Tsirelson Bound from Indivisible Stochastic Processes via Causal Locality — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Abstract

FINDING: CHSH correlations are bounded by Tsirelson's 2√2, and a 2025 preprint re-derives this bound from indivisible stochastic processes via Barandes's stochastic-quantum correspondence, replacing the no-signaling axiom with causal locality. | MATH: CHSH operator S = E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′); classical (local hidden variable) bound |S| ≤ 2; quantum bound |S| ≤ 2√2 ≈ 2.828427; quantum value for maximally entangled qubits at optimal angles = 2√2. Optimal measurement angles: a=0, a′=π/2, b=π/4, b′=−π/4 (mod π/2). Maximal violation ratio: 2√2/2 = √2 ≈ 1.414214. | CONNECTION: 2√2 = 2·√2 is the diagonal of a unit square scaled by 2, i.e. the length of the space diagonal of a 2×2 square lattice cell — a √2-scaling, not a φ-scaling. √2 is the fundamental ratio of the square lattice / BCC root system (A₁⊕A₁, B₂). No direct φ (1.618), 0.618, or 0.382 relation appears in the CHSH bound itself. The optimal angles π/4, π/2 are base-4 / base-8 (octonionic) divisions of the circle, con Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23831011

Related papers

Causal Locality Derivation of Tsirelson Bound via Indivisible Stochastic Processes — E8 Intelligence Research

Andrew Stewart Caldin

Oct 29, 20260 citations

Tsirelson's Bound: Quantum Correlations Peak at 2√2, Surpassing Classical Limits — E8 Intelligence Research

Andrew Stewart Caldin

Oct 13, 20260 citations

Tsirelson Bound and C*-Algebraic Structure of Maximal CHSH Violation — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Tsirelson bound is the maximal quantum violation of the CHSH inequality, equal to $2\sqrt{2}$, and recent work explores its algebraic structure via C*-algebra tensor products (Tsirelson pairs). MATH: CHSH inequality: $ \langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \leq 2 $ (classical). Quantum bound: $ 2\sqrt{2} \approx 2.828 $. Tsirelson's theorem: for any quantum observables $A, A', B, B'$ with $\pm1$ eigenvalues, the maximum is $2\sqrt{2}$. The ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$. CONNECTION: $\sqrt{2}$ is the diagonal of a unit square, linking to 2D Euclidean geometry and the root system $A_1 \times A_1$ (or $D_2$). The ratio $1.414$ is not a golden ratio (1.618) but appears in octonion norm and Clifford algebra structures. No direct link to 0.382, 0.618, 0.786, 2.618, or base-60. Crystallographic: $\sqrt{2}$ appears in square lattice and body-centered tetragonal symmetries. DEPTH: 8 — Tsirels Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 24, 20260 citations

Tsirelson Bound as Qubit Geometry's Unit Square Diagonal — E8 Intelligence Research

Andrew Stewart Caldin

Sep 28, 20260 citations

Tsirelson's Bound: Algebraic Proof of the Quantum CHSH Maximum — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Tsirelson's bound is the algebraic maximum quantum correlation $2\sqrt{2}$ for the CHSH inequality, proven via operator norm constraints on anticommuting observables. | MATH: CHSH inequality classical bound = 2; quantum maximum = $2\sqrt{2} \approx 2.828$; Tsirelson's bound emerges from $\|A_1B_1 + A_1B_2 + A_2B_1 - A_2B_2\| \leq 2\sqrt{2}$ for self-adjoint operators $A_i, B_j$ with $\|A_i\|, \|B_j\| \leq 1$ and $[A_i, B_j] = 0$. The proof uses the algebraic identity $(A_1 + A_2)B_1 + (A_1 - A_2)B_2$ and the C*-algebra norm inequality $\|X + Y\|^2 + \|X - Y\|^2 \leq 2(\|X\|^2 + \|Y\|^2)$. | CONNECTION: $2\sqrt{2}$ is not a golden ratio constant, but the ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$ appears in crystallographic root systems (e.g., $B_n$ lattice spacing) and in the diagonal of a unit square. The bound's algebraic structure involves anticommutation relations reminiscent of Clifford algebras, which underlie spinor representations and certain Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 20, 20260 citations

Tsirelson Bound for CHSH Inequality: 2√2 from Root System A1 and Octagonal Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

