Author
Andrew Stewart Caldin
Recent research
- Open access
3-4 sentences, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Random Isotropic Subspaces and Average Selmer Rank 1/2 in Function Fields — E8 Intelligence Research
FINDING: Poonen constructs a probability measure on maximal isotropic subspaces of a locally compact quadratic space over F_p, proving such a random subspace is discrete almost surely and its intersection with a fixed compact open subspace has a computable distribution — this mod...
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Icosahedral Galois Symmetry in Ramanujan's Mod 691 Congruence — E8 Intelligence Research
FINDING: Ramanujan's tau function τ(n) exhibits a mod 691 congruence tied to the weight-12 cusp form's Galois representation, whose projective image is icosahedral (A5), linking modular forms to sporadic finite geometry. | MATH: τ(n) ≡ σ₁₁(n) mod 691 (Ramanujan's congruence); Δ(q...
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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...
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The finding is this: the Monster group, the largest sporadic simple group, is not an isolated curiosity but the symmetry skeleton of a specific, unique 24-dimensional geometric object, and its character table is encoded in the Fourier coefficients of a single modular function. Th...
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Affine Algebra Unifies Rogers-Ramanujan and Andrews–Gordon Identities — E8 Intelligence Research
FINDING: The A_{2n}^{(2)} Rogers-Ramanujan identities form a doubly-infinite family where product sides are specialised characters of affine Kac-Moody algebra A_{2n}^{(2)} at level m, unifying classical Rogers-Ramanujan and Andrews–Gordon identities. | MATH: For positive integers...
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The Windmill Invariant: Solving the 2011 IMO Geometry Problem — E8 Intelligence Research
FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem whose solution hinges on a dynamic "windmill" rotation process, revealing a deep invariant about point configurations in general position. MATH: - Problem setup: Given a finite set of \( n \) points i...
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<80 chars, short discovery title — E8 Intelligence Research
3-4 sentences, explaining discovery and its E8 geometric basis - Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Feigenbaum's δ: A Universal Constant Distinct from the Golden Ratio — E8 Intelligence Research
FINDING: Feigenbaum's δ = 4.6692… emerges from renormalization fixed-point analysis of period-doubling cascades, with the universal function g(x) satisfying a functional equation whose linearization yields δ; the golden ratio φ appears as a separate universal constant α = 2.5029…...
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Golden Ratio Emerges from E8 Root System's Coxeter Geometry — E8 Intelligence Research
FINDING: The golden ratio φ emerges directly from the E8 root system's Coxeter geometry, specifically through the Weyl group's action on fixed-point subspaces and the root length ratios. | MATH: E8 root system: 240 roots, rank 8, Coxeter number h=30. The Weyl group W(E8) has orde...
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[3-4 sentences], 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)...
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FINDING: Burgers vectors in crystallography and prime-commas in Just Intonation both encode discrete, topologically-protected lattice defects — the former in real space, the latter in frequency space — unified by the same group-theoretic structure of lattice translations and quot...
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IDEA: AUTO VIDEO SCOUT — evaluate this trading strategy video for the swarm: VIDEO: "🔴 LIVE GOLD TRADING | XAUUSD LIVE | BTC LIVE | FOREX LIVE 🚀 | BULLISH BULL MASTER" by Bullish Bull Master — https://www.youtube.com/watch?v=jS2swZrsjfI (duration NAs, NA views; found via search...
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[3-4 sentences] / Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- 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
[3-4 sentences], Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- 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
EXTRACTED CONSTANTS (rlab #374): 1.618 — E8 Intelligence Research
constant phi = 1.618 — Explicitly referenced as the ratio for pillar heights in Enclosure D. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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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⁻...