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This paper aims to finalize the identification of the universal spin-j singlet correlator across all admissible sectors of the quantum chain.

July 13, 2026Open Access

Universal Spin-j Singlet from Admissibility: Completion of the SU(2) Quantum Sector

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This paper aims to finalize the identification of the universal spin-j singlet correlator across all admissible sectors of the quantum chain.
Derived the universal singlet correlator for various spin values without new postulates.
Applied Schur's lemma to prove the diagonal $2I$-invariance of the admissible pairs.
Closed identification gaps by demonstrating the isotropy condition satisfied by the singlet state.
The universal singlet correlator was derived as $E( ext{hat}{a}, ext{hat}{b}) = -\frac{j(j+1)}{3}(\text{hat}{a}\cdot\text{hat}{b})$ for all admissible $j$.
In the limit $p \to \infty$, $j = \frac{1}{2}$ emerges as the unique stable fixed point, retrieving the classic singlet correlator $E(\text{hat}{a},\text{hat}{b}) = -\text{hat}{a}\cdot\text{hat}{b}$.

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Universal singlet correlator identified in the SU(2) quantum sector, implying structural completion of quantum mechanics.

Jérôme Beau (2026) studied this question.

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