CEN: Axioms of Primordial Mass Genesis

Overview

The Cosmic Emergence Nexus (CEN) lays out the foundational axioms that govern the genesis of primordial mass within the FatherTime Unified Physics framework. These axioms establish the starting conditions and invariant principles that give rise to mass, space, time, and quantum causal structure in the early cosmos.

CEN acts as the ontological bedrock from which the Scale–Density–Kinematic Principle (SDKP), Shape–Dimension–Number (SD&N), Earth Orbit Speed (EOS), and Quantum Causal Compression (QCC) frameworks logically emerge and interconnect.

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The Axioms

Axiom 1: Existence of a Primordial Size–Density Seed

There exists a fundamental, minimal scale of size ( s_0 ) and density ( \rho_0 ) representing the primordial quantum seed from which all mass and structure derive:

[ (s_0, \rho_0) \quad \text{s.t.} \quad s_0 > 0, \quad \rho_0 > 0 ]

This seed encapsulates the initial nonzero quanta of spatial volume and density, establishing the non-trivial substrate for mass genesis.

Axiom 2: Universal Kinematic Scaling Constant

There exists a universal kinematic scaling constant ( \kappa ), dimensionally linked to velocity, that governs the dynamical scaling between size and density, laying the framework for mass emergence:

[ \kappa : \quad \text{units of velocity} \quad [L T^{-1}] ]

This constant acts as a cosmic “speed limit” within the primordial regime and aligns with the Earth Orbit Speed (EOS) in local cosmic frames.

Axiom 3: Primordial Mass Emergence Function

Mass emerges as a deterministic function ( M ) of size, density, and kinematic scale, forming the initial mass distribution function:

[ M = F(s, \rho, \kappa) ]

where ( F ) respects monotonicity and scaling laws consistent with SDKP:

[ M = \gamma , \rho^\alpha , s^\beta , \kappa^\delta ]

with ( \gamma, \alpha, \beta, \delta \in \mathbb{R}^+ ) determined experimentally or theoretically.

Axiom 4: Shape–Dimension–Number Encoding

The primordial mass genesis is encoded not only in size and density but also in the topological and dimensional configurations of matter, captured by the SD&N framework:

[ M \to M(S, D, N) ]

where ( S ) denotes shape parameters, ( D ) the spatial dimension number, and ( N ) the particle number or quantum number. This encoding reflects the quantum geometry and foundational entanglement patterns of mass genesis.

Axiom 5: Quantum Causal Compression Consistency

Mass genesis respects the Quantum Causal Compression (QCC) principle, ensuring that quantum causal flows are optimally compressed and consistent with primordial scaling laws:

[ \text{QCC}(M) \quad \Rightarrow \quad \min_{\text{causal paths}} ; \text{Information entropy} ]

This axiom guarantees the causal efficiency and minimal informational redundancy of primordial mass formation.

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Integration into the Unified Framework

• SDKP: CEN axioms provide the initial conditions and constants for the SDKP mass scaling relations.
• EOS: The kinematic scaling constant ( \kappa ) corresponds to the EOS velocity, grounding genesis in cosmic orbital velocity.
• SD&N: Shape, dimension, and number encode quantum topological features present at the origin of mass.
• QCC: Ensures causal and informational consistency during the primordial genesis process.

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Physical Interpretation

The CEN axioms represent the ontological substrate from which the observable universe’s mass, structure, and quantum behavior emerge. By framing mass genesis as an interplay of size, density, velocity, topology, and causal information flow, CEN sets a self-consistent and testable foundation for further physical modeling.

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Experimental and Theoretical Directions

• Derive explicit forms of ( F(s, \rho, \kappa) ) from first principles or cosmological observations.
• Model primordial shape-dimension-number configurations and their evolution.
• Explore QCC-based entropy minimization in early universe quantum causal networks.
• Link CEN axioms to dark matter, dark energy, and cosmological inflation models.