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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19830380 |
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| _version_ | 1866901996702793728 |
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| author | Zilioli, Oscar |
| author_facet | Zilioli, Oscar |
| contents | <p>We establish two results for the Hubble constant H₀ in the CosmicCircle framework, plus <br>document a notable numerical conjecture, all using H₀ = 70.94 km/s/Mpc as the single free <br>dimensional input. <br>H₀ = 70.94 km/s/Mpc is not derived within the framework — it is the one required dimensional <br>input, analogous to c in General Relativity. All other dimensional quantities are obtained by <br>multiplying H₀ by dimensionless numbers derived from S³ geometry. <br>(i) Hopf Duality Conjecture (documented): the GPS map has three topological invariants <br>(Wyler geometric number 1/α_W = 137.036, Big Bang phase π, Hopf CS invariant π/48). <br>Their sum ln N = 1/α_W + π + π/48 = 140.243 satisfies ln(R_H/l_P) = 140.243 to 0.01%. <br>This is a remarkable numerical relation — documented as CONJECTURE, not a derivation <br>of H₀. <br>(ii) GPS Local Hubble Rate (new): the formula H(u) = 2H₀/u, derived from the GPS scale factor <br>a(u) = u/u₀ via first principles, predicts H₀_local = 2H₀/u₀ = 73.61 km/s/Mpc without <br>using the SH0ES measurement as input (error 0.8% vs 73.04 ± 1.04). <br>(iii) CMB Acoustic Scale (new): the GPS framework gives l_A = 303.5, consistent with the <br>Planck measurement l_A = 301.76 ± 0.14 at 0.6% (1.2σ), when the GPS-predicted apparent <br>H₀ at the CMB epoch is used. Results (ii) and (iii) are genuine zero-free-parameter <br>derivations from H₀ = 70.94 km/s/Mpc. The Hopf Duality Conjecture is documented <br>separately as a notable numerical observation requiring independent proof. <br>Two open problems are identified precisely: the GPS antipodal redshift (D_M(CMB) > πR_H by <br>1.64%) and the formal GPS derivation of H₀_CMB without Planck input, identified as a Boltzmann <br>simulation deferred to Paper E v5.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19830380 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | CosmicCircle — Paper II: The Cosmological Sector Zilioli, Oscar <p>We establish two results for the Hubble constant H₀ in the CosmicCircle framework, plus <br>document a notable numerical conjecture, all using H₀ = 70.94 km/s/Mpc as the single free <br>dimensional input. <br>H₀ = 70.94 km/s/Mpc is not derived within the framework — it is the one required dimensional <br>input, analogous to c in General Relativity. All other dimensional quantities are obtained by <br>multiplying H₀ by dimensionless numbers derived from S³ geometry. <br>(i) Hopf Duality Conjecture (documented): the GPS map has three topological invariants <br>(Wyler geometric number 1/α_W = 137.036, Big Bang phase π, Hopf CS invariant π/48). <br>Their sum ln N = 1/α_W + π + π/48 = 140.243 satisfies ln(R_H/l_P) = 140.243 to 0.01%. <br>This is a remarkable numerical relation — documented as CONJECTURE, not a derivation <br>of H₀. <br>(ii) GPS Local Hubble Rate (new): the formula H(u) = 2H₀/u, derived from the GPS scale factor <br>a(u) = u/u₀ via first principles, predicts H₀_local = 2H₀/u₀ = 73.61 km/s/Mpc without <br>using the SH0ES measurement as input (error 0.8% vs 73.04 ± 1.04). <br>(iii) CMB Acoustic Scale (new): the GPS framework gives l_A = 303.5, consistent with the <br>Planck measurement l_A = 301.76 ± 0.14 at 0.6% (1.2σ), when the GPS-predicted apparent <br>H₀ at the CMB epoch is used. Results (ii) and (iii) are genuine zero-free-parameter <br>derivations from H₀ = 70.94 km/s/Mpc. The Hopf Duality Conjecture is documented <br>separately as a notable numerical observation requiring independent proof. <br>Two open problems are identified precisely: the GPS antipodal redshift (D_M(CMB) > πR_H by <br>1.64%) and the formal GPS derivation of H₀_CMB without Planck input, identified as a Boltzmann <br>simulation deferred to Paper E v5.</p> |
| title | CosmicCircle — Paper II: The Cosmological Sector |
| url | https://doi.org/10.5281/zenodo.19830380 |