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This work aims to derive the U(1) phase freedom of quantum mechanics from the K₄ structure, resolving an open problem in the PDL framework.

May 3, 2026Open Access

Born's Rule Level 2: Derivation of U(1) Phase Freedom from the K₄ Pulsation Structure in the PDL Framework

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Demonstrates U(1) phase freedom in quantum mechanics using K₄ pulsation structure, suggesting new insights into foundational theories.

This work aims to derive the U(1) phase freedom of quantum mechanics from the K₄ structure, resolving an open problem in the PDL framework.
Three propositions are established with complete proofs regarding the K₄ coherent configurations and U(1) actions.
Algebraic computations verified across all 8 coherent configurations of K₄ were conducted to demonstrate the stability criterion's invariance.
A unique U(1)-equivariant probability measure on S³ was proved to yield the direct connection to Born's rule.
Proposition 1 establishes a canonical U(1) action created by global sign equivalence in K₄ configurations.
The (A)∧(B) stability criterion was shown to be U(1)-invariant with P₁, P₂ remaining independent of complex phase factors.
Identified the Ginzburg–Landau order parameter phase as a consequence of K₄ pulsation, linking combinatorial foundations to quantum phase coherence.

Cédric Laubscher (2026) studied this question.

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May 3, 2026Open Access

View Full Paper

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Authors

Demonstrates U(1) phase freedom in quantum mechanics using K₄ pulsation structure, suggesting new insights into foundational theories.

This work aims to derive the U(1) phase freedom of quantum mechanics from the K₄ structure, resolving an open problem in the PDL framework.
Three propositions are established with complete proofs regarding the K₄ coherent configurations and U(1) actions.
Algebraic computations verified across all 8 coherent configurations of K₄ were conducted to demonstrate the stability criterion's invariance.
A unique U(1)-equivariant probability measure on S³ was proved to yield the direct connection to Born's rule.
Proposition 1 establishes a canonical U(1) action created by global sign equivalence in K₄ configurations.
The (A)∧(B) stability criterion was shown to be U(1)-invariant with P₁, P₂ remaining independent of complex phase factors.
Identified the Ginzburg–Landau order parameter phase as a consequence of K₄ pulsation, linking combinatorial foundations to quantum phase coherence.

Cédric Laubscher (2026) studied this question.

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