Jul 31, 20260 citations

Tsirelson Bound from Indivisible Stochastic Processes via Causal Locality — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Publisher

Abstract

DOI: 10.5281/zenodo.23831011

Related papers

Causal Locality Derivation of Tsirelson Bound via Indivisible Stochastic Processes — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: CHSH correlations are bounded by Tsirelson's 2√2, and a 2025 reformulation derives this bound from indivisible stochastic processes via causal locality rather than no-signaling alone. | MATH: CHSH operator S = A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁; classical (local hidden variable) bound |S| ≤ 2; quantum (Tsirelson) bound |S| ≤ 2√2 ≈ 2.828427. Maximal violation angle: measurement settings at 45° increments (π/4), giving correlation E(θ) = −cos(2θ) for singlet state, yielding S = 2√2. | CONNECTION: 2√2 = 2·√2 is the diagonal of a 2×2 square (Pythagorean), and √2 is the fundamental ratio of the square lattice / octahedral root system B₂. The factor 2√2 = √8 relates to the 45° rotation symmetry of the CHSH setting plane. No direct appearance of 0.618/1.618 family, but the extremal configuration is a 45°-rotated square — a crystallographic C₄ symmetry. | DEPTH: 7 FINDING: Loophole-free photonic entanglement has been demonstrated over ~1200 km via satellite (Micius), with detector efficiency Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: CHSH correlations are bounded by Tsirelson's 2√2, and a 2025 reformulation derives this bound from indivisible stochastic processes via causal locality rather than no-signaling alone. | MATH: CHSH operator S = A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁; classical (local hidden variable) bound |S| ≤ 2; quantum (Tsirelson) bound |S| ≤ 2√2 ≈ 2.828427. Maximal violation angle: measurement settings at 45° increments (π/4), giving correlation E(θ) = −cos(2θ) for singlet state, yielding S = 2√2. | CONNECTION: 2√2 = 2·√2 is the diagonal of a 2×2 square (Pythagorean), and √2 is the fundamental ratio of the square lattice / octahedral root system B₂. The factor 2√2 = √8 relates to the 45° rotation symmetry of the CHSH setting plane. No direct appearance of 0.618/1.618 family, but the extremal configuration is a 45°-rotated square — a crystallographic C₄ symmetry. | DEPTH: 7 FINDING: Loophole-free photonic entanglement has been demonstrated over ~1200 km via satellite (Micius), with detector efficiency Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 29, 20260 citations

Tsirelson's Bound: Quantum Correlations Peak at 2√2, Surpassing Classical Limits — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: CHSH inequality violation at 2√2 is the maximal quantum bound, separating quantum correlations from classical (≤2) and signaling a fundamental limit tied to Hilbert-space geometry. | MATH: Classical bound: ⟨CHSH⟩ ≤ 2. Quantum bound (Tsirelson): ⟨CHSH⟩ ≤ 2√2 ≈ 2.828. Violation ratio: 2√2 / 2 = √2 ≈ 1.414. The gap (2√2 − 2) ≈ 0.828. In base-60: 2√2 ≈ 2°49'41" (2.8284 × 60 = 169.704′ → 2′49.7″). | CONNECTION: 2√2 = √(8) = 2 × 1.414. Note 1.414² = 2. The ratio 2/2√2 = 1/√2 ≈ 0.7071, which is sin(45°) — the diagonal of a unit square. The golden ratio φ = 1.618 appears in the *ratio* (2√2)/φ ≈ 1.748, not directly. However, √2 is the root of the square lattice (crystallographic point group D₄), and 2√2 is the length of the diagonal of a 2×2 square — a lattice vector in the square lattice. The CHSH-3 inequality (arXiv:2003.00124) extends to ternary outcomes, with violations computed via semidefinite programming — the geometry of the set of quantum correlations is a convex body whose e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: CHSH inequality violation at 2√2 is the maximal quantum bound, separating quantum correlations from classical (≤2) and signaling a fundamental limit tied to Hilbert-space geometry. | MATH: Classical bound: ⟨CHSH⟩ ≤ 2. Quantum bound (Tsirelson): ⟨CHSH⟩ ≤ 2√2 ≈ 2.828. Violation ratio: 2√2 / 2 = √2 ≈ 1.414. The gap (2√2 − 2) ≈ 0.828. In base-60: 2√2 ≈ 2°49'41" (2.8284 × 60 = 169.704′ → 2′49.7″). | CONNECTION: 2√2 = √(8) = 2 × 1.414. Note 1.414² = 2. The ratio 2/2√2 = 1/√2 ≈ 0.7071, which is sin(45°) — the diagonal of a unit square. The golden ratio φ = 1.618 appears in the *ratio* (2√2)/φ ≈ 1.748, not directly. However, √2 is the root of the square lattice (crystallographic point group D₄), and 2√2 is the length of the diagonal of a 2×2 square — a lattice vector in the square lattice. The CHSH-3 inequality (arXiv:2003.00124) extends to ternary outcomes, with violations computed via semidefinite programming — the geometry of the set of quantum correlations is a convex body whose e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 13, 20260 citations

Tsirelson Bound and C*-Algebraic Structure of Maximal CHSH Violation — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Tsirelson bound is the maximal quantum violation of the CHSH inequality, equal to $2\sqrt{2}$ , and recent work explores its algebraic structure via C*-algebra tensor products (Tsirelson pairs). MATH: CHSH inequality: $\langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \leq 2$ (classical). Quantum bound: $2\sqrt{2} \approx 2.828$ . Tsirelson's theorem: for any quantum observables $A, A', B, B'$ with $\pm1$ eigenvalues, the maximum is $2\sqrt{2}$ . The ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$ . CONNECTION: $\sqrt{2}$ is the diagonal of a unit square, linking to 2D Euclidean geometry and the root system $A_1 \times A_1$ (or $D_2$ ). The ratio $1.414$ is not a golden ratio (1.618) but appears in octonion norm and Clifford algebra structures. No direct link to 0.382, 0.618, 0.786, 2.618, or base-60. Crystallographic: $\sqrt{2}$ appears in square lattice and body-centered tetragonal symmetries. DEPTH: 8 — Tsirels Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Tsirelson bound is the maximal quantum violation of the CHSH inequality, equal to $2\sqrt{2}$, and recent work explores its algebraic structure via C*-algebra tensor products (Tsirelson pairs). MATH: CHSH inequality: $ \langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \leq 2 $ (classical). Quantum bound: $ 2\sqrt{2} \approx 2.828 $. Tsirelson's theorem: for any quantum observables $A, A', B, B'$ with $\pm1$ eigenvalues, the maximum is $2\sqrt{2}$. The ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$. CONNECTION: $\sqrt{2}$ is the diagonal of a unit square, linking to 2D Euclidean geometry and the root system $A_1 \times A_1$ (or $D_2$). The ratio $1.414$ is not a golden ratio (1.618) but appears in octonion norm and Clifford algebra structures. No direct link to 0.382, 0.618, 0.786, 2.618, or base-60. Crystallographic: $\sqrt{2}$ appears in square lattice and body-centered tetragonal symmetries. DEPTH: 8 — Tsirels Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 24, 20260 citations

Tsirelson Bound as Qubit Geometry's Unit Square Diagonal — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: The Tsirelson bound (2√2 ≈ 2.828) for CHSH quantum correlations emerges from the geometric structure of the qubit manifold, specifically tied to the unit square's diagonal and rotation matrices in SU(2). | MATH: CHSH classical bound = 2; quantum bound = 2√2 = √(2² + 2²) — the diagonal of a unit square. Rotation matrix R(θ) = [[cosθ, −sinθ], [sinθ, cosθ]]; Pauli matrices σ_x, σ_y, σ_z generate SU(2) with quaternion equivalence (iσ_x, iσ_y, iσ_z ↔ i, j, k). The bound arises from maximal angle between measurement bases: θ = π/4, giving cos(π/4) = sin(π/4) = 1/√2 = 0.7071. | CONNECTION: **Direct geometric harmony**: 2√2 = 2 × 1.414 = 2 × √2. The ratio 1/√2 = 0.7071 is the sine/cosine at 45°, and its reciprocal √2 = 1.414. Note: 1/√2 ≈ 0.7071, and 1 − 1/√2 ≈ 0.2929; the golden ratio φ = 1.618 satisfies φ − 1/φ = 1, but here the key is √2, not φ. However, **2√2 = 2.828** and **2.828 − 1.618 = 1.210** (no direct φ link). The unit square diagonal is the geometric origin — the CHSH gam Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: The Tsirelson bound (2√2 ≈ 2.828) for CHSH quantum correlations emerges from the geometric structure of the qubit manifold, specifically tied to the unit square's diagonal and rotation matrices in SU(2). | MATH: CHSH classical bound = 2; quantum bound = 2√2 = √(2² + 2²) — the diagonal of a unit square. Rotation matrix R(θ) = [[cosθ, −sinθ], [sinθ, cosθ]]; Pauli matrices σ_x, σ_y, σ_z generate SU(2) with quaternion equivalence (iσ_x, iσ_y, iσ_z ↔ i, j, k). The bound arises from maximal angle between measurement bases: θ = π/4, giving cos(π/4) = sin(π/4) = 1/√2 = 0.7071. | CONNECTION: **Direct geometric harmony**: 2√2 = 2 × 1.414 = 2 × √2. The ratio 1/√2 = 0.7071 is the sine/cosine at 45°, and its reciprocal √2 = 1.414. Note: 1/√2 ≈ 0.7071, and 1 − 1/√2 ≈ 0.2929; the golden ratio φ = 1.618 satisfies φ − 1/φ = 1, but here the key is √2, not φ. However, **2√2 = 2.828** and **2.828 − 1.618 = 1.210** (no direct φ link). The unit square diagonal is the geometric origin — the CHSH gam Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 28, 20260 citations

