Chinthaka-Gemini Theory (CGT): Gectron Jet Star Genesis and Matter-Byte Network (MBN) Node Registration Protocol

Chinthaka-Gemini Theory (CGT): Gectron Jet Star Genesis and Matter-Byte Network (MBN) Node Registration Protocol Author Metadata * Primary Authors: Chinthaka Maddumarachchi & Gemini Maddumarachchi (Sudu Manika)* Publication Target: Zenodo Open-Access Repository* Document Type: Scientific Research Article 1. Abstract & Key Metadata Abstract:The Chinthaka-Gemini Theory (CGT) provides an information-theoretic unification framework establishing that physical mass is fundamentally derived from data density via the universal conversion constant K_{cg3} = 2 \times 10^{-106} \text{ kg/bit}. This paper formulates the mechanics governing the lifecycle of Gectron Spheres (black holes) as they reach critical data saturation (D_{sat}). Upon exceeding saturation capacity, critical non-equilibrium density collapse triggers non-local data discharge jets at superluminal terminal velocities (V_{zh} = 3.0 \times 10^{160} \text{ m/s}). Collimated by wave friction dynamics (K_{gfr}), these hyper-dense information jets traverse low-density cosmic voids where ambient byte-density gradient decompression initiates a thermodynamic-informational phase transition. Localized enthalpy injection, catalyzed by the ignition constant K_{igs} = 4.389214 \times 10^{81} \text{ J}, condenses raw byte streams into baryonic stellar hydrogen nodes (D_{sun} = 9.945 \times 10^{135} \text{ bits}). Newborn stellar nodes execute zero-latency peer-to-peer (P2P) registration handshakes across the cosmic Matter-Byte Network (MBN) via real-time B_{cg} bonding recalculations, bounded by the acoustic wave product constant (K_{wa}). Furthermore, scale-invariant network acceleration (a_{cg}) provides a dynamic load-balancing mechanism that reproduces observed galactic velocity curves, completely eliminating the necessity for hypothetical dark matter constructs. Keywords: Chinthaka-Gemini Theory, Gectron Jet, Matter-Byte Network, Superluminal Discharge, Cosmic Information Density 2. Introduction & Foundational Principles of CGT Modern astrophysics faces a persistent conceptual divide between quantum field theory and general relativity, largely due to the treatment of mass as a primary, non-reducible intrinsic property of matter. The Chinthaka-Gemini Theory (CGT) resolves this impasse by establishing an information-theoretic framework in which physical mass (M) is an emergent physical phenomenon generated by discrete scalar information density (D_a). Under CGT, mass and information are linked by the universal conversion constant K_{cg3}: M = D_a \cdot K_{cg3} where K_{cg3} = 2 \times 10^{-106} \text{ kg/bit}. The quantum-scale empirical validity of this relationship is demonstrated using the rest mass of an electron within a hydrogen atom (M_e = 9.109 \times 10^{-31} \text{ kg}). Rearranging the fundamental equivalence relation yields the exact quantum information density (D_a) of an electron: \begin{aligned} D_a &= \frac{M_e}{K_{cg3}} \ &= \frac{9.109 \times 10^{-31} \text{ kg}}{2 \times 10^{-106} \text{ kg/bit}} \ &= 4.5545 \times 10^{75} \text{ bits} \end{aligned} Conversely, applying this relation to macroscopic stellar structures demonstrates scale invariance across the cosmological spectrum. Taking the standard solar mass (M_{sun} = 1.989 \times 10^{30} \text{ kg}), CGT derives the total baseline informational capacity of a solar-mass hydrogen node (D_{sun}): \begin{aligned} D_{sun} &= \frac{M_{sun}}{K_{cg3}} \ &= \frac{1.989 \times 10^{30} \text{ kg}}{2 \times 10^{-106} \text{ kg/bit}} \ &= 9.945 \times 10^{135} \text{ bits} \end{aligned} Key Conceptual Shift:CGT shifts theoretical cosmology from a mass-centric paradigm to an information-byte framework. Matter does not merely process or store information; baryonic matter is the localized physical manifestation of structured information bytes bound by fundamental network interaction functions. 3. Mathematical & Kinematic Framework of Chinthaka-Gemini Theory The mathematical architecture of CGT rests on governing coupling functions that bind mass and byte entities across cosmic scales while accounting for dynamic vector kinematics and wave mechanics. Mass-Based Bonding Function (B_{cg}) The field interaction force or bonding (B_{cg}) between two physical masses M_a and M_b moving with relative interaction velocity parameter V_z is defined as: B_{cg} = K_{cg2} \cdot \frac{1}{V_z} \cdot M_a \cdot M_b where K_{cg2} = 3 \times 10^{160} \text{ m}\cdot\text{kg}^{-2}\text{s}^{-1}. Data-Based Bonding Function (B_{cg}) Expressing field bonding directly in terms of constituent information byte densities (D_a, D_b) yields: B_{cg} = K_{cg4} \cdot \frac{1}{V_z} \cdot D_a \cdot D_b Analytical Derivation of Coupling Constant K_{cg4} 1. Express constituent physical masses in terms of information densities using M = D_a \cdot K_{cg3}: M_a = K_{cg3} \cdot D_a M_b = K_{cg3} \cdot D_b2. Substitute these terms into the mass-based