Pentagonal Symmetry and Golden Ratio Unify Rogers-Ramanujan Identities — E8 Intelligence Research

Q: What does this research mean for the field?

The Rogers-Ramanujan identities are intrinsically tied to the A₄ root system (pentagonal symmetry), with the golden ratio acting as the fundamental scaling constant linking the pentagonal lattice to modular product forms. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22245291

September 2, 2026Open Access

Pentagonal Symmetry and Golden Ratio Unify Rogers-Ramanujan Identities — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Share

Key Points

The study investigates the geometric and algebraic connection between the Rogers-Ramanujan identities, the A4 root system, and the golden ratio.
Algebraic and geometric analysis of the two Rogers-Ramanujan q-series identities and their modular product forms.
Series expansion and continued fraction evaluation of the Rogers-Ramanujan continued fraction R(q) near q=0.
The modular exponents 5n±1 and 5n±2 correspond precisely to the residue classes modulo 5 that define the simple roots of the A4 pentagonal root system with dihedral Weyl group D5.
Series expansion of the continued fraction R(q) reveals the golden ratio φ = (1+√5)/2 ≈ 1.618 as the first non-trivial scaling coefficient linking pentagonal lattice geometry to modular forms.

No abstract yet

We only have this paper's title and publication details.

Read it at the source

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Mathematical analysis demonstrates geometric links between Rogers-Ramanujan identities and A4 pentagonal symmetry, indicating golden ratio scaling in modular forms.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9a861f5d9e33f25c631af5 https://doi.org/10.5281/zenodo.22245291

View Full Paper

Ask AI

Bookmark

Share

Pentagonal Symmetry and Golden Ratio Unify Rogers-Ramanujan Identities — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Pentagonal Symmetry and Golden Ratio Unify Rogers-Ramanujan Identities — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Keep reading

Keep reading