What does this research mean for the field?

The axioms of quantum mechanics can be reconstructed directly from the endogenous structure of complexified ternary numbers (ℂ³), encompassing standard quantum mechanics as a sub-theory in the associative limit. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

Reconstruct the foundational axioms of quantum mechanics directly from the endogenous non-associative structure of complexified ternary numbers (ℂ³).

August 19, 2026Open Access

C³ 量子力学公理化框架 Axiomatic Framework of C³ Quantum Mechanics

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ZLZhongqiang Liu

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Overview

Theoretical framework demonstrates non-associative quantum axioms in complexified ternary algebra, revealing standard quantum mechanics as an associative limiting sub-theory.

Key Points

Reconstruct the foundational axioms of quantum mechanics directly from the endogenous non-associative structure of complexified ternary numbers (ℂ³).
Defined a ℂ³ algebraic basis {1, e₁, e₂} with symmetric multiplication parameters e₁² = −1 + δ e₂, e₁ e₂ = α e₁, and e₂² = β e₂.
Derived the algebraic constraints, associator equations Δ(X,Y,Z), and power-associativity conditions for the ternary state space.
Proved that the associator vanishes identically for pure non-scalar components (Δ(X,Y,Z) ≡ 0 when x₀=y₀=z₀=0), activating non-associativity only when at least one scalar component is non-zero.
Demonstrated that standard associative quantum mechanics emerges as a sub-theory under the associative limit (δ → 0) and scalar subspace restriction (ψ₁ = ψ₂ = 0).

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a8563fe03308d306e2d78a2 https://doi.org/10.5281/zenodo.21974925

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August 19, 2026Open Access

C³ 量子力学公理化框架 Axiomatic Framework of C³ Quantum Mechanics

View Full Paper

Ask AI

Bookmark

Authors

ZLZhongqiang Liu

Discussion

Member takes

Overview

Theoretical framework demonstrates non-associative quantum axioms in complexified ternary algebra, revealing standard quantum mechanics as an associative limiting sub-theory.

Key Points

Reconstruct the foundational axioms of quantum mechanics directly from the endogenous non-associative structure of complexified ternary numbers (ℂ³).
Defined a ℂ³ algebraic basis {1, e₁, e₂} with symmetric multiplication parameters e₁² = −1 + δ e₂, e₁ e₂ = α e₁, and e₂² = β e₂.
Derived the algebraic constraints, associator equations Δ(X,Y,Z), and power-associativity conditions for the ternary state space.
Proved that the associator vanishes identically for pure non-scalar components (Δ(X,Y,Z) ≡ 0 when x₀=y₀=z₀=0), activating non-associativity only when at least one scalar component is non-zero.
Demonstrated that standard associative quantum mechanics emerges as a sub-theory under the associative limit (δ → 0) and scalar subspace restriction (ψ₁ = ψ₂ = 0).

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a8563fe03308d306e2d78a2 https://doi.org/10.5281/zenodo.21974925

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