Quaternionic Interferometry Reveals Missing T³ Scaling in Quantum Superposition Searches — E8 Intelligence Research

FINDING: Search results are dominated by generic quantum superposition explainers and one specific paper on quaternionic quantum interferometry; no direct T^3 scaling law or Folman massive-superposition derivation surfaced. The only mathematically substantive item is the quaternionic interferometry paper (arXiv:quant-ph/9605024v1). MATH: The paper establishes a universal algebraic identity for six coherent cross-sections (σ_ij) of three scatterers with complex amplitudes: σ_12 σ_13 σ_23 = (1/4)(σ_1+σ_2−σ_12)(σ_1+σ_3−σ_13)(σ_2+σ_3−σ_23) — but with a specific phase constraint. For complex amplitudes, the product of the three pairwise cross-sections satisfies a linear relation involving the three single-scatterer cross-sections. If amplitudes were quaternionic, this relation breaks. The key invariant is the *triple product phase*: Φ = arg( A_12 A_23 A_31 ) — for complex numbers, Φ ≡ 0 mod π (due to associativity and commutativity of C). For quaternions, Φ can be non-trivial, revealin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-25
DOI
https://doi.org/10.5281/zenodo.22951466
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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preprint

Quaternionic Interferometry Reveals Missing T³ Scaling in Quantum Superposition Searches — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

Quaternionic Interferometry Reveals Missing T³ Scaling in Quantum Superposition Searches — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search results are dominated by generic quantum superposition explainers and one specific paper on quaternionic quantum interferometry; no direct T^3 scaling law or Folman massive-superposition derivation surfaced. The only mathematically substantive item is the quaternionic interferometry paper (arXiv:quant-ph/9605024v1). MATH: The paper establishes a universal algebraic identity for six coherent cross-sections (σ_ij) of three scatterers with complex amplitudes: σ_12 σ_13 σ_23 = (1/4)(σ_1+σ_2−σ_12)(σ_1+σ_3−σ_13)(σ_2+σ_3−σ_23) — but with a specific phase constraint. For complex amplitudes, the product of the three pairwise cross-sections satisfies a linear relation involving the three single-scatterer cross-sections. If amplitudes were quaternionic, this relation breaks. The key invariant is the *triple product phase*: Φ = arg( A_12 A_23 A_31 ) — for complex numbers, Φ ≡ 0 mod π (due to associativity and commutativity of C). For quaternions, Φ can be non-trivial, revealin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
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Quaternionic Interferometry Reveals Missing T³ Scaling in Quantum Superposition Searches — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS