Author
Andrew Stewart Caldin
Recent research
- Society & EconomicsOpen access
Geometric Complexity Theory: Lie Groups and Orbit Closures in P vs. NP — E8 Intelligence Research
FINDING: Geometric Complexity Theory (GCT) uses Lie group representations and orbit closures to separate complexity classes (e.g., P vs. NP, determinant vs. permanent). | MATH: Permanent vs. determinant: \(\text{per}(X) \in \mathbb{C}[x_{ij}]\) degree \(n\); \(\det(X)\) degree \(...
- Physics & SpaceOpen access
FINDING: MIP*=RE proves quantum entanglement can verify undecidable problems, collapsing the quantum verification hierarchy into the classical recursively enumerable class. | MATH: MIP* = RE (where MIP* = multiprover interactive proofs with quantum entanglement, RE = recursively...
- AI & ComputingOpen access
Plimpton 322: Old Babylonian Exact-Ratio Trigonometry Before Angles — E8 Intelligence Research
FINDING: Plimpton 322 is an Old Babylonian table of 15 rows of Pythagorean triples, likely representing a primitive form of trigonometry based on exact ratios rather than angles. MATH: The tablet lists pairs of numbers (a, c) from Pythagorean triples (a, b, c) with a² + b² = c²....
- Society & EconomicsOpen access
FINDING: Enuma Anu Enlil is a cuneiform compendium of celestial omens; no explicit mathematical constants or equations are extracted from the provided sources. | MATH: None derived from the given texts; the sources are descriptive/historical, not containing recoverable numerical...
- Society & EconomicsOpen access
EuroMillions Breakthrough Mining — 1234 Sources, 7876 Leads Extracted — E8 Intelligence Research
Mined 1234 lottery+quantum breakthroughs. Extracted 7876 leads across 13 categories. 6029 high-value leads found. Categories: {"CORRIDOR": 627, "FORMULA": 487, "GEOMETRIC": 657, "FORWARD_ATTEMPT": 652, "QUANTUM": 863, "TIMING": 169, "CELESTIAL": 573, "GEMATRIA": 611, "CONSTANT":...
- AI & ComputingOpen access
FINDING: Figure-eight knot complement is the simplest hyperbolic knot complement, with volume linked to the golden ratio via ideal tetrahedron decomposition and Dehn surgery limits. MATH: Volume of figure-eight knot complement = \( 2 \cdot \text{Vol}(\text{regular ideal tetrahedr...
- Society & EconomicsOpen access
E8-Icosahedral Spectral Uncomputability Theorem — E8 Intelligence Research
The MIP*=RE uncom Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- AI & ComputingOpen access
FINDING: Plimpton 322 encodes a decreasing sequence of secant-squared values (1/cos²θ) for angles 45° down to 30°, generated by reciprocal pairs in base-60. MATH: - Secant-squared values: \( \sec^2\theta = 1 + \tan^2\theta \), with \(\tan\theta = p/q\) from reciprocal pairs \((p,...
- Materials & EnergyOpen access
FINDING: E8 lattice achieves optimal sphere packing density in 8D via modular forms, with Coxeter number 30 linking root system order to discrete spacetime geometry. MATH: - E8 lattice sphere packing density: \(\pi^4 / 384 \approx 0.25367\) (optimal in \(\mathbb{R}^8\)). - Coxete...
- AI & ComputingOpen access
FINDING: Selberg trace formula links prime geodesics on hyperbolic surfaces to spectral data, with deep connections to quadratic irrationals and the golden ratio's irrationality measure. | MATH: Selberg trace formula: ∑_{λ_j} h(λ_j) = ∑_{γ} ∫_{Γ_γ\G} h(k) dk + (geodesic terms). P...
- AI & ComputingOpen access
Plimpton 322: Old Babylonian Secant Ratios in Base-60 Pythagorean Triples — E8 Intelligence Research
FINDING: Plimpton 322 encodes Old Babylonian secant ratios in base-60, forming a geometric progression of Pythagorean triples linked to surveying and trigonometric tables. MATH: - Base-60 (sexagesimal) system: place value with 60 as radix, enabling precise fractions (e.g., 1/60,...
- Society & EconomicsOpen access
DECISION: REJECT ELEMENT: The filter "min confirmations >= 5" is not a concrete, testable edge compatible with E8 geometry timing. It is a statistical band-aid derived from a backtest sample (n=1271) that conflates correlation with causation. The "confirmation count" is not a def...
- Materials & EnergyOpen access
FINDING: Fibonacci numbers arise from spherical symmetry constraints, not merely growth optimization, linking quantum coherence topological protection in microtubules to golden ratio geometry. | MATH: Golden angle = 137.5077° = 2π(1 - 1/φ) where φ = (1+√5)/2 ≈ 1.6180339; Fibonacc...
- AI & ComputingOpen access
FINDING: Selberg trace formula links prime geodesics on hyperbolic surfaces to spectral data, with deep connections to quadratic irrationals and the golden ratio's irrationality measure. | MATH: Selberg trace formula: ∑_{λ_j} h(λ_j) = ∑_{γ} ∫_{Γ_γ\G} h(k) dk + (geodesic terms). P...
- Materials & EnergyOpen access
3D Quasicrystals from 6D Lattices with Base-60 Rotational Symmetry — E8 Intelligence Research
This Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
- AI & ComputingOpen access
FINDING: Sulba Sutras contain explicit geometric constructions for ritual altars, including early forms of the Pythagorean theorem, square-circle equivalences, and irrational approximations. MATH: - Baudhayana Sulba Sutra (c. 800 BCE): *dīrghachatursrasya akṣṇayā rajjuḥ pārśvamān...
- AI & ComputingOpen access
DECISION: REJECT ELEMENT: Q8-CLUSTER-098 geometric compression at ratio 0.753 fails the hostility filter — it is a fixed scalar applied *before* phi-harmonic extraction, which violates E8's sacred geometry timing principle. The phi-harmonic extraction is already the noise filter;...
- Society & EconomicsOpen access
EuroMillions Breakthrough Mining — 1197 Sources, 7477 Leads Extracted — E8 Intelligence Research
Mined 1197 lottery+quantum breakthroughs. Extracted 7477 leads across 13 categories. 5633 high-value leads found. Categories: {"CORRIDOR": 591, "FORMULA": 451, "GEOMETRIC": 657, "FORWARD_ATTEMPT": 615, "QUANTUM": 827, "TIMING": 168, "CELESTIAL": 536, "GEMATRIA": 575, "CONSTANT":...
- AI & ComputingOpen access
FINDING: Monstrous moonshine links the Monster group's representation theory to the modular j-function, with deep connections to the Leech lattice and Golay code. | MATH: j(τ) = 1/q + 744 + 196884q + 21493760q² + …; Monster group order ≈ 8×10⁵³; Leech lattice kissing number 19656...
- Materials & EnergyOpen access
FINDING: Explicit construction of 3D icosahedral quasicrystals via cut-and-project from 6D hypercubic lattice using golden ratio basis, with polyhedral radial expansions generating rhombic triacontahedra and hexecontahedra. MATH: - Golden ratio φ = (1+√5)/2 ≈ 1.618, with algebrai...