Methodological Foundation

Global Architecture & Hierarchy of SGDM

A rigorous 6-level hierarchical framework: from fundamental massive gravitons and QCD core \(\rho_0\) to Kerr black hole dynamics, cosmological supercycles, and the infinite open Multiverse.

Hierarchical Logic

6 Fundamental Levels of the SGDM Model

Each level logically follows from the previous, bridging quantum field theory and relativistic cosmology without dark energy or artificial scalar fields.

Level 1

Quantum Microworld: Massive Graviton Theory & Baryon Origin

BASIS: Quantum Field Theory (QFT), gauge symmetries, Quantum Chromodynamics (QCD).

Graviton as Fundamental Topological Quantum

Quantum mass \(M_g \approx \frac{\hbar H_0}{c^2} \approx 2.6 \times 10^{-68}\text{ kg} \approx 1.5 \times 10^{-32}\text{ eV}\). Spin \(s=2\), Yukawa screening length \(\lambda_g \approx 15\text{ billion ly}\). Eliminates Seeliger's paradox via \(\Phi(r) = -(GM/r)\exp(-r/\lambda_g)\).

Baryon Quantization: \(N_{\text{grav}} = A\)

Each nucleon carries exactly 1 graviton node: \(^1\text{H} \to 1\), \(^4\text{He} \to 4\), \(^{56}\text{Fe} \to 56\), \(^{238}\text{U} \to 238\). Invariant domain graviton number: \(N_G = M/m_p \approx 1.2 \times 10^{80} = \text{const}\). QED limit \(Z_{\text{max}} \approx 173\).

Level 2

Ultra-dense Quantum Matter: Core \(\rho_0\) & Singularity Prohibition

BASIS: Strange Quark Matter (Bodmer–Witten SQM), Landau Fermi-Liquid, Newton–Birkhoff theorem.

«Quantum Soup» of Core \(\rho_0\)

Status: «Ultra-relativistic deconfined strange quark-gluon Fermi-liquid at saturation density \(\rho_0 \approx 3 \times 10^{17}\text{ kg/m}^3\)». Components: \(uds\) quarks, Color Glass Condensate (CGC), lepton buffer (\(e^-, \nu_e\)), graviton Bose-condensate.

Singularity Prohibition: \(g(0) \equiv 0\)

Point collapse is halted by Pauli pressure (\(P_F \propto n_q^{4/3}\)), QCD hard-core repulsion (\(F \propto 1/r^6\)), and relativistic sound speed (\(c_s = c/\sqrt{3}\)). Gravity cancels out at center (\(g(0)=0\)). Particle conservation holds: \(\Delta B = 0, \Delta L = 0\).

Level 3

Relativistic Black Hole Physics & Sub-horizon Vacuum

BASIS: Kerr GR metric, Gullstrand–Painlevé coordinates, Riemann–Maclaurin equilibrium.

Superluminal Vacuum Waterfall: \(v \to 5.2 \times 10^6\,c\)

Inward space inflow accelerates from \(1.0\,c\) at horizon to \(5\,235\,000 \cdot c\) at core surface (\(36.2\text{ AU}\)), building massive elastic energy for centrifugal decompression. Outward $^{197}\text{Au}$ atom launch is swept backward.

Thick Core Spheroid & 3D Spin Quenching

Core shape is a thick spheroid (\(c/a \approx 0.6\)). Random 3D inflow suppresses spin (\(a^* \propto N^{-3/2} \to 0\)), preventing premature explosion. Detonation occurs only upon complete mass assembly (\(10^{23} M_\odot\)) via Bardeen's 2D disk (\(a^* \ge 0.998\)).

Level 4

Domain Cosmodynamics: Complete Supercycle of Evolution

BASIS: Relativistic kinematics, BBN nucleosynthesis, Chandrasekhar dynamical friction.

Big Bang (\(t=0\)) & Matter Stratification

Centrifugal rupture releases \(7.6 \times 10^{69}\text{ J}\). 95% of mass condenses into primordial black holes (\(w=0\)), while 5% plasma undergoes 3-minute BBN yielding exactly 75% Hydrogen and 25% Helium.

Turnaround (\(S_{\text{max}} \approx 2\text{ trillion ly}\)) & Re-collapse to \(O_2\)

After \(10^{14}\) years radial expansion reaches \(v \to 0\), reversing into gravitational coalescence towards a new displaced barycenter \(O_2\). The supercycle restarts with a new Big Bang at \(\sim 10^{18}\) years.

Level 5

Global Multiverse: Open 4D Macroworld

BASIS: Einstein Field Equations \(G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}\), N-body celestial mechanics.

Lagrange Surfaces & Center Wandering

Domain boundaries are dynamic equipotential surfaces of zero net tidal force (\(\nabla\Phi = 0\)). Centers wander due to Dark Flow (\(1000\text{ km/s}\)), central voiding, and external accretion. Milky Way is displaced by \(1.5 - 3.0\text{ billion ly}\) from epicenter.

Migrant Galaxies (3–5%)

5 identification criteria: polar rings (NGC 4650A), retrograde disks (NGC 4826), anomalous transverse velocities \(\Delta v_\perp > 1000\text{ km/s}\), and premature \(10^{10} M_\odot\) SMBHs at \(z > 10\) on JWST.

Level 6

Experimental Verification: Observational Proofs

BASIS: Popper's falsifiability, empirical data from LIGO, JWST, Planck, NANOGrav, GRANIT.

Astrophysical Observations

1) JWST quasars at \(z > 10\); 2) CMB Quadrupole Anisotropy («Axis of Evil» Planck); 3) Coherent Dark Flow (\(1000\text{ km/s}\) to Centaurus); 4) 3–5% polar ring migrant galaxy population.

GW & Laboratory Tests

1) GW speed test (LIGO GW170817: \(\Delta t \sim 10^{-23}\text{ s}\)); 2) NANOGrav stochastic GW background; 3) GRANIT neutron quantum levels (\(254\text{ Hz}\)); 4) Interferometer decoherence \(\Gamma \propto A^2\).