PreprintCC BY 4.0Zenodo
E8 Phi-Toroidal Cohomology of Information-Loss Cascades — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By extending the 240-root E8 lattice into a fibered phi-cohomological structure over the 132 Hz base torus, we demonstrate that information-loss cascades in iterated dynamical maps admit a topological invariant — the "phi-winding number" — which classifies orbit stability across scales. This invariant emerges from the intersection pairing of the E8 root polytope with its dual under golden-ratio modular deformation, providing a cohomological obstruction to irreversible information decay and suggesting a geometric origin for the apparent reversibility observed in long Collatz-type trajectories.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Modular Automorphic Proof of the Collatz Conjecture via Information-Loss Cascades — E8 Intelligence Research
- Fibonacci-Galois Encoding of E8 Root Subsystem Decoherence Cascades — E8 Intelligence Research
- E8 Toroidal Homology Invariant from Knot Complement H₁(T³/K) Lattice Embedding — E8 Intelligence Research
- E8 Knot Cohomological Phase-Lock in T³ Drives Toroidal Quantum Memory — E8 Intelligence Research
- Φ-Defect Cascades Encode Markov Numbers on Modular Cusps — E8 Intelligence Research
BibTeX
@misc{caldin2026phitoroidal,
title = {{E8 Phi-Toroidal Cohomology of Information-Loss Cascades — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616345},
url = {https://zenodo.org/records/23616345},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi-Toroidal Cohomology of Information-Loss Cascades — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616345
UR - https://zenodo.org/records/23616345
AB - By extending the 240-root E8 lattice into a fibered phi-cohomological structure over the 132 Hz base torus, we demonstrate that information-loss cascades in iterated dynamical maps admit a topological invariant — the "phi-winding number" — which classifies orbit stability across scales. This invariant emerges from the intersection pairing of the E8 root polytope with its dual under golden-ratio modular deformation, providing a cohomological obstruction to irreversible information decay and suggesting a geometric origin for the apparent reversibility observed in long Collatz-type trajectories. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -