Vladimir Khomyakov

Pseudo-Totient Entropy Constants: A One-Parameter Family Extending the Mean Totient Entropy Constant

Pseudo-Totient Entropy Constants: A One-Parameter Family Extending the Mean Totient Entropy Constant For a positive integer s, let g_s = Id_s * μ denote the arithmetic function obtained by Möbius-inverting the s-th power function, so that g_s(p^j) = p^(j−1)s(p^s−1) on prime power...

Information-Geometric Context Window Governance and the Probabilistic Theory of Long-Context Collapse in Large Language Models

This work develops a unified theoretical framework for long-context degradation in transformer-based large language models, combining information geometry and extreme value theory. The central quantity is the observer entropy S_obs(p_θ, ε) defined via Kullback–Leibler divergence...

The Mean Totient Entropy: A New Number-Theoretic Constant and its Dirichlet-Type Representation over the Primes

The Mean Totient Entropy: A New Number-Theoretic Constant and its Dirichlet-Type Representation over the Primes For a positive integer n, the divisors carry a canonical probability vector (φ(d)/n) over d | n (Gauss: Σ_{d|n} φ(d) = n). Its Shannon entropy H(n) = −Σ_{d|n} (φ(d)/n)·...

The Mean Totient Entropy: A New Number-Theoretic Constant and its Dirichlet-Type Representation over the Primes

The Mean Totient Entropy: A New Number-Theoretic Constant and its Dirichlet-Type Representation over the Primes For a positive integer n, the divisors carry a canonical probability vector (φ(d)/n) over d | n (Gauss: Σ_{d|n} φ(d) = n). Its Shannon entropy H(n) = −Σ_{d|n} (φ(d)/n)·...