Aurellion Function: Self-Referential Arrows Surpassing Fast-Growing Hierarchies — E8 Intelligence Research

Q: What does this research mean for the field?

The Aurellion Function defines a fast-growing hierarchy through self-referential arrow counts that exceeds Knuth notation and standard recursive hierarchies, achieving a growth rate at or beyond the fast-growing hierarchy f_ω(n). Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22732552

September 13, 2026Open Access

Aurellion Function: Self-Referential Arrows Surpassing Fast-Growing Hierarchies — E8 Intelligence Research

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Key Points

Formulate and define the growth dynamics of the Aurellion Function, an ultrafast-growing recursive function driven by self-referential Knuth arrow counts.
Established a tritetration base case defined as A_1 = 10 ↑↑↑ 10.
Constructed a recursive sequence where the number of Knuth arrows equals the previous output (A_{n+1} = 10 ↑^{A_n} 10) and analyzed its growth against ordinal hierarchies and fixed-point iterations.
The Aurellion Function achieves a growth rate comparable to or exceeding f_ω(n) in the fast-growing hierarchy via recursive diagonalization.
The recursion operates as a functional fixed-point iteration analogous to golden ratio dynamics without exhibiting direct geometric decimal ratios.

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Implication

Mathematical analysis reveals an ultrafast-growing recursive function using self-referential Knuth arrow counts, demonstrating growth exceeding standard hierarchies through diagonalization.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b41e0926e14a848b3af2 https://doi.org/10.5281/zenodo.22732552

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Aurellion Function: Self-Referential Arrows Surpassing Fast-Growing Hierarchies — E8 Intelligence Research

Key Points

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Implication

Discussion

Cite This Study

Aurellion Function: Self-Referential Arrows Surpassing Fast-Growing Hierarchies — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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