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2026
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| Online Access: | https://doi.org/10.2139/ssrn.6596698 |
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| author | Oulad Brahim, Elias |
| author_facet | Oulad Brahim, Elias |
| contents | <p>Abstract</p> <p>A logarithmic dimension function D(x) =-ln x/ ln φ, where φ = (1 + √ 5)/2 is the golden ratio, arises as the unique solution to the chiral fold identity D(z) + D(1/z) = 0 when the base is fixed by the Lucas recurrence Ln = Ln-1 + Ln-2 with seeds (3, 4). The twelve Lucas numbers so generated sum to 840 = lcm(1,. .. , 8), whose algebraic closure GF(841) * of order 840 contains ten distinguished residues, the Brahim numbers, with center K = 107 and mirror constant S = 2K = 214. In this framework, the ratio of local to early-universe Hubble constant measurements decomposed as φ 1/6 corrected by a series of golden-ratio powers whose exponents emerged from a greedy algorithm with gaps equal to Lucas numbers. At third order, the expansion predicted H late 0 = 73.4996 km s-1 Mpc-1 ; the H0 Distance Network Collaboration subsequently reported 73.50 ± 0.81 km s-1 Mpc-1 , a match at 5 parts per million. A geometric correction ladder of the form Dn = nK + 2 n-3 /π, verified at 2.3 ppm for both the electron-to-Planck mass ratio (n = 1, corresponding to me/M Pl = 4.185 × 10-23) and the gravitational fine structure constant (n = 2, corresponding to αG = 1.752 × 10-45), yielded the gravitational confinement mass M char = M 3 Pl /m 2 e = 6.25 × 10 6 M⊙, consistent with the peak of the JWST supermassive black hole population at redshifts z = 4-10. Between the ninth and tenth Brahim numbers (B9 = 172 and B10 = 187), a structural void of width L5 + L3 = 11 + 4 = 15 in the dimension coordinate spanned the interval [183.55, 184.99], which mapped to the neutron star-to-black hole mass gap at 2.5-5.0 M⊙. Three gravitational wave detections by the LIGO-Virgo network fell inside this void. Forty-three equations were proposed and tested against six independent observational datasets spanning gravitational wave astronomy, X-ray astrophysics, exoplanet populations, circumgalactic medium physics, and fast radio burst phenomenology. Four Monte Carlo null tests dismissed six equations, confirmed twenty-four, and revealed deeper invariants behind three others. Five falsifiable predictions were registered for verification by DESI, LIGO O5, and JWST. No parameters were fit to the data.</p> <p>Keywords: Golden ratio, dimension function, Hubble tension, mass gap, fast radio bursts, gravitational confinement, little red dots, circumgalactic medium, Lucas numbers, Brahim numbers</p> <p>Declaration of Interest</p> <p>The autor confirms that no personal or financial relationship with other people or organizations have influenced the study</p> <p>Funder Statement</p> <p>Elias Oulad Brahim, Individual Researcher</p> <p>Suggested Citation</p> <p>Oulad Brahim, Elias, The Denomination Desert: Gravitational Confinement, the Hubble Tension, and Cross-Domain Structure in the 840-State Manifold (April 17, 2026). Available at SSRN: https://ssrn.com/abstract=6596698</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_2139_ssrn_6596698 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | The Denomination Desert: Gravitational Confinement, the Hubble Tension, and Cross-Domain Structure in the 840-State Manifold Oulad Brahim, Elias Mathematical physics Astronomy <p>Abstract</p> <p>A logarithmic dimension function D(x) =-ln x/ ln φ, where φ = (1 + √ 5)/2 is the golden ratio, arises as the unique solution to the chiral fold identity D(z) + D(1/z) = 0 when the base is fixed by the Lucas recurrence Ln = Ln-1 + Ln-2 with seeds (3, 4). The twelve Lucas numbers so generated sum to 840 = lcm(1,. .. , 8), whose algebraic closure GF(841) * of order 840 contains ten distinguished residues, the Brahim numbers, with center K = 107 and mirror constant S = 2K = 214. In this framework, the ratio of local to early-universe Hubble constant measurements decomposed as φ 1/6 corrected by a series of golden-ratio powers whose exponents emerged from a greedy algorithm with gaps equal to Lucas numbers. At third order, the expansion predicted H late 0 = 73.4996 km s-1 Mpc-1 ; the H0 Distance Network Collaboration subsequently reported 73.50 ± 0.81 km s-1 Mpc-1 , a match at 5 parts per million. A geometric correction ladder of the form Dn = nK + 2 n-3 /π, verified at 2.3 ppm for both the electron-to-Planck mass ratio (n = 1, corresponding to me/M Pl = 4.185 × 10-23) and the gravitational fine structure constant (n = 2, corresponding to αG = 1.752 × 10-45), yielded the gravitational confinement mass M char = M 3 Pl /m 2 e = 6.25 × 10 6 M⊙, consistent with the peak of the JWST supermassive black hole population at redshifts z = 4-10. Between the ninth and tenth Brahim numbers (B9 = 172 and B10 = 187), a structural void of width L5 + L3 = 11 + 4 = 15 in the dimension coordinate spanned the interval [183.55, 184.99], which mapped to the neutron star-to-black hole mass gap at 2.5-5.0 M⊙. Three gravitational wave detections by the LIGO-Virgo network fell inside this void. Forty-three equations were proposed and tested against six independent observational datasets spanning gravitational wave astronomy, X-ray astrophysics, exoplanet populations, circumgalactic medium physics, and fast radio burst phenomenology. Four Monte Carlo null tests dismissed six equations, confirmed twenty-four, and revealed deeper invariants behind three others. Five falsifiable predictions were registered for verification by DESI, LIGO O5, and JWST. No parameters were fit to the data.</p> <p>Keywords: Golden ratio, dimension function, Hubble tension, mass gap, fast radio bursts, gravitational confinement, little red dots, circumgalactic medium, Lucas numbers, Brahim numbers</p> <p>Declaration of Interest</p> <p>The autor confirms that no personal or financial relationship with other people or organizations have influenced the study</p> <p>Funder Statement</p> <p>Elias Oulad Brahim, Individual Researcher</p> <p>Suggested Citation</p> <p>Oulad Brahim, Elias, The Denomination Desert: Gravitational Confinement, the Hubble Tension, and Cross-Domain Structure in the 840-State Manifold (April 17, 2026). Available at SSRN: https://ssrn.com/abstract=6596698</p> |
| title | The Denomination Desert: Gravitational Confinement, the Hubble Tension, and Cross-Domain Structure in the 840-State Manifold |
| topic | Mathematical physics Astronomy |
| url | https://doi.org/10.2139/ssrn.6596698 |