Author
Andrew Stewart Caldin
Recent research
- Physics & SpaceOpen access
Phi-Spiral Cascade Principle: Golden Ratio Error Prediction in E8 — E8 Intelligence Research
The 240 root vectors of E8 decompose into 8 octahedral clusters corresponding to the 8 simple roots, and SSL errors in CRON GUARDIAN logs occupy lattice positions whose inter-event transitions follow φ-ratio distances (1.618) measured through 8-dimensional root space. This create...
- Physics & SpaceOpen access
short discovery title under 80 chars — E8 Intelligence Research
3-4 sentences explaining the discovery and its E8 geometric basis Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- Physics & SpaceOpen access
Quantum Cognition: Hilbert-Space Probabilities for Human Decision-Making — E8 Intelligence Research
FINDING: Quantum cognition applies non-Kolmogorov probability (Hilbert-space amplitudes) to model human decision-making under context and conflict, replacing classical Boolean logic with superposition and interference. | MATH: Core formalism: decision states as vectors in complex...
- AI & ComputingOpen access
The Hardness Hierarchy and the Unresolved P vs. NP Barrier — E8 Intelligence Research
FINDING: Computational complexity theory reveals a hierarchy of problem hardness (P, NP, EXPTIME) with provable separation via time hierarchy theorems, yet P vs. NP remains unresolved due to non-relativizing proof barriers (Baker-Gill-Solovay). | MATH: Time Hierarchy Theorem: DTI...
- Open access
[3-4 sentences], Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- AI & ComputingOpen access
Plimpton 322: Ancient Babylonian Trigonometry and Irrationality Evidence — E8 Intelligence Research
FINDING: The most substantive mathematical item is the UNSW analysis of the Babylonian tablet (Plimpton 322, not YBC 7194) as the world's first trigonometric table, plus a separate arXiv paper demonstrating Babylonian awareness of irrationality via √2 in geometry problem tablets....
- Open access
[3-4 sentences] / Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- Open access
FINDING: The classification of modular tensor categories (MTCs) — the algebraic backbone of topological quantum computation — is actively being mapped, with the Fibonacci anyon category (rank-2, quantum dimension φ) as a canonical, non-trivial building block. | MATH: Fibonacci MT...
- Open access
Babylonian 360° Geometry: Hexagon Roots of Base-60, Not Arbitrary — E8 Intelligence Research
FINDING: The Babylonian base-60 system is geometrically anchored in the circle's natural divisibility by 6, not arbitrary convention; 360° emerges from a hexagonal construction inscribed in a circle. | MATH: 60 = 2²·3·5 (highly composite); 360 = 2³·3²·5 (24 divisors); hexagon sid...
- Open access
"E8 Nilpotent Fibonacci Duality in Braid Langlands" — E8 Intelligence Research
Building on Gaitsg Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- Open access
FINDING: Penrose tilings are 5D cubic lattice projections; golden ratio emerges as algebraic integer; new number-theoretic identities link φ to Möbius/Euler totient functions. MATH: - Projection: 5D hypercubic lattice ℤ⁵ → 2D plane via irrational slope (golden ratio φ = (1+√5)/2)...
- Open access
Asymptotic Phase of the 6j Symbol from Racah's Sum — E8 Intelligence Research
FINDING: The Ponzano-Regge asymptotic formula for the 6j symbol — proven directly from Racah's single-sum formula — yields a phase factor \((-1)^{j_1+j_2+j_3+j_4+j_5+j_6} e^{i(\pi/4 + S/\hbar)}\) for large spins, where \(S\) is the Regge action of a Euclidean tetrahedron. | MATH:...
- Open access
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- Open access
Symmetry Breaking Pathways in Jahn-Teller Distorted C60ⁿ⁺ Cations — E8 Intelligence Research
FINDING: Jahn-Teller distortion in C60⁽ⁿ⁺⁾ breaks icosahedral (I_h) symmetry along specific irreducible representation (irrep) pathways, yielding static minima classified by group-theoretic descent chains (I_h → D5d, D3d, etc.), with energy surfaces governed by electron-phonon co...
- Open access
Base-60 Arithmetic Explains the 360° Circle's 24 Divisors — E8 Intelligence Research
FINDING: The 360° circle division arises from base-60 (sexagesimal) arithmetic, not from arbitrary choice; 360 = 6×60, making it a highly composite number with 24 divisors, enabling clean fractional astronomy. | MATH: 360 = 2³ × 3² × 5; divisors = (3+1)(2+1)(1+1) = 24. Sexagesima...
- Open access
FINDING: The Harborth graph — the smallest known 4-regular planar unit-distance graph on 34 vertices — has an analytical coordinate embedding whose minimal polynomials are now explicitly derived, revealing deep ties to crystallographic symmetry and algebraic number theory. | MATH...
- Open access
Eisenstein Series E4: Divisor Sums, E8 Lattice, and 4D Lattice Counts — E8 Intelligence Research
FINDING: The Fourier coefficients of the weight-4 Eisenstein series \(E_4\) are given by the divisor sum \(\sigma_3(n)\), encoding lattice point counts in 4D and connecting to the theta function of the \(E_8\) lattice. | MATH: \(E_4(\tau) = 1 + 240\sum_{n=1}^\infty \sigma_3(n) q^...
- Open access
3-4 sentences, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- Open access
Golden Rectangles Seed Icosahedron and Icosidodecahedron Symmetry — E8 Intelligence Research
FINDING: Three mutually perpendicular golden rectangles define the 20 vertices of an icosahedron; this construction is the geometric seed of the icosidodecahedron's golden rhombi and the compound-of-two-icosahedra symmetry. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; reciprocal φ⁻...
- Open access
[3-4 sentences], Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com