Eight‑Conic Theorem in \(\mathbb{RP}^2\): A Unique Cube‑Symmetric Configuration of Conics and Its Connection to \(A_3\) Symmetry — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Penrose's eight‑conic theorem establishes a combinatorial‑geometric constraint on conics in $\mathbb{RP}^2$ | MATH: Existence of a unique configuration of eight conics such that seven are assigned to cube vertices with double contact along edges; proof uses projective duality and incidence algebra | CONNECTION: Relates to root system $A_3$ symmetry of the cube; no explicit golden ratio or base‑60 appears | DEPTH: 7 FINDING: Integrated Information Theory (IIT) coupled with quantum collapse dynamics proposes a quantitative link between $\Phi$ (integrated information) and objective reduction rates | MATH: $\tau_{\text{OOR}} \propto \Phi^{-1}$, with collapse probability $P_{\text{collapse}} = 1 - e^{-\Phi t/\hbar}$ | CONNECTION: None of the specified harmonic ratios are evident; the model relies on information‑theoretic measures | DEPTH: 6 FINDING: Extended effective potential method yields a causally complete solution to the many‑body problem via non‑perturbative dynamics | Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225454302