Arthur Haas explained the Hydrogen spectra, 3 years before Niels Bohr, by extending the virial theorem to the Planck energy formula. This suggests the holographic coherence principle: energy conservation means frequency unicity, i.e. the coherence condition for Holography. This is applied to an Hydrogen molecule model, in a black-hole sphere of horizon R = 2GM/c^2: this critical condition being seen as a general holographic conservation, and tied to the Non-Doppler cosmic period tcc. So R/c appears as a period 2GFtcc^2/ħƛe^3≈ 13.8123(1) Gyr, while R = 2ħ^2/Gm_em_pm_H ≈ 13.812(1) Glyr confirms Eddington's Theory. These two formulas displays a G-GF symmetry between Newton and Fermi constants and are compatible with the so-called 'Universe age' 13.81(5) Gyr of standard cosmology. The cosmic microwave background (CMB) wavelength enters an associated special holographic conservation, confirming a come-back to the steady-state cosmology, for which the factor Wm = 3/10 for matter density is trivial, eliminating the 'dark energy problem', and confirming the Eddington prediction M/m_H = 136 × 2^256, while the real Hydrogen density is √(m_e/m_H) ≈ 0.0233, nearly compatible with the Helium density and CMB temperature, and connected to Wm. From Sanchez-Maruani matter-antimatter vibration viewpoint, dark matter would be usual matter vibrating in quadrature. A cosmic Hydrogen atom model relates directly R, ƛe and the Bohr radius rB with R' = 2r_e^3/l_P^2≈ 4R/3, seen as the radius of a sphere representing a Grandcosmos. This rules out several common conjectures: 1) the Primordial Big-Bang, 2) the Planck Wall, 3) the Cosmic Anthropic Principle, 4) the Multiverse. The holographic relations can be represented in a topological axis, involving a double exponential function, and showing the special string dimension series n = 2 + 4p. It yields R and rB for the canonic values n = 26 (tachyo-bosonic) and 10 (superstring), with a non-standard Gluon mass for p = 1. The Grandcosmos is the lacking concept in 1) the CMB interpretation (not a fossil radiation) 2) the steady-state model (no need for an internal thermostat) 3) the lacking point p = 7. The physical parameters are shown to connect with music numbers, economic numbers and biological parameters, pointing to a Grand Theory. Keywords Quantum Theory, Steady-state Cosmology, Holographic Principle, Eddington Theory, Cosmic Oscillation, Antimatter, Dark matter, Combinatorial Physics, String Theory.