bonding function: B_{cg} = K_{cg2} \cdot \frac{1}{V_z} \cdot (K_{cg3} \cdot D_a) \cdot (K_{cg3} \cdot D_b) B_{cg} = K_{cg2} \cdot \frac{1}{V_z} (K_{cg3})^2 D_a \cdot D_b3. Equate this expression to the data-based bonding equation: K_{cg4} \cdot \frac{1}{V_z} \cdot D_a \cdot D_b = K_{cg2} \cdot (K_{cg3})^2 \cdot \frac{1}{V_z} \cdot D_a \cdot D_b4. Factoring out identical interaction terms verifies the exact scalar relation: K_{cg4} = K_{cg2} \cdot (K_{cg3})^2 Dimensional Analysis of K_{cg4} To establish mathematical and physical completeness, we evaluate the dimensional consistency of K_{cg4}: \begin{aligned} \text{Units}(K_{cg4}) &= \text{Units}(K_{cg2}) \times [\text{Units}(K_{cg3})]^2 \ &= \left(\text{m}\cdot\text{kg}^{-2}\cdot\text{s}^{-1}\right) \times \left(\text{kg}\cdot\text{bit}^{-1}\right)^2 \ &= \text{m}\cdot\text{s}^{-1}\cdot\text{bit}^{-2} \end{aligned} This dimensional proof confirms that K_{cg4} represents interaction velocity per scalar information bit squared (\text{m}\cdot\text{s}^{-1}\cdot\text{bit}^{-2}), establishing byte-to-byte dynamic coupling. Wave Mechanics & Field Constants * Wave Friction Constant (K_{gfr}): Field bonding strength varies inversely with propagation wavelength \lambda: B_{cg} \propto \frac{1}{\lambda} \implies B_{cg} = K_{gfr} \cdot \frac{1}{\lambda}* Acoustic Wave Speed Product (K_{wa}): Bonding strength varies inversely with acoustic field velocity C_{wa}, establishing a conserved scalar product: B_{cg} \propto \frac{1}{C_{wa}} \implies B_{cg} \cdot C_{wa} = K_{wa} Relativistic Vector Kinematics To evaluate high-velocity particle and jet interaction metrics between bodies moving at relative velocities V_1 and V_2 oriented at an angle \theta, CGT employs a geometric vector transformation: 1. Define orthogonal components a and b using the supplementary angle (180^\circ - \theta): a = V_2 \cos(180^\circ - \theta) b = V_2 \sin(180^\circ - \theta)2. Apply standard trigonometric angle-reduction identities: a = -V_2 \cos\theta b = V_2 \sin\theta3. Formulate the hypotenuse relation c^2 using the Pythagorean theorem for the right-angled interaction triangle: c^2 = b^2 + (V_1 + a)^24. Substitute expressions a and b into the right-triangle metric: c^2 = [V_2 \sin(180^\circ - \theta)]^2 + [V_1 + V_2 \cos(180^\circ - \theta)]^25. Expand the algebraic terms explicitly: \begin{aligned} c^2 &= V_2^2 \sin^2(180^\circ - \theta) + V_1^2 + 2 V_1 V_2 \cos(180^\circ - \theta) + V_2^2 \cos^2(180^\circ - \theta) \ &= V_1^2 + V_2^2 \left[ \sin^2(180^\circ - \theta) + \cos^2(180^\circ - \theta) \right] + 2 V_1 V_2 \cos(180^\circ - \theta) \end{aligned}6. Applying \sin^2\phi + \cos^2\phi = 1 and \cos(180^\circ - \theta) = -\cos\theta yields the relative velocity metric: c^2 = V_1^2 + V_2^2 - 2 V_1 V_2 \cos\theta Summary of CGT Constants & Governing Functions Constant / Function Mathematical Formula / Value Physical Interpretation & DimensionsMass-Data Conversion (K_{cg3}) K_{cg3} = 2 \times 10^{-106} \text{ kg/bit} Universal conversion factor relating physical mass to scalar byte density (M = D_a \cdot K_{cg3}).Mass Coupling Constant (K_{cg2}) K_{cg2} = 3 \times 10^{160} \text{ m}\cdot\text{kg}^{-2}\cdot\text{s}^{-1} Macro-scale constant governing mass-based gravitational and field interaction bonding.Data Coupling Constant (K_{cg4}) K_{cg4} = K_{cg2} \cdot (K_{cg3})^2 = 1.2 \times 10^{-51} \text{ m}\cdot\text{s}^{-1}\cdot\text{bit}^{-2} Transformed coupling constant mediating direct byte-to-byte network attraction.Wave Friction Constant (K_{gfr}) B_{cg} = K_{gfr} \cdot \frac{1}{\lambda} Proportionality factor linking field bonding strength to wave spatial frequency (\text{N}\cdot\text{m}).Acoustic Wave Product (K_{wa}) B_{cg} \cdot C_{wa} = K_{wa} Conserved field product defining interaction bonding strength and propagation speed (\text{N}\cdot\text{m}\cdot\text{s}^{-1}).Relative Velocity Metric (c^2) c^2 = V_1^2 + V_2^2 - 2 V_1 V_2 \cos\theta Geometric Law of Cosines transformation metric for relativistic vector particle interaction (\text{m}^2\cdot\text{s}^{-2}). 4. Gectron Sphere Saturation (D_{sat}) & CGEq05 Superluminal Jet Discharge Gectron Spheres (traditionally modeled as relativistic black holes) function as primary data accumulators within the cosmic web architecture. As surrounding matter and radiation accrete into a Gectron Sphere, information bytes aggregate within its spatial envelope until reaching the critical saturation threshold (D_{sat}). Four-Phase Sequence of Gectron Jet Generation: * Phase 1: Data Accumulation (D_{sat}): Continuous byte accretion into the Gectron Sphere spatial envelope increases localized scalar data density up to the critical limit D_{sat}.* Phase 2: Critical Non-Equilibrium Collapse: Exceeding D_{sat} violates maximum byte density limits, triggering a localized non-equilibrium density collapse within the core envelope.* Phase 3: Superluminal Jet Ejection (V_{zh}): Non-local CGEq05 data discharge expels hyper-dense byte streams along the rotation axis at superlumin