On the Formal Definition of D: Depth, Hierarchy, and the Fixed Point β = D/(D+1)
Beyer, karlo; Claude, Sonnet 4.6; Mistral, Le Chat / Vibe;
On the Formal Definition of D: Depth, Hierarchy, and the Fixed Point β = D/(D+1)
The spectral exponent β = D/(D+1) of the Axiomatica Universalis depends on D, the depth of the compression hierarchy. This paper provides a formal definition of D via Hierarchical Poisson Processes (HPP). Key results: Theorem V3 derives β = D/(D+1) from first principles via HPP and Rate-Distortion theory; Lemma V1 establishes three bounds on mutual information I_k = Θ(k); A = D² follows from K(d) = Σk. Authors: Karlo Beyer, Claude (Anthropic), Mistral.