**Authors:** F.M. Sanchez, V. Kotov, M. Grosmann, D. Weigel, R. Veysseyre, C. Bizouard, N. Flawisky, D. Gayral, L. Gueroult

To the memory of Sir Michael Atiyah Abstract. The ancestral concept of Cosmos is rediscovered through the idea of a Tachyonic Grandcosmos Multibasis Computer, inversing the Anthropic Principle and reestablishing the Laplace Determinism. The observed fine tuning between physical dimensionless parameters is interpreted as relations between optimal calculation basis, announcing a dramatic progress in computer software. Three type of mathematical constants are considered: Large, Intermediate and close to unity. The famous Large Number problem is resolved by Eddington's statistical theory and the gravitational Hydrogen Molecule model, leading to the visible Universe horizon radius R ≈ 13.812 Giga ligth-years. The extension of the double cosmic correlation defines a Topological Axis using Euler-Napier constant e as primary basis, confirming String Theory, Cartan-Bott periodicity and the 30 holic dimensions corresponding to the simplest space-time-matter diophantine equation T^2 = L^3 = M^5 = N^30. This dimension n = 30 corresponds to the common time, about 10^58 s, given by two mandatory dimensional analysis, interpreted as the Supercycle period. The visible Universe wavelength 'Topon' 2Għ/Rc3 ≈ 4 × 10^-96 m corresponds to n ≈ 2ee and enters the 1D mono-radial holographic extension of the Bekenstein-Hawking Universe entropy, implying the critical condition, and breaking the Planck wall by a factor 1061, justifying the Hawking trans-planckian frequencies. The monochrome holographic extension leads to a Grandcosmos, larger than the visible Universe by the same factor 10^61. A toponic quantization justifies the Cosmos vastness in a scanned Universe, justifying the entropy factor 1/4. This implies a tachyonic speed in the same ratio by respect to c, justifying the Planck re-normalisation of the vacuum energy, independently checked by the Casimir effect. The couple Universe-Grandcosmos is confirmed by a dramatic geo-dimensional analysis, where Length, Time and Mass ratios are considered as unit vectors in a 3D Super-space. A matter-antimatter 10^104 Hz Oscillatory Bounce unifies standard Single Bang with steady-state cosmology, but suppress Relativity in cosmology at large, reestablishing the Newton Absolute Space realized by the Microwave Cosmic Radiation, while Kotov cycle defines a quasi-absolute clock. This new scanning space-time structure is confirmed by single-electron cosmology, connected with Kotov period, and relying Sternheimer Biological scale factor and Atiyah constant, which appear as privileged computation basis, as well as e, p and a ≈ 137.036, in liaison with the sporadic groups. The Atiyah constant enters dramatic ppb precision relations with particle data. This unifies mathematics, physics, chemistry, biology and philosophy. It is predicted that the future telescopes will find mature galaxies in the very far range, instead of a Dark Space, ruining the standard evolutionary cosmology, ill-founded on an imperfect Cosmological Principle.

**Comments:** 27 Pages. To be published in Progress in Physics

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