness warning: the Lucas match is not reproduced.

Note: Proximity = 100 min(observed,target)/max(observed,target); it is descriptive and must not be read as a probability.

Scientific interpretation

The pattern is internally coherent because the two separate CF3 repellers occupy the Fibonacci branch F_n ≈ Φⁿ/√5, while the merged CF4 centre occupies the Lucas/Φⁿ branch L_n ≈ Φⁿ. The ratio 230/140 ≈ Φ is the most defensible bridge because it is independent of the chosen physical unit. A one-common-scale least-squares fit of (140, 197.95, 230) to (144, 199, 233) reaches 99.240% mean proximity, but this adds a fitted parameter and is therefore secondary to the direct 98.469% result.

Limitations and prospective falsification

The absolute-number matches depend on the conventional normalization by 100 km s⁻¹. The Cold Spot value is not a precision estimate, and the three principal coordinates are correlated reconstructions of largely the same cosmic underdensity rather than independent systems. Most importantly, the grouped CF4 reconstruction gives 177.64 instead of 197.95; its proximity to L₁₁ is only 89.266%. Moreover, the 1.05-unit difference between 197.95 and 199 is below the approximately 7.8 h⁻¹ Mpc CF4 voxel size.[3] An exploratory multiplicative phase scan found about 6.43% of Fibonacci-Lucas phases at least as close; this is not a p-value.

A decisive study should pre-register the coordinate r₁₀₀ and the targets F₁₂ - L₁₁ - F₁₃; propagate full posterior uncertainties across grouped and ungrouped reconstructions; compare with phase-shifted Fibonacci-Lucas lattices, Pell sequences and generic second-order recurrences; and apply the same statistic to independent surveys and ΛCDM simulations.

Conclusion. The double-repeller system provides a compact and reproducible hypothesis-generating fit to Geier's Φ-Fibonacci-Lucas programme: 140 ≈ F₁₂, 197.95 ≈ L₁₁ ≈ Φ¹¹ and 230 ≈ F₁₃. The coherence justifies prospective testing, but the grouped CF4 counter-result, unit dependence and absence of a derived cosmological recurrence prevent interpretation as evidence for a new physical law.

References

[1] Hoffman, Y., Pomarède, D., Tully, R. B. & Courtois, H. M. The dipole repeller. Nature Astronomy 1, 0036 (2017). doi:10.1038/s41550-016-0036.

[2] Courtois, H. M. et al. Cosmicflows-3: Cold Spot Repeller? The Astrophysical Journal Letters (2017). doi:10.3847/2041-8213/aa88b2.

[3] Dupuy, A. & Courtois, H. M. Dynamic cosmography of the local Universe: Laniakea and five more watershed superclusters. Astronomy & Astrophysics 678, A176 (2023). doi:10.1051/0004-6361/202346802.

[4] Geier, S. A. When are Φ and 1/Φ attractors? Projective dynamics and empirical meaning - A first approach. ResearchGate preprint (2026).

Gravitational attraction induces movement towards more dense areas and at the same time the gravitational repulsion pushes the matter back from an empty zone, according to the 'dipole repeller' model. 30 January 2018, Wikipedia, Evan Mason