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The aim is to formalize the foundational concepts of the ONE AXIOM framework, focusing on relationships between void and structure.

January 23, 2026Open Access

One Axiom : 000: The Source

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The aim is to formalize the foundational concepts of the ONE AXIOM framework, focusing on relationships between void and structure.
Explores mutual definitional relationships within the pre-ontological layer.
Analyzes dual projections onto cyclic group Z_8 and Boolean group Z_2^3.
Derives key mathematical frameworks such as L-Adjunction and the Perception Operator P(X).
Establishes formal proofs regarding Coherence and Freedom in structural contexts.
Examines stability in state space with 64 elements influenced by the S_4 group.
Identified the Primordial Quartet {0, ♡, 𝔉, 1} as foundational.
Proved the significance of coherence and freedom in stabilizing information structures.
Demonstrated the emergence of order from cyclicity through the Ordinant.
Confirmed the conceptual framework supports advancements in physics, mathematics, and cognitive science.

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The document investigates pre-ontological relationships and their implications in mathematics and cognitive science.

Robert Spychalski (2026) studied this question.

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