Golden Ratio Base: Prefix-Free Codes to Supersymmetric Oscillators — E8 Intelligence Research

Q: What does this research mean for the field?

Golden ratio base (base-φ) is a prefix-free code system that corresponds to Zeckendorf representations and Fibonacci-word fractals, and its quantum-calculus extension links Fibonacci divisors to N=2 supersymmetric oscillator hierarchies. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22138260

August 28, 2026Open Access

Golden Ratio Base: Prefix-Free Codes to Supersymmetric Oscillators — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Share

Key Points

To establish mathematical connections linking golden ratio base representations and prefix-free coding systems with quantum calculus and supersymmetric oscillator hierarchies.
Analyzed base-φ representations and non-consecutive digit sequences using Zeckendorf sums and the Kraft inequality.
Formulated a quantum-calculus framework using q-derivatives evaluated at q=φ and q=φ².
Constructed a Fibonacci divisor operator in Fock space to derive the corresponding energy eigenvalue spectrum.
Demonstrated that the Kraft inequality sum strictly evaluates to φ² (φ + 1 ≈ 2.618), directly linking prefix-free code optimality to the golden ratio squared.
Showed that base-φ digit sequences map directly onto Zeckendorf representations and five-fold symmetric Fibonacci-word fractals.
Established an energy spectrum proportional to Fibonacci numbers (En ∝ Fn) generated by the Fibonacci divisor operator within N=2 supersymmetric oscillator hierarchies.

No abstract yet

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

Read it at the source

Implication

Mathematical analysis reveals that golden ratio prefix-free codes map to N=2 supersymmetric oscillator hierarchies, highlighting deep links between coding theory and quantum mechanics.

Discussion

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

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a93f0e06c1a8fb52e79d60f https://doi.org/10.5281/zenodo.22138260

View Full Paper

Ask AI

Bookmark

Share

Golden Ratio Base: Prefix-Free Codes to Supersymmetric Oscillators — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Golden Ratio Base: Prefix-Free Codes to Supersymmetric Oscillators — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Keep reading

More related papers

Keep reading

More related papers