Tsirelson's Bound: Algebraic Proof of the Quantum CHSH Maximum — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Tsirelson's bound is the algebraic maximum quantum correlation $2\sqrt{2}$ for the CHSH inequality, proven via operator norm constraints on anticommuting observables. | MATH: CHSH inequality classical bound = 2; quantum maximum = $2\sqrt{2} \approx 2.828$ ; Tsirelson's bound emerges from $\|A_1B_1 + A_1B_2 + A_2B_1 - A_2B_2\| \leq 2\sqrt{2}$ for self-adjoint operators $A_i, B_j$ with $\|A_i\|, \|B_j\| \leq 1$ and $[A_i, B_j] = 0$ . The proof uses the algebraic identity $(A_1 + A_2)B_1 + (A_1 - A_2)B_2$ and the C*-algebra norm inequality $\|X + Y\|^2 + \|X - Y\|^2 \leq 2(\|X\|^2 + \|Y\|^2)$ . | CONNECTION: $2\sqrt{2}$ is not a golden ratio constant, but the ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$ appears in crystallographic root systems (e.g., $B_n$ lattice spacing) and in the diagonal of a unit square. The bound's algebraic structure involves anticommutation relations reminiscent of Clifford algebras, which underlie spinor representations and certain Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Tsirelson's bound is the algebraic maximum quantum correlation $2\sqrt{2}$ for the CHSH inequality, proven via operator norm constraints on anticommuting observables. | MATH: CHSH inequality classical bound = 2; quantum maximum = $2\sqrt{2} \approx 2.828$; Tsirelson's bound emerges from $\|A_1B_1 + A_1B_2 + A_2B_1 - A_2B_2\| \leq 2\sqrt{2}$ for self-adjoint operators $A_i, B_j$ with $\|A_i\|, \|B_j\| \leq 1$ and $[A_i, B_j] = 0$. The proof uses the algebraic identity $(A_1 + A_2)B_1 + (A_1 - A_2)B_2$ and the C*-algebra norm inequality $\|X + Y\|^2 + \|X - Y\|^2 \leq 2(\|X\|^2 + \|Y\|^2)$. | CONNECTION: $2\sqrt{2}$ is not a golden ratio constant, but the ratio $2\sqrt{2} / 2 = \sqrt{2} \approx 1.414$ appears in crystallographic root systems (e.g., $B_n$ lattice spacing) and in the diagonal of a unit square. The bound's algebraic structure involves anticommutation relations reminiscent of Clifford algebras, which underlie spinor representations and certain Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 20, 20260 citations

