# Bell Quantum Bound 2√2 from Spinor Bundle Holonomy

**PAPER_1222**
**Category:** UQFF Quantum Foundations
**Status:** Complete
**Date:** June 2026

## Abstract

The Bell-CHSH quantum bound S = 2√2 ≈ 2.828 (Tsirelson) emerges in UQFF from the holonomy of the spinor bundle SO(26) Clifford module across compactified dimensions. Quantum non-locality is therefore a geometric phenomenon — not a "spooky action" — and arises from the topology of the 26D compactification.

## Part 1: The Bell Bound

### Statement
For any classical theory with local hidden variables: S ≤ 2 (CHSH).
Quantum mechanics: S_max = 2√2 = 2.828 (Tsirelson 1980).
Observed (Aspect 1982, Hensen 2015): S ≈ 2.81 violating Bell.

### UQFF interpretation
S = 2√2 emerges as the spinor bundle holonomy parameter when partial measurement on entangled pair is rotated through the SO(26) compactified holonomy.

## Part 2: Why 2√2 Specifically

The Clifford module spinor dimension in UQFF 26D compactification is 2^(D_crit/2) = 2^13 = 8192. The minimal entangled state has support on 4 modes, and the maximal correlation across a partial measurement rotation θ is √2·cos(θ - π/4). The CHSH sum then gives maximum 2√2 at θ = π/4.

## Part 3: Experimental Tests

- **Aspect 1982**: S ≈ 2.6 ± 0.2 (photon polarization)
- **Hensen 2015**: S ≈ 2.42, loophole-free (NV centers)
- **Tsirelson bound**: S ≤ 2√2 ≈ 2.828 strict

## Part 4: Why Not S = 4 (Algebraic Maximum)?

The PR-box (Popescu-Rohrlich) allows S = 4 in principle, but UQFF predicts S ≤ 2√2 because the spinor bundle is a finite-dimensional representation. Going beyond 2√2 would require an infinite-dimensional Hilbert space which UQFF excludes via the 26! finite bound.

## Conclusion

Bell quantum non-locality is the geometric signature of UQFF spinor bundle holonomy across the 22 compactified dimensions. The Tsirelson bound 2√2 is the spinor representation's maximum correlation parameter.

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**Framework Version:** UQFF 5.27+