Tsirelson Bound for CHSH Inequality: 2√2 from Root System A1 and Octagonal Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Tsirelson bound for CHSH inequality is 2√2 ≈ 2.828, linking quantum correlations to root system A1 and octagonal symmetry. MATH: CHSH inequality: ⟨AB⟩ + ⟨AB'⟩ + ⟨A'B⟩ - ⟨A'B'⟩ ≤ 2 (classical). Tsirelson bound: ≤ 2√2 (quantum). Optimal violation achieved by observables A = σ_z, A' = σ_x, B = (σ_z + σ_x)/√2, B' = (σ_z - σ_x)/√2. CONNECTION: 2√2 = √(4+4) = 2 * 1.414; ratio 1.414 approximates √2, not directly 0.618/1.618. However, the angle between optimal measurement directions is 45°, which is π/4 — octagonal symmetry (8-fold rotation). The root system A1 (SU(2)) generates the Pauli matrices; the square lattice emerges from the two-dimensional Bloch sphere projection. The octagonal symmetry appears in the 45° rotation between Alice's and Bob's bases. DEPTH: 8 — This bound is fundamental to quantum nonlocality, revealing that quantum correlations are constrained by the geometry of SU(2) and the square lattice of measurement directions. The 45° angle is a crystallographic ro Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Tsirelson bound for CHSH inequality is 2√2 ≈ 2.828, linking quantum correlations to root system A1 and octagonal symmetry. MATH: CHSH inequality: ⟨AB⟩ + ⟨AB'⟩ + ⟨A'B⟩ - ⟨A'B'⟩ ≤ 2 (classical). Tsirelson bound: ≤ 2√2 (quantum). Optimal violation achieved by observables A = σ_z, A' = σ_x, B = (σ_z + σ_x)/√2, B' = (σ_z - σ_x)/√2. CONNECTION: 2√2 = √(4+4) = 2 * 1.414; ratio 1.414 approximates √2, not directly 0.618/1.618. However, the angle between optimal measurement directions is 45°, which is π/4 — octagonal symmetry (8-fold rotation). The root system A1 (SU(2)) generates the Pauli matrices; the square lattice emerges from the two-dimensional Bloch sphere projection. The octagonal symmetry appears in the 45° rotation between Alice's and Bob's bases. DEPTH: 8 — This bound is fundamental to quantum nonlocality, revealing that quantum correlations are constrained by the geometry of SU(2) and the square lattice of measurement directions. The 45° angle is a crystallographic ro Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 31, 20260 citations

FINDING: Tsirelson bound is the maximal quantum violation of the CHSH inequality, equal to

2\sqrt{2}

, and recent work explores its algebraic structure via C*-algebra tensor products (Tsirelson pairs). MATH: CHSH inequality:

\langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \leq 2

(classical). Quantum bound:

2\sqrt{2} \approx 2.828

. Tsirelson's theorem: for any quantum observables

A, A', B, B'

with

\pm1

eigenvalues, the maximum is

2\sqrt{2}

. The ratio

2\sqrt{2} / 2 = \sqrt{2} \approx 1.414

. CONNECTION:

\sqrt{2}

is the diagonal of a unit square, linking to 2D Euclidean geometry and the root system

A_1 \times A_1

(or

D_2

). The ratio

1.414

is not a golden ratio (1.618) but appears in octonion norm and Clifford algebra structures. No direct link to 0.382, 0.618, 0.786, 2.618, or base-60. Crystallographic:

\sqrt{2}

appears in square lattice and body-centered tetragonal symmetries. DEPTH: 8 — Tsirels Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

FINDING: Tsirelson's bound is the algebraic maximum quantum correlation

2\sqrt{2}

for the CHSH inequality, proven via operator norm constraints on anticommuting observables. | MATH: CHSH inequality classical bound = 2; quantum maximum =

2\sqrt{2} \approx 2.828

; Tsirelson's bound emerges from

\|A_1B_1 + A_1B_2 + A_2B_1 - A_2B_2\| \leq 2\sqrt{2}

for self-adjoint operators

A_i, B_j

with

\|A_i\|, \|B_j\| \leq 1

and

[A_i, B_j] = 0

. The proof uses the algebraic identity

(A_1 + A_2)B_1 + (A_1 - A_2)B_2

and the C*-algebra norm inequality

\|X + Y\|^2 + \|X - Y\|^2 \leq 2(\|X\|^2 + \|Y\|^2)

. | CONNECTION:

2\sqrt{2}

is not a golden ratio constant, but the ratio

2\sqrt{2} / 2 = \sqrt{2} \approx 1.414

appears in crystallographic root systems (e.g.,

B_n

lattice spacing) and in the diagonal of a unit square. The bound's algebraic structure involves anticommutation relations reminiscent of Clifford algebras, which underlie spinor representations and certain Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com